{"appState":{"pageLoadApiCallsStatus":true},"categoryState":{"relatedCategories":{"headers":{"timestamp":"2022-05-13T12:31:08+00:00"},"categoryId":33769,"data":{"title":"Physics","slug":"physics","image":{"src":null,"width":0,"height":0},"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"parentCategory":{"categoryId":33756,"title":"Science","slug":"science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"}},"childCategories":[],"description":"Hundreds of articles spanning the basic laws of motion, advanced physics calculations, handy reference material, and even string theory.","relatedArticles":{"self":"https://dummies-api.dummies.com/v2/articles?category=33769&offset=0&size=5"}},"_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"relatedCategoriesLoadedStatus":"success"},"listState":{"list":{"count":10,"total":460,"items":[{"headers":{"creationTime":"2016-03-27T16:47:22+00:00","modifiedTime":"2022-03-28T16:19:31+00:00","timestamp":"2022-03-28T18:01:06+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Physics I: 500 Practice Problems For Dummies Cheat Sheet","strippedTitle":"physics i: 500 practice problems for dummies cheat sheet","slug":"physics-i-practice-problems-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Keep this handy reference for some of the most common unit prefixes and unit conversions you’re bound to encounter in your physics homework.","noIndex":0,"noFollow":0},"content":"Solving physics problems correctly is a lot easier when you have a couple tricks under your belt. In fact, you can greatly improve your odds of getting the right answer if you make sure that what you calculated is plausible in the real world. Another trick is to draw your own visual when one isn’t provided for you — no artistic ability required.\r\n\r\nIt also helps to have this handy reference for some of the most common unit prefixes and unit conversions you’re bound to encounter in your physics homework.","description":"Solving physics problems correctly is a lot easier when you have a couple tricks under your belt. In fact, you can greatly improve your odds of getting the right answer if you make sure that what you calculated is plausible in the real world. 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Problems","slug":"how-to-check-for-physically-reasonable-answers-when-solving-physics-problems","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144608"}},{"articleId":144633,"title":"Solving Force Problems in Physics by Using Free-Body Diagrams","slug":"solving-force-problems-in-physics-by-using-free-body-diagrams","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144633"}},{"articleId":144607,"title":"Physics Reference Charts for Unit Prefixes and Unit Conversion","slug":"physics-reference-charts-for-unit-prefixes-and-unit-conversion","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144607"}}],"content":[{"title":"How to check for physically reasonable answers in physics problems","thumb":null,"image":null,"content":"<p>Because physics describes reality, your solutions to any physics problems you tackle should be able to describe reality, too. You can avoid many mistakes by checking that your answers have the following properties:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>They have the right units.</b> If a problem asks you to find a speed and you get 5 kilograms, you know you made a mistake somewhere. (Note that this check only works if you keep track of your units throughout the whole problem.)</p>\n</li>\n<li>\n<p class=\"first-para\"><b>They’re the right size.</b> If you calculate that the mass of a planet is 53 grams, that the speed of a soccer ball is 3 trillion meters per second, or that the temperature of ice is 350 degrees Celsius, start searching for the mistake.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>They point in the right direction.</b> When you’re looking for a vector, sometimes you know roughly what direction it should point.</p>\n</li>\n<li>\n<p class=\"first-para\"><b>They have the right sign. </b>If you find that the density of a liquid is –1,200 kilograms per cubic meter, you made a sign error along the way.</p>\n</li>\n</ul>\n"},{"title":"Solving force problems in physics by using free-body diagrams","thumb":null,"image":null,"content":"<p>In physics, force problems typically ask you to predict what will happen when you apply force to an object, and usually there’s no handy illustration to help you visualize what’s being described. Fortunately, you can create your own diagram so you can better picture what a question is asking you. Follow this seven-step method to solve force problems:</p>\n<ol class=\"level-one\">\n<li>\n<p class=\"first-para\">Draw each of the objects you’re interested in.</p>\n<p class=\"child-para\">Here’s an example:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/470175.image0.jpg\" alt=\"image0.jpg\" width=\"388\" height=\"158\" /></li>\n<li>\n<p class=\"first-para\">Identify the forces acting <b>on</b> each object.</p>\n<p class=\"child-para\">For each force acting on one of the objects from Step 1, draw an arrow that indicates the direction of the force, as shown in the following figure. Note that the tail of the arrow indicates which part of the object the force is acting on.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/470176.image1.jpg\" alt=\"image1.jpg\" width=\"535\" height=\"255\" /></li>\n<li>\n<p class=\"first-para\">Draw a free-body diagram for each object.</p>\n<p class=\"child-para\">If you’re following this step-by-step guide, you’ve already drawn a free-body diagram. It’s listed separately because it’s the most important step!</p>\n</li>\n<li>\n<p class=\"first-para\">Choose a coordinate system for each object.</p>\n<p class=\"child-para\">Usually you draw the <i>x</i>-direction horizontally and the <i>y</i>-direction vertically, as shown in the following figure. However, when dealing with inclined planes, sometimes you want to choose your coordinate axes parallel and perpendicular to the plane.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/470177.image2.jpg\" alt=\"image2.jpg\" width=\"535\" height=\"137\" /></li>\n<li>\n<p class=\"first-para\">For each object, write down each component of Newton’s second law.</p>\n<p class=\"child-para\">For angular motion problems, choose an axis of rotation and write down the angular version of Newton’s second law.</p>\n</li>\n<li>\n<p class=\"first-para\">Include any constraints.</p>\n<p class=\"child-para\">Sometimes you have more variables than equations at this point. Write down any other information you know. For example, if a car is driving on a flat road, you know that the vertical component of its acceleration is zero.</p>\n</li>\n<li>\n<p class=\"first-para\">Solve the equations.</p>\n<p class=\"child-para\">Now that you’ve used all your physics knowledge, all you have to do is the algebra.</p>\n</li>\n</ol>\n"},{"title":"Physics reference charts for unit prefixes and unit conversion","thumb":null,"image":null,"content":"<p>When solving physics problems, you’ll often encounter unit prefixes that you need to know. You also need to be familiar with common unit symbols and their corresponding SI units. The following tables list some of the typical prefixes and symbols that you may see.</p>\n<table>\n<caption>Commonly Used Unit Prefixes in Physics Problems</caption>\n<tbody>\n<tr>\n<th>Unit Prefix Name</th>\n<th>Symbol</th>\n<th>Factor</th>\n</tr>\n<tr>\n<td>tera-</td>\n<td>T</td>\n<td>10<sup>12</sup></td>\n</tr>\n<tr>\n<td>giga-</td>\n<td>G</td>\n<td>10<sup>9</sup></td>\n</tr>\n<tr>\n<td>mega-</td>\n<td>M</td>\n<td>10<sup>6</sup></td>\n</tr>\n<tr>\n<td>kilo-</td>\n<td>k</td>\n<td>10<sup>3</sup></td>\n</tr>\n<tr>\n<td>centi-</td>\n<td>c</td>\n<td>10<sup>–2</sup></td>\n</tr>\n<tr>\n<td>milli-</td>\n<td>m</td>\n<td>10<sup>–3</sup></td>\n</tr>\n<tr>\n<td>micro-</td>\n<td>ì</td>\n<td>10<sup>–6</sup></td>\n</tr>\n<tr>\n<td>nano-</td>\n<td>n</td>\n<td>10<sup>–9</sup></td>\n</tr>\n<tr>\n<td>pico-</td>\n<td>p</td>\n<td>10<sup>–12</sup></td>\n</tr>\n</tbody>\n</table>\n<table>\n<caption>Handy Unit Conversions for Physics Problems</caption>\n<tbody>\n<tr>\n<th>Derived Units</th>\n<th>Symbol</th>\n<th>SI Units</th>\n</tr>\n<tr>\n<td>Newton</td>\n<td>N</td>\n<td>kilogram meter per second squared</td>\n</tr>\n<tr>\n<td>Joule</td>\n<td>J</td>\n<td>kilogram meter squared per second squared</td>\n</tr>\n<tr>\n<td>Watt</td>\n<td>W</td>\n<td>kilogram meter squared per second cubed</td>\n</tr>\n<tr>\n<td>Hertz</td>\n<td>Hz</td>\n<td>inverse second</td>\n</tr>\n<tr>\n<td>Pascal</td>\n<td>P</td>\n<td>kilogram per meter per second squared</td>\n</tr>\n<tr>\n<td>Degree Celsius</td>\n<td>°C</td>\n<td>kelvin</td>\n</tr>\n</tbody>\n</table>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-01-28T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":207542},{"headers":{"creationTime":"2016-03-27T16:48:17+00:00","modifiedTime":"2022-03-10T19:28:59+00:00","timestamp":"2022-03-11T00:01:05+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Physics I Workbook For Dummies Cheat Sheet","strippedTitle":"physics i workbook for dummies cheat sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Whether you're pursuing a career involving physics or just trying to excel on your next exam, here's a handy guide to keep by your side.","noIndex":0,"noFollow":0},"content":"Avoid difficulties when working on physics by knowing the common issues that can cause trouble in physics problems, understanding physical constants, and grasping principal physics equations.","description":"Avoid difficulties when working on physics by knowing the common issues that can cause trouble in physics problems, understanding physical constants, and grasping principal physics equations.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. 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data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119716471&quot;]}]\" id=\"du-slot-622a9141cb4db\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":155822,"title":"10 Issues to Avoid When Solving Physics Problems","slug":"10-issues-to-avoid-when-solving-physics-problems","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/155822"}},{"articleId":155804,"title":"9 Physics Constants to Know","slug":"9-physics-constants-to-know","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/155804"}},{"articleId":155821,"title":"Important Physics Equations to Remember","slug":"important-physics-equations-to-remember-2","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/155821"}}],"content":[{"title":"10 issues to avoid when solving physics problems","thumb":null,"image":null,"content":"<p>If you get stumped working on physics formulas, take a deep breath, and recheck your work. Go through these common physics-problem issues to make sure you have avoided them:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Mixing units</p>\n</li>\n<li>\n<p class=\"first-para\">Expressing the answer in the wrong units</p>\n</li>\n<li>\n<p class=\"first-para\">Swapping radians and degrees</p>\n</li>\n<li>\n<p class=\"first-para\">Getting sines and cosines mixed up</p>\n</li>\n<li>\n<p class=\"first-para\">Failing to treat vectors as vectors</p>\n</li>\n<li>\n<p class=\"first-para\">Neglecting latent heat</p>\n</li>\n<li>\n<p class=\"first-para\">Getting the Direction of Forces Wrong</p>\n</li>\n<li>Getting the signs wrong in Kirchhoff’s loops</li>\n<li>Adding resistors incorrectly</li>\n</ul>\n"},{"title":"9 physics constants to know","thumb":null,"image":null,"content":"<p>Physics constants, like the mass of a proton or speed of light, are physical quantities with fixed numerical values. This list contains the most common physics constants:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Avogadro&#8217;s Number: N<sub>A</sub> = 6.022 × 10<sup>23</sup> mol<sup>–1</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Boltzmann&#8217;s constant: k = 1.380 × 10<sup>–23</sup> J/K</p>\n</li>\n<li>\n<p class=\"first-para\">Coulomb&#8217;s constant: k = 8.99 × 10<sup>9</sup> N–m<sup>2</sup>/C<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Gas constant: R = 8.314 J/(mol–K)</p>\n</li>\n<li>\n<p class=\"first-para\">Gravitational constant: G = 6.672 × 10<sup>–11</sup> N–m<sup>2</sup>/kg<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Speed of light: c = 2.997 × 10<sup>8</sup> m/s</p>\n</li>\n<li>\n<p class=\"first-para\">Charge of electron: e = 1.602 × 10<sup>–19</sup> C</p>\n</li>\n<li>\n<p class=\"first-para\">Mass of proton: m<sub>p</sub> = 1.672 × 10<sup>–27</sup> kg</p>\n</li>\n<li>\n<p class=\"first-para\">Mass of electron: m<sub>e</sub> = 9.109 × 10<sup>–31</sup> kg</p>\n</li>\n</ul>\n"},{"title":"Important physics equations to remember","thumb":null,"image":null,"content":"<p><a href=\"https://dummies-wp-content.dummies.com/education/science/discovering-what-physics-is-all-about/\" target=\"_blank\" rel=\"noopener\">Physics</a> is packed with formulas and equations. This comprehensive list, arranged by topic, represents essential physics equations you need to keep handy when you&#8217;re dealing with physics formulas.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/417333.image0.jpg\" alt=\"image0.jpg\" width=\"414\" height=\"875\" /></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2021-10-22T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":207736},{"headers":{"creationTime":"2016-03-27T16:53:37+00:00","modifiedTime":"2022-02-18T19:09:30+00:00","timestamp":"2022-02-24T17:07:34+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Optics For Dummies Cheat Sheet","strippedTitle":"optics for dummies cheat sheet","slug":"optics-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"If you're looking to get into optics, it's a bright idea to study up on reflection, refraction, and diffraction.","noIndex":0,"noFollow":0},"content":"Optics covers the study of light. Three phenomena — reflection, refraction, and diffraction — help you predict where a ray or rays of light will go. Study up on other important optics topics, too, including interference, polarization, and fiber optics.","description":"Optics covers the study of light. Three phenomena — reflection, refraction, and diffraction — help you predict where a ray or rays of light will go. Study up on other important optics topics, too, including interference, polarization, and fiber optics.","blurb":"","authors":[{"authorId":10156,"name":"Galen C. Duree Jr.","slug":"galen-c-duree","description":"Galen Duree, Jr., PhD, is professor of physics and optical engineering at Rose-Hulman Institute of Technology in Indiana, where he is also the director of the Center for Applied Optics Studies. Duree jointly established the Ultrashort Pulse Laser Laboratory at RHIT and continues to work with the Navy.