Physics I For Dummies
Overview
An easy-to-follow guide to introductory physics, from the Big Bang to relativity
All science, technology, engineering, and math majors in college and university require some familiarity with physics. Other career paths, like medicine, are also only open to students who understand this fundamental science. But don’t worry if you find physics to be intimidating or confusing. You just need the right guide!
In Physics I For Dummies, you’ll find a roadmap to physics success that walks you through every major topic in introductory physics, including motion, energy, waves, thermodynamics, electromagnetism, relativity, and more. You’ll learn the basic principles and math formulas of physics through clear and straightforward examples and instruction, and without unnecessary jargon or complicated theory.
In this book, you’ll also find:
- Up-to-date examples and explanations appearing alongside the latest discoveries and research in physics, discussed at a level appropriate for beginning students
- All the info found in an intro physics course, arranged in an intuitive sequence that will give first-year students a head start in their high school or college physics class
- The latest teaching techniques to ensure that you remember and retain what you read and practice in the book
Physics I For Dummies is proof that physics can fun, accessible, challenging, and rewarding, all at the same time! Whether you’re a high school or undergraduate student looking for a leg-up on basic physics concepts or you’re just interested in how our universe works, this book will help you understand the thermodynamic, electromagnetic, relativistic, and everything in between.
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About The Author
Dr. Steven Holzner has written more than 40 books about physics and programming. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Dr. Holzner received his PhD at Cornell.
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physics i for dummies
CHEAT SHEET
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 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.
Avogadro’s
In physics, absolute zero is considered the lower limit for the temperature of any system, and the third law of thermodynamics can be formulated in terms of this temperature. The third law of thermodynamics is pretty straightforward — it just says that you can’t reach absolute zero (0 kelvin, or about –273.15 degrees Celsius) through any process that uses a finite number of steps.
Physics
If you fire a projectile at an angle, you can use physics to calculate how far it will travel. When you calculate projectile motion, you need to separate out the horizontal and vertical components of the motion. This is because the force of gravity only acts on the projectile in the vertical direction, and the horizontal component of the trajectory’s velocity remains uniform.
Physics
If you know the radius of a circular track, you can use physics to calculate how fast an object needs to move in order to stay in contact with the track without falling when it reaches the top of the loop.
Maybe you’ve watched extreme sports on television and wondered how bikers or skateboarders can ride into a loop on a track and go upside down without falling to the ground.
Physics
In physics, average speed is the total distance you travel divided by the total time it takes. Speed is represented by the variable v, and average speed is sometimes written as
A bar over a variable means average in physics terms.
Say, for example, that you want to pound the pavement from New York City to Los Angeles to visit your uncle’s family, a distance of about 2,781 miles.
Physics
In physics, an object is in equilibrium when it has zero acceleration — when the net force acting on it is zero. The object doesn’t actually have to be at rest, as in the example below, which uses a pulley to suspend a sign — it can be going 1,000 miles per hour as long as the net force on it is zero and it isn’t accelerating.
In physics, you can calculate how much heat energy is required to raise an object of a certain mass by a certain temperature — all you need is the object’s specific heat.
At a given temperature, different materials can hold different amounts of thermal energy. For instance, if you warm up a potato, it can hold its heat longer (as your tongue can testify) than a lighter material such as cotton candy.
Physics
You can use physics to calculate how far an object will slide down an inclined surface, such as a ramp. For example, say you and your friends are pushing a refrigerator up a ramp onto a moving van, when suddenly your combined strength gives out and the refrigerator begins to plummet back down the 3.0-meter ramp.
Molecules have very little mass, but gases contain many, many molecules, and because they all have kinetic energy, the total kinetic energy can pile up pretty fast. Using physics, can you find how much total kinetic energy there is in a certain amount of gas? Yes! Each molecule has this average kinetic energy:
To figure the total kinetic energy, you multiply the average kinetic energy by the number of molecules you have, which is nNA, where n is the number of moles:
NAk equals R, the universal gas constant, so this equation becomes the following:
If you have 6.
Physics
In physics, objects can have both linear and rotational kinetic energy. This can occur when an object rolls down a ramp instead of sliding, as some of its gravitational potential energy goes into its linear kinetic energy, and some of it goes into its rotational kinetic energy.
A solid cylinder and a hollow cylinder ready to race down a ramp.