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/10156"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":187412,"title":"Reflection and Refraction Equations for Predicting Light's Direction","slug":"reflection-and-refraction-equations-for-predicting-lights-direction","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187412"}},{"articleId":187397,"title":"Equations for the Characteristics of Fiber-Optic Fibers","slug":"equations-for-the-characteristics-of-fiber-optic-fibers","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187397"}},{"articleId":187394,"title":"Optical Interference Equations","slug":"optical-interference-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187394"}},{"articleId":187391,"title":"Optical Diffraction Equations","slug":"optical-diffraction-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187391"}},{"articleId":187393,"title":"Optical Polarization Equations","slug":"optical-polarization-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187393"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat Sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207736"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282432,"slug":"optics-for-dummies","isbn":"9781118017234","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1118017234/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118017234/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118017234-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118017234/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118017234/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/optics-for-dummies-cover-9781118017234-203x255.jpg","width":203,"height":255},"title":"Optics For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"\n <p><b data-author-id=\"10156\">Galen Duree, Jr., PhD,</b> is Professor of Physics and Optical Engineering at Rose-Hulman Institute of Technology in Indiana, where he is also the Director of the Center for Applied Optics Studies. Duree jointly established the Ultrashort Pulse Laser Laboratory at RHIT and continues to work with the Navy. </p>","authors":[{"authorId":10156,"name":"Galen C. Duree Jr.","slug":"galen-c-duree","description":"Galen Duree, Jr., PhD, is professor of physics and optical engineering at Rose-Hulman Institute of Technology in Indiana, where he is also the director of the Center for Applied Optics Studies. Duree jointly established the Ultrashort Pulse Laser Laboratory at RHIT and continues to work with the Navy.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/10156"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118017234&quot;]}]\" id=\"du-slot-6217bb56d1846\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118017234&quot;]}]\" id=\"du-slot-6217bb56d21e4\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":187412,"title":"Reflection and Refraction Equations for Predicting Light's Direction","slug":"reflection-and-refraction-equations-for-predicting-lights-direction","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187412"}},{"articleId":187390,"title":"Equations for Optical Imaging","slug":"equations-for-optical-imaging","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187390"}},{"articleId":187393,"title":"Optical Polarization Equations","slug":"optical-polarization-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187393"}},{"articleId":187394,"title":"Optical Interference Equations","slug":"optical-interference-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187394"}},{"articleId":187391,"title":"Optical Diffraction Equations","slug":"optical-diffraction-equations","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187391"}},{"articleId":187397,"title":"Equations for the Characteristics of Fiber-Optic Fibers","slug":"equations-for-the-characteristics-of-fiber-optic-fibers","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187397"}}],"content":[{"title":"Reflection and refraction equations for predicting light's direction","thumb":null,"image":null,"content":"<p><i>Reflection </i>and <i>refraction</i> are two processes that change the direction light travels. Using the equations for calculating reflection and refraction, you can predict where rays encountering a surface will go — whether they reflect or refract (bounce off the surface or bend through it) — which is an important concept in the study of optics. The following equations help you determine reflection and refraction angles:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>The law of reflection:</b> The <i>law of reflection</i> shows the relationship between the incident angle and the reflected angle for a ray of light incident on a surface. The angles are measured relative to the <i>surface normal</i><i> </i>(a line that is perpendicular to the surface), not relative to the surface itself. Here&#8217;s the formula:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277323.image0.jpg\" alt=\"image0.jpg\" width=\"34\" height=\"12\" /></li>\n<li>\n<p class=\"first-para\"><b>The index of refraction:</b> This quantity describes the effect of atoms and molecules on the light as it travels through a transparent material. Use this basic formula for the index of refraction:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277324.image1.jpg\" alt=\"image1.jpg\" width=\"63\" height=\"24\" /></li>\n<li>\n<p class=\"first-para\"><b>Snell&#8217;s law or the law of refraction:</b> <i>Snell</i><i>&#8216;</i><i>s law</i> shows the relationship between the incident angle and the transmitted angle (refracted angle) for a ray of light incident on a surface of a transparent material. You can see how Snell&#8217;s law works in the following formula:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277325.image2.jpg\" alt=\"image2.jpg\" width=\"135\" height=\"15\" /></li>\n<li>\n<p class=\"first-para\"><b>The critical angle for total internal reflection: </b><i>Total internal reflection</i> is the situation where light hits and reflects off the surface of a transparent material without transmitting through the surface. It utilizes the <i>critical angle</i> (the minimum angle of incidence where total internal reflection takes place.). For total internal reflection to occur, the light must start in the material with the higher index. Here&#8217;s the formula:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277326.image3.jpg\" alt=\"image3.jpg\" width=\"86\" height=\"30\" /></li>\n</ul>\n"},{"title":"Equations for optical imaging","thumb":null,"image":null,"content":"<p>Imaging is a key function of optics. Specific optics equations can help you determine the basic characteristics of an image and predict where it will form. Use the following optics equations for your imaging needs:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Lateral magnification:</b> <i>Lateral magnification</i> is one way you can describe how big the image is compared to the original object. Here are the equations:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277863.image0.jpg\" alt=\"image0.jpg\" width=\"45\" height=\"53\" /></li>\n<li>\n<p class=\"first-para\"><b>Locating images formed by mirrors:</b> An object placed a certain distance away from a mirror will produce an image at a certain distance from the mirror. In some cases where the mirrors are curved, you may be given the focal length of a mirror. Use these equations:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277864.image1.jpg\" alt=\"image1.jpg\" width=\"52\" height=\"52\" /></li>\n<li>\n<p class=\"first-para\"><b>Location of images formed by a refracting surface:</b> An object placed a certain distance away from a refracting surface will produce an image at a certain distance from the surface. The equation for this is</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277865.image2.jpg\" alt=\"image2.jpg\" width=\"95\" height=\"21\" /></li>\n<li>\n<p class=\"first-para\"><b>The lens maker&#8217;s formula:</b> This equation allows you to calculate the focal length of a lens if all you know is the curvature of the two surfaces. Here&#8217;s the lens maker&#8217;s formula:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277866.image3.jpg\" alt=\"image3.jpg\" width=\"125\" height=\"31\" /></li>\n<li>\n<p class=\"first-para\"><b>The thin lens equation:</b> An object placed a certain distance away from a lens will produce an image at a certain distance from the lens, and the <i>thin lens </i><i>equation</i><i> </i>relates the image location to the object distance and focal length. The following is the thin lens equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277867.image4.jpg\" alt=\"image4.jpg\" width=\"52\" height=\"23\" /></li>\n</ul>\n"},{"title":"Optical polarization equations","thumb":null,"image":null,"content":"<p><i>Optical polarization</i> is the orientation of the planes of oscillation of the electric field vectors for many light waves. Optical polarization is often a major consideration in the construction of many optical systems, so equations for working with polarization come in handy. The following equations highlight some important polarization concepts. The equations listed here allow you to calculate how to make polarized light by reflection and to determine how much light passes through multiple polarizers:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Polarizing angle or Brewster&#8217;s angle: </b>This angle is the angle of incidence where the reflected light is linearly polarized. Here&#8217;s the equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277869.image0.jpg\" alt=\"image0.jpg\" width=\"91\" height=\"30\" /></li>\n<li>\n<p class=\"first-para\"><b>Malus&#8217; law: </b>This equation allows you to calculate how much polarized light passes through a linear polarizer. The equation for Malus&#8217; law is</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277870.image1.jpg\" alt=\"image1.jpg\" width=\"66\" height=\"14\" /></li>\n<li>\n<p class=\"first-para\"><b>Phase retardation in a birefringent material: </b>A <i>birefringent</i> material has two indexes of refraction. When you send polarized light into a birefringent material, the two components travel through the material with different speeds. This discrepancy can result in a change in the polarization state or simply rotate the polarization state. Use this equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277871.image2.jpg\" alt=\"image2.jpg\" width=\"92\" height=\"23\" /></li>\n</ul>\n"},{"title":"Optical interference equations","thumb":null,"image":null,"content":"<p><i>Optical</i> <i>interference </i>is just the interaction of two or more light waves. Optical interference is useful in many applications, so you need to understand some basic equations related to this optical phenomenon. The following equations allow you to calculate various quantities related to optical interference in the two most common interference arrangements.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>The location of the bright and dark fringes in Young&#8217;s two-slit interference arrangement:</b> The following equations allow you to calculate the location of the <i>bright fringes</i> (where constructive interference occurs) and <i>dark fringes</i> (where destructive interference occurs):</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277873.image0.jpg\" alt=\"image0.jpg\" width=\"99\" height=\"53\" /></li>\n<li>\n<p class=\"first-para\"><b>The phase shift due to the film thickness in thin film interference:</b> When light is incident straight onto a thin film (such as an oil slick on the surface of a pool of water), light rays reflecting from the top and the bottom of the film interfere (either constructively or destructively depending on the film thickness and the wavelength of the light). The following equations determine constructive or destructive interference depending on whether the phase shift produced by reflection needs to be shifted by half the wavelength (the first equation) or maintained (the second equation):</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277874.image1.jpg\" alt=\"image1.jpg\" width=\"88\" height=\"45\" /></li>\n</ul>\n"},{"title":"Optical diffraction equations","thumb":null,"image":null,"content":"<p><i>Diffraction</i> is light&#8217;s response to having something mess with its path, so diffraction occurs only when something blocks part of the wavefront. Diffraction is the phenomenon where light bends around an obstacle (this bending is <i>not</i> due to refraction, because the material doesn&#8217;t change as refraction requires). The following equations cover the most common situations involving diffraction, including resolution.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Resolution:</b> <i>Resolution </i>is<i> </i>the minimum angular separation between two objects such that you can tell that there are two distinct objects. Here&#8217;s the equation for determining resolution:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277876.image0.jpg\" alt=\"image0.jpg\" width=\"68\" height=\"23\" /></p>\n<p class=\"child-para\"><b>The location of the dark fringes produced by diffraction through a single slit:</b> Because a slit has a width larger than the wavelength, light rays from different parts of the slit interfere with each other, creating a fringe pattern. You can relatively easily locate the points where the light destructively interferes by using the following equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277877.image1.jpg\" alt=\"image1.jpg\" width=\"68\" height=\"23\" /></li>\n<li>\n<p class=\"first-para\"><b>The location of the different diffraction orders from a diffraction grating:</b> A diffraction grating has a very large number of slits spaced closely together, such that the light from each of these slits interferes with the light from the others. You can pretty easily identify where the light constructively interferes by using the following equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277878.image2.jpg\" alt=\"image2.jpg\" width=\"68\" height=\"10\" /></li>\n</ul>\n"},{"title":"Equations for the characteristics of fiber-optics fibers","thumb":null,"image":null,"content":"<p>Besides imaging, fiber-optic networks are probably the largest application of optics. Fiber optics are very long, thin glass fibers that transfer information-bearing light from one place to another, but that may not be in direct sight of each other. You need to be aware of a few characteristics of the particular fiber you&#8217;re using so that you can ensure the information is accurately transmitted from one end of the fiber to the other. The following equations cover three of the basic parameters necessary for proper use of optical fibers.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>The maximum acceptance angle for a fiber:</b> This angle is the largest angle of incidence at which light can enter the end of the fiber and be totally internally reflected inside the fiber. Angles of incidence larger than this angle will transmit through the sides of the fiber and not make it to the other end. The equation for this angle is</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277880.image0.jpg\" alt=\"image0.jpg\" width=\"147\" height=\"30\" /></li>\n<li>\n<p class=\"first-para\"><b>The numerical aperture for a fiber: </b>The <i>numerical aperture</i> is a measure of the light-gathering power of the fiber. It has a maximum value of 1 (all the light remains trapped inside the fiber) and a minimum value of 0 (only light incident at an angle of 0 degrees on the end of the fiber remains trapped in the fiber). Use this equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277881.image1.jpg\" alt=\"image1.jpg\" width=\"150\" height=\"18\" /></li>\n<li>\n<p class=\"first-para\"><b>Intermodal dispersion in a fiber: </b>This characteristic measures the difference in time that different fiber modes take to reach the end of the fiber. The larger this time difference, the shorter the fiber has to be so that the information on this light doesn&#8217;t turn into junk. Here&#8217;s the equation:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/277882.image2.jpg\" alt=\"image2.jpg\" width=\"97\" height=\"30\" /></li>\n</ul>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Two years","lifeExpectancySetFrom":"2022-02-18T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":208578},{"headers":{"creationTime":"2016-03-27T16:53:43+00:00","modifiedTime":"2022-02-15T19:41:38+00:00","timestamp":"2022-02-24T17:07:32+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Thermodynamics For Dummies Cheat Sheet","strippedTitle":"thermodynamics for dummies cheat sheet","slug":"thermodynamics-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Equations, conversions, and constants: all important elements of thermodynamics. Wrap your mind around all of them here.","noIndex":0,"noFollow":0},"content":"Thermodynamics sounds intimidating, and it can be. However, if you focus on the most important thermodynamic formulas and equations, get comfortable converting from one unit of physical measurement to another, and become familiar with the physical constants related to thermodynamics, you’ll be at the head of the class.","description":"Thermodynamics sounds intimidating, and it can be. However, if you focus on the most important thermodynamic formulas and equations, get comfortable converting from one unit of physical measurement to another, and become familiar with the physical constants related to thermodynamics, you’ll be at the head of the class.","blurb":"","authors":[{"authorId":10165,"name":"Mike Pauken","slug":"mike-pauken","description":"Michael Pauken, PhD, is a senior mechanical engineer at NASA's Jet Propulsion Laboratory, an operating division of the California Institute of Technology, where he also teaches courses on thermodynamics and heat transfer. ","_links":{"self":"https://dummies-api.dummies.com/v2/authors/10165"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":187449,"title":"Conversion Factors for Physical Measurements","slug":"conversion-factors-for-physical-measurements","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187449"}},{"articleId":187444,"title":"Physical Constants in Thermodynamics","slug":"physical-constants-in-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187444"}},{"articleId":187441,"title":"Important Thermodynamic Equations and Formulas","slug":"important-thermodynamic-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187441"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat Sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207736"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282631,"slug":"thermodynamics-for-dummies","isbn":"9781118002919","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1118002911/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118002911/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118002911-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118002911/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118002911/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/thermodynamics-for-dummies-cover-9781118002919-203x255.jpg","width":203,"height":255},"title":"Thermodynamics For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"\n <b data-author-id=\"10165\">Michael Pauken</b>, PhD, is a senior mechanical engineer at NASA's Jet Propulsion Laboratory, an operating division of the California Institute of Technology, where he also teaches courses on thermodynamics and heat transfer. ","authors":[{"authorId":10165,"name":"Mike Pauken","slug":"mike-pauken","description":"Michael Pauken, PhD, is a senior mechanical engineer at NASA's Jet Propulsion Laboratory, an operating division of the California Institute of Technology, where he also teaches courses on thermodynamics and heat transfer. ","_links":{"self":"https://dummies-api.dummies.com/v2/authors/10165"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118002919&quot;]}]\" id=\"du-slot-6217bb54c7f4c\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118002919&quot;]}]\" id=\"du-slot-6217bb54c88d0\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":187441,"title":"Important Thermodynamic Equations and Formulas","slug":"important-thermodynamic-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187441"}},{"articleId":187449,"title":"Conversion Factors for Physical Measurements","slug":"conversion-factors-for-physical-measurements","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187449"}},{"articleId":187444,"title":"Physical Constants in Thermodynamics","slug":"physical-constants-in-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187444"}}],"content":[{"title":"Important thermodynamic equations and formulas","thumb":null,"image":null,"content":"<p>Thermodynamics is filled with equations and formulas. Here’s a list of the most important ones you need to do the calculations necessary for solving thermodynamics problems.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Combustion equations:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Air-fuel ratio:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275463.image0.png\" alt=\"image0.png\" width=\"150\" height=\"55\" /></li>\n<li>\n<p class=\"first-para\"><b>Hydrocarbon fuel combustion reaction:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275464.image1.png\" alt=\"image1.png\" width=\"535\" height=\"44\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Compressibility calculations:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Compressibility factor Z:</b> <i>Pv = </i><i>Z</i><i>RT</i></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Reduced temperature:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275465.image2.png\" alt=\"image2.png\" width=\"136\" height=\"76\" /></li>\n<li>\n<p class=\"first-para\"><b>Reduced pressure:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275466.image3.png\" alt=\"image3.png\" width=\"138\" height=\"75\" /></li>\n<li>\n<p class=\"first-para\"><b>Pseudo-reduced specific volume:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275467.image4.png\" alt=\"image4.png\" width=\"138\" height=\"68\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Efficiency equations:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Thermal efficiency:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275468.image5.png\" alt=\"image5.png\" width=\"150\" height=\"37\" /><br />\n<img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275469.image6.png\" alt=\"image6.png\" width=\"150\" height=\"44\" /></li>\n<li>\n<p class=\"first-para\"><b>Coefficient of performance (refrigerator):</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275470.image7.png\" alt=\"image7.png\" width=\"200\" height=\"29\" /></li>\n<li>\n<p class=\"first-para\"><b>Coefficient of performance (heat pump):</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275471.image8.png\" alt=\"image8.png\" width=\"200\" height=\"29\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Energy equations:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275472.image9.png\" alt=\"image9.png\" width=\"150\" height=\"25\" /><br />\n<img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275473.image10.png\" alt=\"image10.png\" width=\"150\" height=\"29\" /><br />\n<img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275474.image11.png\" alt=\"image11.png\" width=\"150\" height=\"21\" /></li>\n<li>\n<p class=\"first-para\"><b>Entropy equations:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Entropy change for ideal gas, constant specific heat:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275475.image12.png\" alt=\"image12.png\" width=\"200\" height=\"37\" /><br />\n<img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275476.image13.png\" alt=\"image13.png\" width=\"200\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\"><b>Entropy change for ideal gas, variable specific heat:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275477.image14.png\" alt=\"image14.png\" width=\"200\" height=\"38\" /></li>\n<li>\n<p class=\"first-para\"><b>Irreversibility for a process:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275478.image15.png\" alt=\"image15.png\" width=\"200\" height=\"34\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Ideal-gas formulas:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Ideal-gas law:</b> <i>Pv = RT</i></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Gas constant:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275479.image16.png\" alt=\"image16.png\" width=\"114\" height=\"74\" /></li>\n<li>\n<p class=\"first-para\"><b>Ratio of specific heats:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275480.image17.png\" alt=\"image17.png\" width=\"108\" height=\"76\" /></li>\n<li>\n<p class=\"first-para\"><b>Isentropic process for ideal gas:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275481.image18.png\" alt=\"image18.png\" width=\"300\" height=\"47\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Moist air properties:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Relative humidity:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275482.image19.png\" alt=\"image19.png\" width=\"150\" height=\"43\" /></li>\n<li>\n<p class=\"first-para\"><b>Specific humidity:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275483.image20.png\" alt=\"image20.png\" width=\"150\" height=\"61\" /></li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Properties of mixtures:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Quality liquid-vapor mixture:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275484.image21.png\" alt=\"image21.png\" width=\"150\" height=\"60\" /></li>\n<li>\n<p class=\"first-para\"><b>Saturated mixture property, <i>y</i>:</b> <i>y</i> = <i>y</i><i><sub>f</sub></i> + <i>x</i> · <i>y</i><i><sub>fg</sub></i></p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><b>Work calculations:</b></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\"><b>Isobaric process:</b> <i>W</i><i><sub>b</sub></i><i> = P</i><i><sub>0</sub></i><i>(V</i><i><sub>2</sub></i><i> – V</i><i><sub>1</sub></i><i>)</i></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Polytropic process:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275485.image22.png\" alt=\"image22.png\" width=\"150\" height=\"40\" /></li>\n<li>\n<p class=\"first-para\"><b>Isothermal process of an ideal gas:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275486.image23.png\" alt=\"image23.png\" width=\"300\" height=\"38\" /></li>\n<li>\n<p class=\"first-para\"><b>Shaft power:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275487.image24.png\" alt=\"image24.png\" width=\"150\" height=\"30\" /></li>\n<li>\n<p class=\"first-para\"><b>Spring work:</b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275488.image25.png\" alt=\"image25.png\" width=\"200\" height=\"38\" /></li>\n</ul>\n</li>\n</ul>\n"},{"title":"Conversion factors for physical measurements","thumb":null,"image":null,"content":"<p>Sooner or later, you’re going to have to convert from one unit of physical measurement to another. This list gives you some of the most common conversion factors you need in thermodynamics.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Acceleration:</b> 1 m/s<sup>2</sup> = 100 cm/s<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Area:</b> 1 m<sup>2</sup> = 10<sup>4</sup> cm<sup>2</sup> = 10<sup>6</sup> mm<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Density:</b> 1 g/cm<sup>3</sup> = 1 kg/L = 1,000 kg/m<sup>3</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Energy, heat, work, internal energy, enthalpy:</b> 1 kJ = 1,000 J = 1,000 N·m = 1 kPa·m<sup>3</sup></p>\n<p class=\"child-para\">1 kJ/kg = 1,000 m<sup>2</sup>/s<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Force:</b> 1 N = 1 kg·m/s<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Length:</b> 1 m = 100 cm = 1,000 mm</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Mass:</b> 1 kg = 1,000 g</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Power, heat transfer rate:</b> 1 W = 1 J/s, 1 kW = 1,000 W</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Pressure:</b> 1 Pa = 1 N/m<sup>2</sup>, 1 kPa = 1,000 kPa, 1 MPa = 1,000 kPa</p>\n<p class=\"child-para\">1 atmosphere (atm) = 101.325 kPa</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Specific heat, entropy:</b> 1 kJ/kg · °C = 1 kJ/kg · K = 1 J/g·°C</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Specific volume:</b> 1 m<sup>3</sup>/kg = 1,000 L/kg = 1,000 cm<sup>3</sup>/kg</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Temperature:</b> T(K) = T(°C) + 273.15, T(°C) = (5/9) T(°F) – 32, T(°F) = (9/5) T(°C) + 32</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Velocity:</b> 1m/s = 3.6 km/hr</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Volume:</b> 1 m<sup>3</sup> = 1,000 L = 10<sup>6</sup> cm<sup>3</sup></p>\n</li>\n</ul>\n"},{"title":"Physical constants in thermodynamics","thumb":null,"image":null,"content":"<p>You run across a few physical constants when working out thermodynamics problems. Following is a list of the constants you need when you’re working with potential energy, pressure, or the ideal gas law.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><b>Acceleration of gravity:</b> g = 9.81 m/s<sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\"><b>Standard atmospheric pressure:</b> 1 atm = 101.3 kPa</p>\n</li>\n<li>\n<p class=\"first-para\"><b>Universal gas constant: </b></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/275491.image0.jpg\" alt=\"image0.jpg\" width=\"153\" height=\"18\" /></li>\n</ul>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-02-15T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":208592},{"headers":{"creationTime":"2016-03-27T16:56:14+00:00","modifiedTime":"2022-02-11T21:41:57+00:00","timestamp":"2022-02-24T17:07:31+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Physics II For Dummies Cheat Sheet","strippedTitle":"physics ii for dummies cheat sheet","slug":"physics-ii-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"Keep this Cheat Sheet handy while learning Physics II for a quick reference on topics like waves and optics, special relativity, and more.","noIndex":0,"noFollow":0},"content":"Here’s a list of some of the most important equations in Physics II courses. You can use these physics formulas as a quick reference for when you’re solving problems in electricity and magnetism, light waves and optics, special relativity, and modern physics.","description":"Here’s a list of some of the most important equations in Physics II courses. You can use these physics formulas as a quick reference for when you’re solving problems in electricity and magnetism, light waves and optics, special relativity, and modern physics.