In physics, tangential acceleration is a measure of how the tangential velocity of a point at a certain radius changes with time. Tangential acceleration is just like linear acceleration, but it’s specific to the tangential direction, which is relevant to circular motion. You start with the magnitude of the angular acceleration,
which tells you how the speed of the object in the tangential direction is changing.
When an object moves in a circle, if you know the magnitude of the angular velocity, then you can use physics to calculate the tangential velocity of the object on the curve.At any point on a circle, you can pick two special directions: The direction that points directly away from the center of the circle (along the radius) is called the radial direction, and the direction that’s perpendicular to this is called the tangential direction.
Physics
In physics, how much torque you exert on an object depends on two things: the force you exert, F; and the lever arm. Also called the moment
arm, the lever arm is the perpendicular distance from the pivot point to the point at which you exert your force and is related to the distance from the axis, r, byis the angle between the force and a line from the axis to the point where the force is applied.
Physics
In physics, you can examine how much potential and kinetic energy is stored in a spring when you compress or stretch it. The work you do compressing or stretching the spring must go into the energy stored in the spring. That energy is called elastic potential energy and is equal to the force, F, times the distance, s:W = FsAs you stretch or compress a spring, the force varies, but it varies in a linear way (because in Hooke’s law, force is proportional to the displacement).
Physics
In physics, you can calculate the acceleration of an object in simple harmonic motion as it moves in a circle; all you need to know is the object’s path radius and angular velocity.
You can find the displacement of an object undergoing simple harmonic motion with the equation
and you can find the object’s velocity with the equation
But you have another factor to account for when describing an object in simple harmonic motion: its acceleration at any particular point.
In physics, density is the ratio of mass to volume. Any solid object that’s less dense than water floats. Density is an important property of a fluid because mass is continuously distributed throughout a fluid; the static forces and motions within the fluid depend on the concentration of mass (density) rather than the fluid’s overall mass.
Physics
In physics, when frictional forces are acting on a sloped surface such as a ramp, the angle of the ramp tilts the normal force at an angle. When you work out the frictional forces, you need to take this fact into account.
Normal force, N, is the force that pushes up against an object, perpendicular to the surface the object is resting on.
Physics
In physics, just as you can add two numbers to get a third number, you can add two vectors to get a resultant vector. To show that you’re adding two vectors, put the arrows together so that one arrow starts where the other arrow ends. The sum is a new arrow that starts at the base of the first arrow and ends at the head (pointy end) of the other.
Physics
An object with uniform circular motion travels in a circle with a constant speed. Outside a physics class, practical examples may be hard to come by, unless you see a race car driver on a perfectly circular track with his accelerator stuck, a clock with a seconds hand that’s in constant motion, or the moon orbiting the Earth.
Physics
In physics, the first law of thermodynamics deals with energy conservation. The law states that internal energy, heat, and work energy are conserved. The initial internal energy in a system, Ui, changes to a final internal energy, Uf, when heat, Q, is absorbed or released by the system and the system does work, W, on its surroundings (or the surroundings do work on the system), such that
The most confusing part about using this equation is figuring out which signs to use.
Physics
In physics, it’s important to know the difference between conservative and nonconservative forces. The work a conservative force does on an object is path-independent; the actual path taken by the object makes no difference. Fifty meters up in the air has the same gravitational potential energy whether you get there by taking the steps or by hopping on a Ferris wheel.
Physics
In physics, the first law of thermodynamics deals with energy conservation. One of the forms of energy involved is the internal energy that resides in the motion of the atoms and molecules (vibrations and random jostling). Another of the terms in this law is heat, which is a transfer of thermal energy. And finally, there is work, which is a transfer of mechanical energy; for example, work is done on a gas when it is compressed.
To look at gases on the molecular level, you need to know how many molecules you have in a certain sample. Physicists use a measurement called a mole to relate the mass of a sample to the number of molecules it contains, and they use Avogadro’s number to represent the number of atoms in one mole.
A mole (abbreviated mol) is the number of atoms in 12.
In physics, motion that takes place in the real world is often in two dimensions. As a result, you need to find both the distance and direction traveled to tell the whole story.
If you want to examine motion in two dimensions, you need two intersecting meter sticks (or number lines), called axes. You have a horizontal axis (the x-axis) and a vertical axis (the y-axis).