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":192451,"title":"Light Wave and Optics Formulas","slug":"light-wave-and-optics-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192451"}},{"articleId":192450,"title":"Quantum Mechanics and Other Modern Physics Topics","slug":"quantum-mechanics-and-other-modern-physics-topics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192450"}},{"articleId":192447,"title":"Formulas from Einstein’s Theory of Special Relativity","slug":"formulas-from-einsteins-theory-of-special-relativity","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192447"}},{"articleId":192446,"title":"Physics Equations for Electricity and Magnetism","slug":"physics-equations-for-electricity-and-magnetism","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192446"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat Sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207736"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282470,"slug":"physics-ii-for-dummies","isbn":"9780470538067","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/0470538066/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/0470538066/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/0470538066-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/0470538066/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/0470538066/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/physics-ii-for-dummies-cover-9780470538067-203x255.jpg","width":203,"height":255},"title":"Physics II For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"\n <b data-author-id=\"8967\">Steven Holzner</b>, PhD, taught physics at Cornell University for more than a decade. He is the author of <i>Physics For Dummies</i>, <i>Physics Workbook For Dummies</i>, <i>Quantum Physics For Dummies</i>, and <i>Quantum Physics Workbook For Dummies</i>. ","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470538067&quot;]}]\" id=\"du-slot-6217bb5346ebf\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470538067&quot;]}]\" id=\"du-slot-6217bb5347864\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":192446,"title":"Physics Equations for Electricity and Magnetism","slug":"physics-equations-for-electricity-and-magnetism","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192446"}},{"articleId":192451,"title":"Light Wave and Optics Formulas","slug":"light-wave-and-optics-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192451"}},{"articleId":192447,"title":"Formulas from Einstein’s Theory of Special Relativity","slug":"formulas-from-einsteins-theory-of-special-relativity","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192447"}},{"articleId":192450,"title":"Quantum Mechanics and Other Modern Physics Topics","slug":"quantum-mechanics-and-other-modern-physics-topics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/192450"}}],"content":[{"title":"Physics equations for electricity and magnetism","thumb":null,"image":null,"content":"<p>Electricity and magnetism make up one of the most successful fields of study in physics. When working mathematically with electricity and magnetism, you can figure out the force between electric charges, the magnetic field from wires, and more. Keep the following equations handy as you study these topics:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/198823.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"857\" /></p>\n"},{"title":"Light wave and optics formulas","thumb":null,"image":null,"content":"<p>Light waves — that is, electromagnetic waves — behave like other waves: They can reflect, refract (bend), and interfere with each other. Here are some wave formulas that are useful when you’re working with optics. You can determine the wave frequency and period, predict how fast light travels in various materials, and determine how light will bend in lenses and bounce off mirrors.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/198826.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"1049\" /></p>\n"},{"title":"Formulas from Einstein's theory of special relativity","thumb":null,"image":null,"content":"<p>Einstein’s theory of special relativity describes what happens as things near the speed of light. Here are some important special-relativity equations that deal with time dilation, length contraction, and more.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/198829.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"625\" /></p>\n"},{"title":"Quantum mechanics and other modern physics topics","thumb":null,"image":null,"content":"<p>Modern physics includes all sorts of topics, such as quantum mechanics, matter waves, radioactivity, the spectrum of hydrogen, and more.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/198832.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"828\" /></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-02-11T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":209012},{"headers":{"creationTime":"2016-03-27T16:52:56+00:00","modifiedTime":"2022-01-24T21:15:48+00:00","timestamp":"2022-02-24T17:07:26+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Physics I For Dummies Cheat Sheet","strippedTitle":"physics i for dummies cheat sheet","slug":"physics-i-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"As you're learning physics, keep this handy guide nearby for a quick reference to equations, formulas, and constants.","noIndex":0,"noFollow":0},"content":"Physics involves a lot of calculations and problem solving. Having on hand the most frequently used physics equations and formulas helps you perform these tasks more efficiently and accurately. This Cheat Sheet also includes a list physics constants that you’ll find useful in a broad range of physics problems.","description":"Physics involves a lot of calculations and problem solving. Having on hand the most frequently used physics equations and formulas helps you perform these tasks more efficiently and accurately. This Cheat Sheet also includes a list physics constants that you’ll find useful in a broad range of physics problems.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184049"}},{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184043"}},{"articleId":174308,"title":"Calculating Tangential Velocity on a Curve","slug":"calculating-tangential-velocity-on-a-curve","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174308"}},{"articleId":174307,"title":"Flowing from Hot to Cold: The Second Law of Thermodynamics","slug":"flowing-from-hot-to-cold-the-second-law-of-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174307"}},{"articleId":174306,"title":"How to Calculate the Momentum of Inertia for Different Shapes and Solids","slug":"how-to-calculate-the-momentum-of-inertia-for-different-shapes-and-solids","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174306"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat Sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207736"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282467,"slug":"physics-i-for-dummies","isbn":"9781119872221","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119872227-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119872221-203x255.jpg","width":203,"height":255},"title":"Physics I For Dummies, 3rd Edition","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"\n <p><strong><b data-author-id=\"8967\">Steven Holzner</b></strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.</p>","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119872221&quot;]}]\" id=\"du-slot-6217bb4e1f0ed\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119872221&quot;]}]\" id=\"du-slot-6217bb4e1fa91\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184043"}},{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184049"}}],"content":[{"title":"Physics equations and formulas","thumb":null,"image":null,"content":"<p>Physics is filled with equations and formulas that deal with angular motion, Carnot engines, fluids, forces, moments of inertia, linear motion, simple harmonic motion, thermodynamics, and work and energy.</p>\n<p>Here’s a list of some important physics formulas and equations to keep on hand — arranged by topic — so you don’t have to go searching to find them.</p>\n<h2>Angular motion</h2>\n<p>Equations of angular motion are relevant wherever you have rotational motions around an axis. When the object has rotated through an angle of <em>θ</em> with an angular velocity of <em>ω</em> and an angular acceleration of <em>α</em>, then you can use these equations to tie these values together.</p>\n<p class=\"Remember\">You must use radians to measure the angle. Also, if you know that the distance from the axis is <em>r,</em> then you can work out the linear distance traveled, <em>s</em>, velocity, <em>v</em>, centripetal acceleration, <em>a</em><em><sub>c</sub></em>, and force, <em>F</em><em><sub>c</sub></em>. When an object with moment of inertia, <em>I</em> (the angular equivalent of mass), has an angular acceleration, <em>α</em>, then there is a net torque <em>Στ.</em></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293034.image0.png\" alt=\"image0.png\" width=\"187\" height=\"405\" /></p>\n<h2>Carnot engines</h2>\n<p>A heat engine takes heat, <em>Q</em><em><sub>h</sub></em>, from a high temperature source at temperature <em>T</em><em><sub>h</sub></em> and moves it to a low temperature sink (temperature <em>T</em><em><sub>c</sub></em>) at a rate <em>Q</em><em><sub>c</sub></em> and, in the process, does mechanical work, <em>W</em>. (This process can be reversed such that work can be performed to move the heat in the opposite direction — a heat pump.) The amount of work performed in proportion to the amount of heat extracted from the heat source is the efficiency of the engine. A Carnot engine is reversible and has the maximum possible efficiency, given by the following equations. The equivalent of efficiency for a heat pump is the coefficient of performance.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293035.image1.png\" alt=\"image1.png\" width=\"369\" height=\"217\" /></p>\n<h2>Fluids</h2>\n<p>A volume, <em>V</em><em>,</em> of fluid with mass, <em>m</em><em>,</em> has density,<em> ρ</em>. A force, <em>F</em><em>,</em> over an area, <em>A</em><em>,</em> gives rise to a pressure, <em>P</em>. The pressure of a fluid at a depth of <em>h</em> depends on the density and the gravitational constant, <em>g</em>. Objects immersed in a fluid causing a mass of weight, <em>W</em><em><sub>water</sub></em> <em><sub>displaced</sub></em>, give rise to an upward directed buoyancy force, <em>F</em><em><sub>buoyancy</sub></em>. Because of the conservation of mass, the volume flow rate of a fluid moving with velocity, <em>v</em><em>,</em> through a cross-sectional area, <em>A</em>, is constant. Bernoulli’s equation relates the pressure and speed of a fluid.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293036.image2.png\" alt=\"image2.png\" width=\"251\" height=\"219\" /></p>\n<h2>Forces</h2>\n<p>A mass, <em>m</em><em>,</em> accelerates at a rate, <em>a</em>, due to a force, <em>F</em><em>,</em> acting. Frictional forces, <em>F</em><em><sub>F</sub></em>, are in proportion to the normal force between the materials, <em>F</em><em><sub>N</sub></em>, with a coefficient of friction, <em>μ.</em> Two masses, <em>m</em><em><sub>1</sub></em> and <em>m</em><em><sub>2</sub></em>, separated by a distance, <em>r</em><em>,</em> attract each other with a gravitational force, given by the following equations, in proportion to the gravitational constant <em>G</em><em>:</em></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293037.image3.png\" alt=\"image3.png\" width=\"81\" height=\"103\" /></p>\n<h2>Moments of inertia</h2>\n<p>The rotational equivalent of mass is inertia, <em>I</em><em>, </em>which depends on how an object’s mass is distributed through space. The moments of inertia for various shapes are shown here:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Disk rotating around its center:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293038.image4.png\" alt=\"image4.png\" width=\"64\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Hollow cylinder rotating around its center: <em>I</em> = <em>mr</em><sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Hollow sphere rotating an axis through its center:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293039.image5.png\" alt=\"image5.png\" width=\"64\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Hoop rotating around its center: <em>I</em> = <em>mr</em><sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Point mass rotating at radius <em>r:</em> <em>I</em> = <em>mr</em><sup>2</sup></p>\n</li>\n<li>\n<p class=\"first-para\">Rectangle rotating around an axis along one edge where the other edge is of length <em>r</em><em>:</em></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293040.image6.png\" alt=\"image6.png\" width=\"64\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Rectangle rotating around an axis parallel to one edge and passing through the center, where the length of the other edge is <em>r</em><em>:</em></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293041.image7.png\" alt=\"image7.png\" width=\"71\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Rod rotating around an axis perpendicular to it and through its center:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293042.image8.png\" alt=\"image8.png\" width=\"71\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Rod rotating around an axis perpendicular to it and through one end:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293043.image9.png\" alt=\"image9.png\" width=\"64\" height=\"37\" /></li>\n<li>\n<p class=\"first-para\">Solid cylinder, rotating around an axis along its center line:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293044.image10.png\" alt=\"image10.png\" width=\"64\" height=\"37\" /></li>\n<li>\n<p class=\"child-para\">The kinetic energy of a rotating body, with moment of inertia, <em>I</em>, and angular velocity, <em>ω</em>:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293045.image11.png\" alt=\"image11.png\" width=\"76\" height=\"37\" /></li>\n<li>\n<p class=\"child-para\">The angular momentum of a rotating body with moment of inertia, <em>I</em>, and angular velocity, <em>ω</em>:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293046.image12.png\" alt=\"image12.png\" width=\"44\" height=\"17\" /></li>\n</ul>\n<h2>Linear motion</h2>\n<p>When an object at position <em>x</em> moves with velocity, <em>v</em><em>,</em> and acceleration, <em>a,</em> resulting in displacement, <em>s</em>, each of these components is related by the following equations:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293047.image13.png\" alt=\"image13.png\" width=\"184\" height=\"189\" /></p>\n<h2>Simple harmonic motion</h2>\n<p>Particular kinds of force result in periodic motion, where the object repeats its motion with a period, <em>T</em>, having an angular frequency, <em>ω,</em> and amplitude, <em>A</em>. One example of such a force is provided by a spring with spring constant, <em>k</em>. The position, <em>x</em>, velocity, <em>v</em>, and acceleration, <em>a,</em> of an object undergoing simple harmonic motion can be expressed as sines and cosines.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293048.image14.png\" alt=\"image14.png\" width=\"108\" height=\"159\" /></p>\n<h2>Thermodynamics</h2>\n<p>The random vibrational and rotational motions of the molecules that make up an object of substance have energy; this energy is called <em>thermal energy. </em>When thermal energy moves from one place to another, it’s called <em>heat,</em> <em>Q</em>. When an object receives an amount of heat, its temperature, <em>T</em><em>,</em> rises.</p>\n<p>Kelvin (<em>K</em>), Celsius (<em>C</em>), and Fahrenheit (F<em>)</em> are temperature scales. You can use these formulas to convert from one temperature scale to another:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293049.image15.png\" alt=\"image15.png\" width=\"100\" height=\"108\" /></p>\n<p>The heat required to cause a change in temperature of a mass, <em>m</em><em>,</em> increases with a constant of proportionality, <em>c</em><em>,</em> called the <em>specific heat capacity.</em> In a bar of material with a cross-sectional area <em>A</em>, length <em>L</em>, and a temperature difference across the ends of <em>ΔT</em>, there is a heat flow over a time, <em>t</em><em>,</em> given by these formulas:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293050.image16.png\" alt=\"image16.png\" width=\"85\" height=\"103\" /></p>\n<p>The pressure, <em>P</em>, and volume, <em>V</em><em>,</em> of <em>n </em>moles of an ideal gas at temperature <em>T</em> is given by this formula, where <em>R</em> is the gas constant:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293051.image17.png\" alt=\"image17.png\" width=\"71\" height=\"16\" /></p>\n<p>In an ideal gas, the average energy of each molecule <em>KE</em><em><sub>avg</sub></em>, is in proportion to the temperature, with the Boltzman constant <em>k</em><em>:</em></p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293052.image18.png\" alt=\"image18.png\" width=\"92\" height=\"37\" /></p>\n<h2>Work and energy</h2>\n<p>When a force, <em>F</em><em>,</em> moves an object through a distance,<em> s</em>, which is at an angle of <em>Θ</em>,then work, <em>W</em><em>,</em> is done. Momentum, <em>p</em>, is the product of mass, <em>m</em><em>,</em> and velocity, <em>v</em>. The energy that an object has on account of its motion is called <em>KE</em>.</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293053.image19.png\" alt=\"image19.png\" width=\"87\" height=\"120\" /></p>\n"},{"title":"A list of physics constants","thumb":null,"image":null,"content":"<p>Physics constants are physical quantities with fixed numerical values. The following list contains the most common physics constants, including Avogadro’s number, Boltzmann’s constant, the mass of electron, the mass of a proton, the speed of light, the gravitational constant, and the gas constant.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Avogadro’s number:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293055.image0.png\" alt=\"image0.png\" width=\"159\" height=\"28\" /></li>\n<li>\n<p class=\"first-para\">Boltzmann’s constant:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293056.image1.png\" alt=\"image1.png\" width=\"141\" height=\"24\" /></li>\n<li>\n<p class=\"first-para\">Mass of electron:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293057.image2.png\" alt=\"image2.png\" width=\"147\" height=\"28\" /></li>\n<li>\n<p class=\"first-para\">Mass of proton:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293058.image3.png\" alt=\"image3.png\" width=\"147\" height=\"31\" /></li>\n<li>\n<p class=\"first-para\">Speed of light:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293059.image4.png\" alt=\"image4.png\" width=\"131\" height=\"23\" /></li>\n<li>\n<p class=\"first-para\">Gravitational constant:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293060.image5.png\" alt=\"image5.png\" width=\"188\" height=\"27\" /></li>\n<li>\n<p class=\"first-para\">Gas constant:</p>\n<p><img loading=\"lazy\" src=\"https://www.dummies.com/wp-content/uploads/293061.image6.png\" alt=\"image6.png\" width=\"136\" height=\"27\" /></li>\n</ul>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2022-01-24T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":208460},{"headers":{"creationTime":"2016-03-27T16:58:15+00:00","modifiedTime":"2022-01-19T19:02:14+00:00","timestamp":"2022-02-24T17:07:25+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"String Theory For Dummies Cheat Sheet","strippedTitle":"string theory for dummies cheat sheet","slug":"string-theory-for-dummies-cheat-sheet","canonicalUrl":"","seo":{"metaDescription":"The study of string theory is still young and evolving. Here's a handy guide on its history, and its basic features and concepts.","noIndex":0,"noFollow":0},"content":"String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.","description":"String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.","blurb":"","authors":[{"authorId":9499,"name":"Andrew Zimmerman Jones","slug":"andrew-zimmerman-jones","description":"Andrew Zimmerman Jones earned his physics degree and graduated with honors from Wabash College, where he earned the Harold Q. Fuller Prize in Physics.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/9499"}},{"authorId":9500,"name":"Daniel Robbins","slug":"daniel-robbins","description":"Daniel Robbins earned his PhD in physics from the University of Chicago and teaches physics at the University at Albany.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/9500"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":195185,"title":"Key Events in String Theory History","slug":"key-events-in-string-theory-history","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195185"}},{"articleId":195183,"title":"String Theory Features","slug":"string-theory-features","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195183"}},{"articleId":195180,"title":"Superpartners in String Theory","slug":"superpartners-in-string-theory","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195180"}},{"articleId":195173,"title":"Keeping Track of String Theory’s Many Names","slug":"keeping-track-of-string-theorys-many-names","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195173"}},{"articleId":193393,"title":"The Successes of String Theory","slug":"the-successes-of-string-theory","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/193393"}}],"fromCategory":[{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat Sheet","slug":"physics-i-workbook-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207736"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282613,"slug":"string-theory-for-dummies","isbn":"9780470467244","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/047046724X/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/047046724X/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/047046724X-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/047046724X/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/047046724X/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/string-theory-for-dummies-cover-9780470467244-203x255.jpg","width":203,"height":255},"title":"String Theory For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"\n <p><b data-author-id=\"9499\">Andrew Zimmerman Jones</b> received his physics degree and graduated with honors from Wabash College, where he earned the Harold Q. Fuller Prize in Physics. He is the Physics Guide for the New York Times' About.com Web site. <b data-author-id=\"9500\">Daniel Robbins</b> received his PhD in physics from the University of Chicago and currently studies string theory and its implications at Texas A&amp;M University. </p>","authors":[{"authorId":9499,"name":"Andrew Zimmerman Jones","slug":"andrew-zimmerman-jones","description":"Andrew Zimmerman Jones earned his physics degree and graduated with honors from Wabash College, where he earned the Harold Q. Fuller Prize in Physics.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/9499"}},{"authorId":9500,"name":"Daniel Robbins","slug":"daniel-robbins","description":"Daniel Robbins earned his PhD in physics from the University of Chicago and teaches physics at the University at Albany.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/9500"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470467244&quot;]}]\" id=\"du-slot-6217bb4d33308\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9780470467244&quot;]}]\" id=\"du-slot-6217bb4d33cc6\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":195183,"title":"String Theory Features","slug":"string-theory-features","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195183"}},{"articleId":195180,"title":"Superpartners in String Theory","slug":"superpartners-in-string-theory","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195180"}},{"articleId":195173,"title":"Keeping Track of String Theory’s Many Names","slug":"keeping-track-of-string-theorys-many-names","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195173"}},{"articleId":195185,"title":"Key Events in String Theory History","slug":"key-events-in-string-theory-history","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/195185"}}],"content":[{"title":"String theory features","thumb":null,"image":null,"content":"<p>String theory is a work in progress, so trying to pin down exactly what the science is, or what its fundamental elements are, can be kind of tricky. The key string theory features include:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">All objects in our universe are composed of vibrating filaments (strings) and membranes (branes) of energy.</p>\n</li>\n<li>\n<p class=\"first-para\">String theory attempts to reconcile general relativity (gravity) with quantum physics.</p>\n</li>\n<li>\n<p class=\"first-para\">A new connection (called <i>supersymmetry</i>) exists between two fundamentally different types of particles, <i>bosons</i> and <i>fermions.</i></p>\n</li>\n<li>\n<p class=\"first-para\">Several extra (usually unobservable) dimensions to the universe must exist.</p>\n</li>\n</ul>\n<p>There are also other possible string theory features, depending on what theories prove to have merit in the future. Possibilities include:</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">A landscape of string theory solutions, allowing for possible parallel universes.</p>\n</li>\n<li>\n<p class=\"first-para\">The holographic principle, which states how information in a space can relate to information on the surface of that space.</p>\n</li>\n<li>\n<p class=\"first-para\">The anthropic principle, which states that scientists can use the fact that humanity exists as an explanation for certain physical properties of our universe.</p>\n</li>\n<li>\n<p class=\"first-para\">Our universe could be “stuck” on a brane, allowing for new interpretations of string theory.</p>\n</li>\n<li>\n<p class=\"first-para\">Other principles or features, waiting to be discovered.</p>\n</li>\n</ul>\n"},{"title":"Superpartners in string theory","thumb":null,"image":null,"content":"<p>String theory’s concept of <i>supersymmetry</i> is a fancy way of saying that each particle has a related particle called a <i>superpartner.</i> Keeping track of the names of these superpartners can be tricky, so here are the rules in a nutshell.</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">The superpartner of a fermion begins with an <em>s</em>, so the superpartner of an electron is the selectron and the superpartner of the quark is the squark.</p>\n</li>\n<li>\n<p class=\"first-para\">The superpartner of a boson ends in <em>ino</em>, so the superpartner of a photon is the photino and of the graviton is the gravitino.</p>\n</li>\n</ul>\n<p>Use the following table to see some examples of the superpartner names.</p>\n<table>\n<caption>Some Superpartner Names</caption>\n<tbody>\n<tr>\n<th>Standard Particle</th>\n<th>Superpartner</th>\n</tr>\n<tr>\n<td>Higgs boson</td>\n<td>Higgsino</td>\n</tr>\n<tr>\n<td>Neutrino</td>\n<td>Sneutrino</td>\n</tr>\n<tr>\n<td>Lepton</td>\n<td>Slepton</td>\n</tr>\n<tr>\n<td>Z boson</td>\n<td>Zino</td>\n</tr>\n<tr>\n<td>W boson</td>\n<td>Wino</td>\n</tr>\n<tr>\n<td>Gluon</td>\n<td>Gluino</td>\n</tr>\n<tr>\n<td>Muon</td>\n<td>Smuon</td>\n</tr>\n<tr>\n<td>Top quark</td>\n<td>Stop squark</td>\n</tr>\n</tbody>\n</table>\n"},{"title":"Keeping track of string theory's many names","thumb":null,"image":null,"content":"<p>String theory has gone through many name changes over the years. The list below provides an at-a-glance look at some of the major names for different types of string theory.</p>\n<p>Some versions have more specific variations, which are shown as subentries. (These different variants are related in complex ways and sometimes overlap, so this breakdown into subentries is based on the order in which the theories developed.) Now, if you hear these names, you’ll know they’re talking about string theory!</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\">Bosonic string theory</p>\n</li>\n<li>\n<p class=\"first-para\">Superstring theory (or Supersymmetric string theory)</p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">Type I, Type IIA, Type IIB, Heterotic string theories (Type HE, Type HO)</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\">M-theory</p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">Matrix theory</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\">Brane world scenarios</p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">Randall-Sundrum models (or RS1 and RS2)</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\">F-theory</p>\n</li>\n</ul>\n"},{"title":"Key events in string theory","thumb":null,"image":null,"content":"<p>Although string theory is a young science, it has had many notable achievements. What follows are some landmark events in the history of string theory.</p>\n<p><b>1968:</b> Gabriele Veneziano originally proposes the dual resonance model.</p>\n<p><b>1970:</b> String theory is created when physicists interpret Veneziano’s model as describing a universe of vibrating strings.</p>\n<p><b>1971:</b> Supersymmetry is incorporated, creating superstring theory.</p>\n<p><b>1974:</b> String theories are shown to require extra dimensions. An object similar to the graviton is found in superstring theories.</p>\n<p><b>1984:</b> The first superstring revolution begins when it’s shown that anomalies are absent in superstring theory.</p>\n<p><b>1985:</b> Heterotic string theory is developed. Calabi-Yau manifolds are shown to compactify the extra dimensions.</p>\n<p><b>1995:</b> Edward Witten proposes M-theory as unification of superstring theories, starting the second superstring revolution. Joe Polchinski shows branes are necessarily included in string theory.</p>\n<p><b>1996:</b> String theory is used to analyze black hole thermodynamics, matching earlier predictions from other methods.</p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Two years","lifeExpectancySetFrom":"2022-01-19T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":209405},{"headers":{"creationTime":"2016-03-26T17:23:25+00:00","modifiedTime":"2021-10-29T19:44:00+00:00","timestamp":"2022-02-24T17:07:06+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"How to Calculate a Spring Constant Using Hooke's Law","strippedTitle":"how to calculate a spring constant using hooke's law","slug":"how-to-calculate-a-spring-constant-using-hookes-law","canonicalUrl":"","seo":{"metaDescription":"Learn about Hooke's law and how to calculate the spring constant, including the formula and insight on a spring's impact on force.","noIndex":0,"noFollow":0},"content":"Any physicist knows that if an object applies a force to a spring, then the spring applies an equal and opposite force to the object. <a href=\"https://www.dummies.com/education/science/using-a-generalized-hookes-law-for-stress-and-strain/\" target=\"_blank\" rel=\"noopener\">Hooke’s law</a> gives the force a spring exerts on an object attached to it with the following equation:\r\n\r\n<i>F</i> = –<i>kx</i>\r\n\r\nThe minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring. The variables of the equation are <em>F,</em> which represents force, <em>k, </em>which is called the spring constant and measures how stiff and strong the spring is, and <em>x,</em> the distance the spring is stretched or compressed away from its equilibrium or rest position.\r\n\r\nThe force exerted by a spring is called a <i>restoring force;</i> it always acts to restore the spring toward equilibrium. In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement.\r\n<h2 id=\"tab1\" >Understanding springs and their direction of force</h2>\r\n<img class=\"aligncenter wp-image-239155 size-full\" src=\"https://www.dummies.com/wp-content/uploads/direction-of-force-in-springs.jpg\" alt=\"direction of force exzerted in springs\" width=\"535\" height=\"285\" />\r\n<div class=\"imageBlock\" style=\"width: 535px;\">\r\n<div class=\"imageCaption\">The direction of force exerted by a spring</div>\r\n</div>\r\nThe preceding figure shows a ball attached to a spring. You can see that if the spring isn’t stretched or compressed, it exerts no force on the ball. If you push the spring, however, it pushes back, and if you pull the spring, it pulls back.\r\n<p class=\"Remember\">Hooke’s law is valid as long as the elastic material you’re dealing with stays elastic — that is, it stays within its <i><a href=\"https://www.dummies.com/education/science/physics/how-to-calculate-the-potential-and-kinetic-energy-in-a-spring/\" target=\"_blank\" rel=\"noopener\">elastic limit</a>.</i> If you pull a spring too far, it loses its stretchy ability. As long as a spring stays within its elastic limit, you can say that <i>F</i> = –<i>kx</i>. When a spring stays within its elastic limit and obeys Hooke’s law, the spring is called an <i>ideal spring.</i></p>\r\n\r\n<h2 id=\"tab2\" >How to find the spring constant (example problem)</h2>\r\nSuppose that a group of car designers knocks on your door and asks whether you can help design a suspension system. “Sure,” you say. They inform you that the car will have a mass of 1,000 kilograms, and you have four shock absorbers, each 0.5 meters long, to work with. How strong do the springs have to be? Assuming these shock absorbers use springs, each one has to support a mass of at least 250 kilograms, which weighs the following:\r\n\r\n<i>F</i> = <i>mg</i> = (250 kg)(9.8 m/s<sup>2</sup>) = 2,450 N\r\n\r\nwhere <i>F</i> equals force, <i>m</i> equals the mass of the object, and <i>g</i> equals the acceleration due to gravity, 9.8 meters per second<sup>2</sup>. The spring in the shock absorber will, at a minimum, have to give you 2,450 newtons of force at the maximum compression of 0.5 meters. What does this mean the spring constant should be? In order to figure out <strong>how to calculate the spring constant</strong>, we must remember what Hooke’s law says:\r\n\r\n<i>F</i> = –<i>kx</i>\r\n\r\nNow, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or <em>k</em>. Looking only at the magnitudes and therefore omitting the negative sign, you get\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/330102.image1.png\" alt=\"image1.png\" width=\"41\" height=\"37\" />\r\n\r\nTime to plug in the numbers:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/330103.image2.png\" alt=\"image2.png\" width=\"195\" height=\"39\" />\r\n\r\nThe springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. The car designers rush out, ecstatic, but you call after them, “Don’t forget, you need to at least double that if you actually want your car to be able to handle potholes.”","description":"Any physicist knows that if an object applies a force to a spring, then the spring applies an equal and opposite force to the object. <a href=\"https://www.dummies.com/education/science/using-a-generalized-hookes-law-for-stress-and-strain/\" target=\"_blank\" rel=\"noopener\">Hooke’s law</a> gives the force a spring exerts on an object attached to it with the following equation:\r\n\r\n<i>F</i> = –<i>kx</i>\r\n\r\nThe minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring. The variables of the equation are <em>F,</em> which represents force, <em>k, </em>which is called the spring constant and measures how stiff and strong the spring is, and <em>x,</em> the distance the spring is stretched or compressed away from its equilibrium or rest position.\r\n\r\nThe force exerted by a spring is called a <i>restoring force;</i> it always acts to restore the spring toward equilibrium. In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement.\r\n<h2 id=\"tab1\" >Understanding springs and their direction of force</h2>\r\n<img class=\"aligncenter wp-image-239155 size-full\" src=\"https://www.dummies.com/wp-content/uploads/direction-of-force-in-springs.jpg\" alt=\"direction of force exzerted in springs\" width=\"535\" height=\"285\" />\r\n<div class=\"imageBlock\" style=\"width: 535px;\">\r\n<div class=\"imageCaption\">The direction of force exerted by a spring</div>\r\n</div>\r\nThe preceding figure shows a ball attached to a spring. You can see that if the spring isn’t stretched or compressed, it exerts no force on the ball. If you push the spring, however, it pushes back, and if you pull the spring, it pulls back.\r\n<p class=\"Remember\">Hooke’s law is valid as long as the elastic material you’re dealing with stays elastic — that is, it stays within its <i><a href=\"https://www.dummies.com/education/science/physics/how-to-calculate-the-potential-and-kinetic-energy-in-a-spring/\" target=\"_blank\" rel=\"noopener\">elastic limit</a>.</i> If you pull a spring too far, it loses its stretchy ability. As long as a spring stays within its elastic limit, you can say that <i>F</i> = –<i>kx</i>. When a spring stays within its elastic limit and obeys Hooke’s law, the spring is called an <i>ideal spring.</i></p>\r\n\r\n<h2 id=\"tab2\" >How to find the spring constant (example problem)</h2>\r\nSuppose that a group of car designers knocks on your door and asks whether you can help design a suspension system. “Sure,” you say. They inform you that the car will have a mass of 1,000 kilograms, and you have four shock absorbers, each 0.5 meters long, to work with. How strong do the springs have to be? Assuming these shock absorbers use springs, each one has to support a mass of at least 250 kilograms, which weighs the following:\r\n\r\n<i>F</i> = <i>mg</i> = (250 kg)(9.8 m/s<sup>2</sup>) = 2,450 N\r\n\r\nwhere <i>F</i> equals force, <i>m</i> equals the mass of the object, and <i>g</i> equals the acceleration due to gravity, 9.8 meters per second<sup>2</sup>. The spring in the shock absorber will, at a minimum, have to give you 2,450 newtons of force at the maximum compression of 0.5 meters. What does this mean the spring constant should be? In order to figure out <strong>how to calculate the spring constant</strong>, we must remember what Hooke’s law says:\r\n\r\n<i>F</i> = –<i>kx</i>\r\n\r\nNow, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or <em>k</em>. Looking only at the magnitudes and therefore omitting the negative sign, you get\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/330102.image1.png\" alt=\"image1.png\" width=\"41\" height=\"37\" />\r\n\r\nTime to plug in the numbers:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/330103.image2.png\" alt=\"image2.png\" width=\"195\" height=\"39\" />\r\n\r\nThe springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. The car designers rush out, ecstatic, but you call after them, “Don’t forget, you need to at least double that if you actually want your car to be able to handle potholes.”","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Understanding springs and their direction of force","target":"#tab1"},{"label":"How to find the spring constant (example problem)","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184049"}},{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184043"}},{"articleId":174308,"title":"Calculating Tangential Velocity on a Curve","slug":"calculating-tangential-velocity-on-a-curve","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174308"}},{"articleId":174307,"title":"Flowing from Hot to Cold: The Second Law of Thermodynamics","slug":"flowing-from-hot-to-cold-the-second-law-of-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174307"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282467,"slug":"physics-i-for-dummies","isbn":"9781119872221","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119872227-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119872221-203x255.jpg","width":203,"height":255},"title":"Physics I For Dummies, 3rd Edition","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"\n <p><strong><b data-author-id=\"8967\">Steven Holzner</b></strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.</p>","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119872221&quot;]}]\" id=\"du-slot-6217bb3a48c41\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119872221&quot;]}]\" id=\"du-slot-6217bb3a495c3\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2021-09-10T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":174221},{"headers":{"creationTime":"2016-03-26T10:52:24+00:00","modifiedTime":"2021-10-29T19:11:57+00:00","timestamp":"2022-02-24T17:07:06+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"How to Find a Vector’s Magnitude and Direction","strippedTitle":"how to find a vector’s magnitude and direction","slug":"how-to-find-a-vectors-magnitude-and-direction","canonicalUrl":"","seo":{"metaDescription":"When you're working with vectors in physics and you have the vector components, you can use trigonometry to express them. Here's how.","noIndex":0,"noFollow":0},"content":"In physics, when you’re given the <a href=\"https://www.dummies.com/education/science/physics/how-to-find-vector-components\" target=\"_blank\" rel=\"noopener\">vector components</a>, such as (3, 4), you can easily convert to the magnitude/angle way of expressing <a href=\"https://www.dummies.com/education/science/physics/what-is-a-vector/\" target=\"_blank\" rel=\"noopener\">vectors </a>using trigonometry.\r\n\r\nFor example, take a look at the vector in the image.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442633.image0.jpg\" alt=\"image0.jpg\" width=\"463\" height=\"208\" />\r\n\r\nSuppose that you’re given the coordinates of the end of the vector and want to find its magnitude, <i>v</i>, and angle, theta. Because of your knowledge of trigonometry, you know\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442634.image1.jpg\" alt=\"image1.jpg\" width=\"219\" height=\"57\" />\r\n\r\nWhere tan theta<i> </i>is the tangent of the angle. This means that\r\n<blockquote>theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>)</blockquote>\r\nSuppose that the coordinates of the vector are (3, 4). You can find the angle theta as the tan<sup>–1</sup>(4/3) = 53 degrees.\r\n\r\nYou can use the <a href=\"https://www.dummies.com/education/math/geometry/applying-the-pythagorean-theorem/\" target=\"_blank\" rel=\"noopener\">Pythagorean theorem</a> to find the <i>hypotenuse</i> — the magnitude, <i>v</i> — of the triangle formed by <i>x, y,</i> and <i>v:</i>\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442635.image2.jpg\" alt=\"image2.jpg\" width=\"142\" height=\"37\" />\r\n\r\nPlug in the numbers for this example to get\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442636.image3.jpg\" alt=\"image3.jpg\" width=\"178\" height=\"31\" />\r\n\r\nSo if you have a vector given by the coordinates (3, 4), its magnitude is 5, and its angle is 53 degrees.\r\n<h2 id=\"tab1\" >Sample question</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector given by the coordinates (1.0, 5.0) into magnitude/angle format.</p>\r\n<p class=\"child-para\">The correct answer is magnitude 5.1, angle 79 degrees.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\"><b></b>Apply the Pythagorean theorem to find the magnitude. Plug in the numbers to get 5.1.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><b></b>Apply the equation theta= tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle. Plug in the numbers to get tan<sup>–1</sup>(5.0/1.0) = 79 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Practice questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (5.0, 7.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (13.0, 13.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (–1.0, 1.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (–5.0, –7.0) into magnitude/angle form.</p>\r\n</li>\r\n</ol>\r\nFollowing are answers to the practice questions:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 8.6, angle 54 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442637.image4.jpg\" alt=\"image4.jpg\" width=\"142\" height=\"37\" /></li>\r\n</ol>\r\n<p class=\"child-para\">to find the magnitude, which is 8.6.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(7.0/5.0) = 54 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 18.4, angle 45 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442638.image5.jpg\" alt=\"image5.jpg\" width=\"142\" height=\"37\" /></li>\r\n</ol>\r\n<p class=\"child-para\">to find the magnitude, which is 18.4.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(13.0/13.0) = 45 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 1.4, angle 135 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442639.image6.jpg\" alt=\"image6.jpg\" width=\"142\" height=\"37\" />\r\n<p class=\"child-para\">to find the magnitude, which is 1.4.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(1.0/–1.0) = –45 degrees.</p>\r\n<p class=\"child-para\">However, note that the angle must really be between 90 degrees and 180 degrees because the first vector component is negative and the second is positive. That means you should add 180 degrees to –45 degrees, giving you 135 degrees (the tangent of 135 degrees is also 1.0/–1.0 = –1.0).</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 8.6, angle 234 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442640.image7.jpg\" alt=\"image7.jpg\" width=\"142\" height=\"37\" />\r\n<p class=\"child-para\">to find the magnitude, which is 8.6.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan–1(y/x) to find the angle: tan–1(–7.0/–5.0) = 54 degrees.</p>\r\n<p class=\"child-para\">However, note that the angle must really be between 180 degrees and 270 degrees because both vector components are negative. That means you should add 180 degrees to 54 degrees, giving you 234 degrees (the tangent of 234 degrees is also –7.0/–5.0 = 7.0/5.0).</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>","description":"In physics, when you’re given the <a href=\"https://www.dummies.com/education/science/physics/how-to-find-vector-components\" target=\"_blank\" rel=\"noopener\">vector components</a>, such as (3, 4), you can easily convert to the magnitude/angle way of expressing <a href=\"https://www.dummies.com/education/science/physics/what-is-a-vector/\" target=\"_blank\" rel=\"noopener\">vectors </a>using trigonometry.\r\n\r\nFor example, take a look at the vector in the image.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442633.image0.jpg\" alt=\"image0.jpg\" width=\"463\" height=\"208\" />\r\n\r\nSuppose that you’re given the coordinates of the end of the vector and want to find its magnitude, <i>v</i>, and angle, theta. Because of your knowledge of trigonometry, you know\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442634.image1.jpg\" alt=\"image1.jpg\" width=\"219\" height=\"57\" />\r\n\r\nWhere tan theta<i> </i>is the tangent of the angle. This means that\r\n<blockquote>theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>)</blockquote>\r\nSuppose that the coordinates of the vector are (3, 4). You can find the angle theta as the tan<sup>–1</sup>(4/3) = 53 degrees.\r\n\r\nYou can use the <a href=\"https://www.dummies.com/education/math/geometry/applying-the-pythagorean-theorem/\" target=\"_blank\" rel=\"noopener\">Pythagorean theorem</a> to find the <i>hypotenuse</i> — the magnitude, <i>v</i> — of the triangle formed by <i>x, y,</i> and <i>v:</i>\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442635.image2.jpg\" alt=\"image2.jpg\" width=\"142\" height=\"37\" />\r\n\r\nPlug in the numbers for this example to get\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442636.image3.jpg\" alt=\"image3.jpg\" width=\"178\" height=\"31\" />\r\n\r\nSo if you have a vector given by the coordinates (3, 4), its magnitude is 5, and its angle is 53 degrees.\r\n<h2 id=\"tab1\" >Sample question</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector given by the coordinates (1.0, 5.0) into magnitude/angle format.</p>\r\n<p class=\"child-para\">The correct answer is magnitude 5.1, angle 79 degrees.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\"><b></b>Apply the Pythagorean theorem to find the magnitude. Plug in the numbers to get 5.1.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><b></b>Apply the equation theta= tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle. Plug in the numbers to get tan<sup>–1</sup>(5.0/1.0) = 79 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Practice questions</h2>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (5.0, 7.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (13.0, 13.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (–1.0, 1.0) into magnitude/angle form.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Convert the vector (–5.0, –7.0) into magnitude/angle form.</p>\r\n</li>\r\n</ol>\r\nFollowing are answers to the practice questions:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 8.6, angle 54 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442637.image4.jpg\" alt=\"image4.jpg\" width=\"142\" height=\"37\" /></li>\r\n</ol>\r\n<p class=\"child-para\">to find the magnitude, which is 8.6.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(7.0/5.0) = 54 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 18.4, angle 45 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442638.image5.jpg\" alt=\"image5.jpg\" width=\"142\" height=\"37\" /></li>\r\n</ol>\r\n<p class=\"child-para\">to find the magnitude, which is 18.4.</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(13.0/13.0) = 45 degrees.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 1.4, angle 135 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442639.image6.jpg\" alt=\"image6.jpg\" width=\"142\" height=\"37\" />\r\n<p class=\"child-para\">to find the magnitude, which is 1.4.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan<sup>–1</sup>(<i>y</i>/<i>x</i>) to find the angle: tan<sup>–1</sup>(1.0/–1.0) = –45 degrees.</p>\r\n<p class=\"child-para\">However, note that the angle must really be between 90 degrees and 180 degrees because the first vector component is negative and the second is positive. That means you should add 180 degrees to –45 degrees, giving you 135 degrees (the tangent of 135 degrees is also 1.0/–1.0 = –1.0).</p>\r\n</li>\r\n</ol>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Magnitude 8.6, angle 234 degrees</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/442640.image7.jpg\" alt=\"image7.jpg\" width=\"142\" height=\"37\" />\r\n<p class=\"child-para\">to find the magnitude, which is 8.6.</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Apply the equation theta = tan–1(y/x) to find the angle: tan–1(–7.0/–5.0) = 54 degrees.</p>\r\n<p class=\"child-para\">However, note that the angle must really be between 180 degrees and 270 degrees because both vector components are negative. That means you should add 180 degrees to 54 degrees, giving you 234 degrees (the tangent of 234 degrees is also –7.0/–5.0 = 7.0/5.0).</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Sample question","target":"#tab1"},{"label":"Practice questions","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":207736,"title":"Physics I Workbook For Dummies Cheat 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Friction","slug":"basic-physics-force-and-friction","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/155820"}},{"articleId":155822,"title":"10 Issues to Avoid When Solving Physics Problems","slug":"10-issues-to-avoid-when-solving-physics-problems","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/155822"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282469,"slug":"physics-i-workbook-for-dummies","isbn":"9781119716471","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1119716470/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119716470/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119716470-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119716470/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119716470/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119716471-204x255.jpg","width":204,"height":255},"title":"Physics I Workbook For Dummies with Online Practice, 3rd Edition","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":null,"authors":[{"authorId":34660,"name":"Consumer Dummies","slug":"consumer-dummies","description":"","_links":{"self":"https://dummies-api.dummies.com/v2/authors/34660"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119716471&quot;]}]\" id=\"du-slot-6217bb3a40254\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;science&quot;,&quot;physics&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119716471&quot;]}]\" id=\"du-slot-6217bb3a40bc1\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2021-09-10T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":148768},{"headers":{"creationTime":"2016-03-26T17:21:29+00:00","modifiedTime":"2021-10-07T18:38:04+00:00","timestamp":"2022-02-24T17:07:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"How to Calculate Force Based on Pressure","strippedTitle":"how to calculate force based on pressure","slug":"how-to-calculate-force-based-on-pressure","canonicalUrl":"","seo":{"metaDescription":"Pressure and force are related, so you can calculate one if you know the other. Here's the physics equation and how to solve it.","noIndex":0,"noFollow":0},"content":"Pressure and force are related, and so you can calculate one if you know the other by using the physics equation, <em>P</em> = <em>F/A</em>. Because pressure is force divided by area, its meter-kilogram-second (MKS) units are newtons per square meter, or N/m<sup>2</sup>. In the foot-pound-second (FPS) system, the units are pounds per square inch, or psi.\r\n<p class=\"Remember\">The unit <em>newtons per square meter</em> is so common in physics that it has a special name: the <em>pascal,</em> which equals 1 newton per square meter. The pascal is abbreviated as Pa.</p>\r\nYou don’t have to be underwater to experience pressure from a fluid. Air exerts pressure, too, due to the weight of the air above you. Here’s how much pressure the air exerts on you at sea level:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331301.image0.png\" alt=\"image0.png\" width=\"235\" height=\"28\" />\r\n\r\nThe air pressure at sea level is a standard pressure that people refer to as 1<em> atmosphere</em> (abbreviated atm):\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331302.image1.png\" alt=\"image1.png\" width=\"283\" height=\"28\" />\r\n\r\nIf you convert an atmosphere to pounds per square inch, it’s about 14.7 psi. That means that 14.7 pounds of force are pressing in on every square inch of your body at sea level.\r\n\r\nYour body pushes back with 14.7 psi, so you don’t feel any pressure on you at all. But if you suddenly got transported to outer space, the inward pressure of the air pushing on you would be gone, and all that would remain would be the 14.7 pounds per square inch your body exerted outward. You wouldn’t explode, but your lungs could burst if you tried to hold your breath. The change in pressure could also cause the nitrogen in your blood to form bubbles and give you the bends!\r\n\r\nHere’s a pressure example problem using water pressure. Say you’re in your neighbor’s pool, waiting near the bottom until your neighbors give up trying to chase you off and go back into the house. You’re near the deep end of the pool, and using the handy pressure gauge you always carry, you measure the pressure on the back of your hand as\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331303.image2.png\" alt=\"image2.png\" width=\"119\" height=\"27\" />\r\n\r\nWhat force does the water exert on the back of your hand? The back of your hand has an area of about\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331304.image3.png\" alt=\"image3.png\" width=\"171\" height=\"27\" />\r\n\r\nYou reason that if <em>P</em> = <em>F/A, </em>then the following is true:\r\n\r\n<em>F = PA</em>\r\n\r\nPlugging in the numbers and solving gives you the answer:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331305.image4.png\" alt=\"image4.png\" width=\"235\" height=\"133\" />\r\n\r\nYikes. A thousand newtons! You whip out your underwater calculator to find that’s about 230 pounds. Forces add up quickly when you’re underwater because water is a heavy liquid. The force you feel is the weight of the water above you.","description":"Pressure and force are related, and so you can calculate one if you know the other by using the physics equation, <em>P</em> = <em>F/A</em>. Because pressure is force divided by area, its meter-kilogram-second (MKS) units are newtons per square meter, or N/m<sup>2</sup>. In the foot-pound-second (FPS) system, the units are pounds per square inch, or psi.\r\n<p class=\"Remember\">The unit <em>newtons per square meter</em> is so common in physics that it has a special name: the <em>pascal,</em> which equals 1 newton per square meter. The pascal is abbreviated as Pa.</p>\r\nYou don’t have to be underwater to experience pressure from a fluid. Air exerts pressure, too, due to the weight of the air above you. Here’s how much pressure the air exerts on you at sea level:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331301.image0.png\" alt=\"image0.png\" width=\"235\" height=\"28\" />\r\n\r\nThe air pressure at sea level is a standard pressure that people refer to as 1<em> atmosphere</em> (abbreviated atm):\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331302.image1.png\" alt=\"image1.png\" width=\"283\" height=\"28\" />\r\n\r\nIf you convert an atmosphere to pounds per square inch, it’s about 14.7 psi. That means that 14.7 pounds of force are pressing in on every square inch of your body at sea level.\r\n\r\nYour body pushes back with 14.7 psi, so you don’t feel any pressure on you at all. But if you suddenly got transported to outer space, the inward pressure of the air pushing on you would be gone, and all that would remain would be the 14.7 pounds per square inch your body exerted outward. You wouldn’t explode, but your lungs could burst if you tried to hold your breath. The change in pressure could also cause the nitrogen in your blood to form bubbles and give you the bends!\r\n\r\nHere’s a pressure example problem using water pressure. Say you’re in your neighbor’s pool, waiting near the bottom until your neighbors give up trying to chase you off and go back into the house. You’re near the deep end of the pool, and using the handy pressure gauge you always carry, you measure the pressure on the back of your hand as\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331303.image2.png\" alt=\"image2.png\" width=\"119\" height=\"27\" />\r\n\r\nWhat force does the water exert on the back of your hand? The back of your hand has an area of about\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331304.image3.png\" alt=\"image3.png\" width=\"171\" height=\"27\" />\r\n\r\nYou reason that if <em>P</em> = <em>F/A, </em>then the following is true:\r\n\r\n<em>F = PA</em>\r\n\r\nPlugging in the numbers and solving gives you the answer:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/331305.image4.png\" alt=\"image4.png\" width=\"235\" height=\"133\" />\r\n\r\nYikes. A thousand newtons! You whip out your underwater calculator to find that’s about 230 pounds. Forces add up quickly when you’re underwater because water is a heavy liquid. The force you feel is the weight of the water above you.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"<strong>Steven Holzner</strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.","_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}},{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184049"}},{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184043"}},{"articleId":174308,"title":"Calculating Tangential Velocity on a Curve","slug":"calculating-tangential-velocity-on-a-curve","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174308"}},{"articleId":174307,"title":"Flowing from Hot to Cold: The Second Law of Thermodynamics","slug":"flowing-from-hot-to-cold-the-second-law-of-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174307"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282467,"slug":"physics-i-for-dummies","isbn":"9781119872221","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119872227-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119872221-203x255.jpg","width":203,"height":255},"title":"Physics I For Dummies, 3rd Edition","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"\n <p><strong><b data-author-id=\"8967\">Steven Holzner</b></strong> was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. 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Physics Physics I: 500 Practice Problems For Dummies Cheat Sheet

Cheat Sheet / Updated 03-28-2022

Solving physics problems correctly is a lot easier when you have a couple tricks under your belt. In fact, you can greatly improve your odds of getting the right answer if you make sure that what you calculated is plausible in the real world. Another trick is to draw your own visual when one isn’t provided for you — no artistic ability required. It also helps to have this handy reference for some of the most common unit prefixes and unit conversions you’re bound to encounter in your physics homework.

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Physics Physics I Workbook For Dummies Cheat Sheet

Cheat Sheet / Updated 03-10-2022

Avoid difficulties when working on physics by knowing the common issues that can cause trouble in physics problems, understanding physical constants, and grasping principal physics equations.

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Physics Optics For Dummies Cheat Sheet

Cheat Sheet / Updated 02-18-2022

Optics covers the study of light. Three phenomena — reflection, refraction, and diffraction — help you predict where a ray or rays of light will go. Study up on other important optics topics, too, including interference, polarization, and fiber optics.

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Physics Thermodynamics For Dummies Cheat Sheet

Cheat Sheet / Updated 02-15-2022

Thermodynamics sounds intimidating, and it can be. However, if you focus on the most important thermodynamic formulas and equations, get comfortable converting from one unit of physical measurement to another, and become familiar with the physical constants related to thermodynamics, you’ll be at the head of the class.

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Physics Physics II For Dummies Cheat Sheet

Cheat Sheet / Updated 02-11-2022

Here’s a list of some of the most important equations in Physics II courses. You can use these physics formulas as a quick reference for when you’re solving problems in electricity and magnetism, light waves and optics, special relativity, and modern physics.

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Physics Physics I For Dummies Cheat Sheet

Cheat Sheet / Updated 01-24-2022

Physics involves a lot of calculations and problem solving. Having on hand the most frequently used physics equations and formulas helps you perform these tasks more efficiently and accurately. This Cheat Sheet also includes a list physics constants that you’ll find useful in a broad range of physics problems.

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Physics String Theory For Dummies Cheat Sheet

Cheat Sheet / Updated 01-19-2022

String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.

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Physics How to Calculate a Spring Constant Using Hooke's Law

Article / Updated 10-29-2021

Any physicist knows that if an object applies a force to a spring, then the spring applies an equal and opposite force to the object. Hooke’s law gives the force a spring exerts on an object attached to it with the following equation: F = –kx The minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring. The variables of the equation are F, which represents force, k, which is called the spring constant and measures how stiff and strong the spring is, and x, the distance the spring is stretched or compressed away from its equilibrium or rest position. The force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium. In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement. Understanding springs and their direction of force The direction of force exerted by a spring The preceding figure shows a ball attached to a spring. You can see that if the spring isn’t stretched or compressed, it exerts no force on the ball. If you push the spring, however, it pushes back, and if you pull the spring, it pulls back. Hooke’s law is valid as long as the elastic material you’re dealing with stays elastic — that is, it stays within its elastic limit. If you pull a spring too far, it loses its stretchy ability. As long as a spring stays within its elastic limit, you can say that F = –kx. When a spring stays within its elastic limit and obeys Hooke’s law, the spring is called an ideal spring. How to find the spring constant (example problem) Suppose that a group of car designers knocks on your door and asks whether you can help design a suspension system. “Sure,” you say. They inform you that the car will have a mass of 1,000 kilograms, and you have four shock absorbers, each 0.5 meters long, to work with. How strong do the springs have to be? Assuming these shock absorbers use springs, each one has to support a mass of at least 250 kilograms, which weighs the following: F = mg = (250 kg)(9.8 m/s2) = 2,450 N where F equals force, m equals the mass of the object, and g equals the acceleration due to gravity, 9.8 meters per second2. The spring in the shock absorber will, at a minimum, have to give you 2,450 newtons of force at the maximum compression of 0.5 meters. What does this mean the spring constant should be? In order to figure out how to calculate the spring constant, we must remember what Hooke’s law says: F = –kx Now, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or k. Looking only at the magnitudes and therefore omitting the negative sign, you get Time to plug in the numbers: The springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. The car designers rush out, ecstatic, but you call after them, “Don’t forget, you need to at least double that if you actually want your car to be able to handle potholes.”

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Physics How to Find a Vector’s Magnitude and Direction

Article / Updated 10-29-2021

In physics, when you’re given the vector components, such as (3, 4), you can easily convert to the magnitude/angle way of expressing vectors using trigonometry. For example, take a look at the vector in the image. Suppose that you’re given the coordinates of the end of the vector and want to find its magnitude, v, and angle, theta. Because of your knowledge of trigonometry, you know Where tan theta is the tangent of the angle. This means that theta = tan–1(y/x) Suppose that the coordinates of the vector are (3, 4). You can find the angle theta as the tan–1(4/3) = 53 degrees. You can use the Pythagorean theorem to find the hypotenuse — the magnitude, v — of the triangle formed by x, y, and v: Plug in the numbers for this example to get So if you have a vector given by the coordinates (3, 4), its magnitude is 5, and its angle is 53 degrees. Sample question Convert the vector given by the coordinates (1.0, 5.0) into magnitude/angle format. The correct answer is magnitude 5.1, angle 79 degrees. Apply the Pythagorean theorem to find the magnitude. Plug in the numbers to get 5.1. Apply the equation theta= tan–1(y/x) to find the angle. Plug in the numbers to get tan–1(5.0/1.0) = 79 degrees. Practice questions Convert the vector (5.0, 7.0) into magnitude/angle form. Convert the vector (13.0, 13.0) into magnitude/angle form. Convert the vector (–1.0, 1.0) into magnitude/angle form. Convert the vector (–5.0, –7.0) into magnitude/angle form. Following are answers to the practice questions: Magnitude 8.6, angle 54 degrees Apply the equation to find the magnitude, which is 8.6. Apply the equation theta = tan–1(y/x) to find the angle: tan–1(7.0/5.0) = 54 degrees. Magnitude 18.4, angle 45 degrees Apply the equation to find the magnitude, which is 18.4. Apply the equation theta = tan–1(y/x) to find the angle: tan–1(13.0/13.0) = 45 degrees. Magnitude 1.4, angle 135 degrees Apply the equation to find the magnitude, which is 1.4. Apply the equation theta = tan–1(y/x) to find the angle: tan–1(1.0/–1.0) = –45 degrees. However, note that the angle must really be between 90 degrees and 180 degrees because the first vector component is negative and the second is positive. That means you should add 180 degrees to –45 degrees, giving you 135 degrees (the tangent of 135 degrees is also 1.0/–1.0 = –1.0). Magnitude 8.6, angle 234 degrees Apply the equation to find the magnitude, which is 8.6. Apply the equation theta = tan–1(y/x) to find the angle: tan–1(–7.0/–5.0) = 54 degrees. However, note that the angle must really be between 180 degrees and 270 degrees because both vector components are negative. That means you should add 180 degrees to 54 degrees, giving you 234 degrees (the tangent of 234 degrees is also –7.0/–5.0 = 7.0/5.0).

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Physics How to Calculate Force Based on Pressure

Article / Updated 10-07-2021

Pressure and force are related, and so you can calculate one if you know the other by using the physics equation, P = F/A. Because pressure is force divided by area, its meter-kilogram-second (MKS) units are newtons per square meter, or N/m2. In the foot-pound-second (FPS) system, the units are pounds per square inch, or psi. The unit newtons per square meter is so common in physics that it has a special name: the pascal, which equals 1 newton per square meter. The pascal is abbreviated as Pa. You don’t have to be underwater to experience pressure from a fluid. Air exerts pressure, too, due to the weight of the air above you. Here’s how much pressure the air exerts on you at sea level: The air pressure at sea level is a standard pressure that people refer to as 1 atmosphere (abbreviated atm): If you convert an atmosphere to pounds per square inch, it’s about 14.7 psi. That means that 14.7 pounds of force are pressing in on every square inch of your body at sea level. Your body pushes back with 14.7 psi, so you don’t feel any pressure on you at all. But if you suddenly got transported to outer space, the inward pressure of the air pushing on you would be gone, and all that would remain would be the 14.7 pounds per square inch your body exerted outward. You wouldn’t explode, but your lungs could burst if you tried to hold your breath. The change in pressure could also cause the nitrogen in your blood to form bubbles and give you the bends! Here’s a pressure example problem using water pressure. Say you’re in your neighbor’s pool, waiting near the bottom until your neighbors give up trying to chase you off and go back into the house. You’re near the deep end of the pool, and using the handy pressure gauge you always carry, you measure the pressure on the back of your hand as What force does the water exert on the back of your hand? The back of your hand has an area of about You reason that if P = F/A, then the following is true: F = PA Plugging in the numbers and solving gives you the answer: Yikes. A thousand newtons! You whip out your underwater calculator to find that’s about 230 pounds. Forces add up quickly when you’re underwater because water is a heavy liquid. The force you feel is the weight of the water above you.

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