Physics
In physics, there is a difference between average speed and average velocity. Say, for example, that while you were driving in Ohio on a cross-country trip, you wanted to make a detour to visit your sister in Michigan after you dropped off a hitchhiker in Indiana.
A trip from Ohio to Michigan.
Your travel path may have looked like the straight lines in this figure — first 80 miles to Indiana and then 30 miles to Michigan.
Physics
In a physics equation, given initial velocity, time, and acceleration, you can find an object’s displacement. Here’s an example: There you are, the Tour de France hero, ready to give a demonstration of your bicycling skills. There will be a time trial of 8.0 seconds. Your initial speed is 6.0 meters/second, and when the whistle blows, you accelerate at 2.
Physics
You can use physics to determine the force of gravity on an object that moves along an inclined plane. You can break the weight of the object down into components that are parallel to and perpendicular to the plane. The component perpendicular to the plane presses the object into the surface of the plane. The component of the weight that acts along the plane accelerates the object down the plane.
Physics
In physics, you can calculate the velocity of an object as it moves along an inclined plane as long as you know the object’s initial velocity, displacement, and acceleration. Just plug this information into the following equation:
The figure shows an example of a cart moving down a ramp. You can use the formula with the information in the figure to find the cart’s final velocity.
Physics
In physics, the second law of thermodynamics says that heat flows naturally from an object at a higher temperature to an object at a lower temperature, and heat doesn’t flow in the opposite direction of its own accord.
The law is certainly borne out in everyday observation — when was the last time you noticed an object getting colder than its surroundings unless another object was doing some kind of work?
In physics, because of Newton’s third law, whenever you apply a force to an object, say, by pulling it, the object applies an equal and opposite force on you. Here’s an example that lets you work out how much force you’re subject to when you drag something along. For fantasy physics purposes, say that a hockey game ends, and you get the job of dragging a 31-slug hockey puck off the rink.
If the angular velocity vector points out of the plane of rotation on a wheel, you can use physics to determine what happens when the angular velocity changes — when the wheel speeds up or slows down. A change in velocity signifies the presence of angular acceleration. Like angular velocity,
angular acceleration,
is a vector, meaning it has a magnitude and a direction.
Physics
In physics, when an object travels in uniform circular motion, its speed is constant, which means that the magnitude of the object’s velocity doesn’t change. Therefore, acceleration can have no component in the same direction as the velocity; if it did, the velocity’s magnitude would change.
Velocity constantly changes direction, but not magnitude, when an object is in circular motion.
Physics
According to the laws of physics, in order to keep an object moving in circular motion, its velocity constantly changes direction. Whenever velocity changes, you have acceleration. Specifically, you have centripetal acceleration — the acceleration needed to keep the object moving in circular motion. The centripetal acceleration always points inward along the radius toward the center of the circle.
You know that pressure increases the farther you go underwater, but by how much? As a physicist, you can put some numbers in and get numerical results out. Just what pressure would you expect for a given depth?
A cube of water has different pressures on the top and bottom faces.
Say that you’re underwater and you’re considering the imaginary cube of water you see in the figure.
Nuclear fusion is essentially the opposite of nuclear fission. In fission, a heavy nucleus is split into smaller nuclei. With fusion, lighter nuclei are fused into a heavier nucleus. ©Uday / Adobe StockThe fusion process is the reaction that powers the sun. On the sun, in a series of nuclear reactions, four isotopes of hydrogen-1 are fused into a helium-4 with the release of a tremendous amount of energy.
You can use physics to calculate how friction affects rotational equilibrium. For example, say a hardware store owner comes to you for help with a problem. A clerk has climbed near the top of a ladder to hang a sign for the company’s upcoming sale. The owner doesn’t want the ladder to slip — lawsuits, he explains — so he asks you whether the ladder is going to fall.
According to the laws of physics, the force of friction, Ffriction, always acts to oppose the force you apply when you try to move an object. Friction is proportional to the force with which an object pushes against the surface you’re trying to slide it along.
The forces acting on a bar of gold.
As you can see in the figure, the force with which the gold ingot presses against the ground in this situation is just its weight, or mg.
Friction is an important concept in physics. It’s the force that hinders two materials from sliding past each other. Friction is essential for everyday living. Imagine a world without friction: no way to drive a car on the road, no way to walk on pavement, no way to pick up that tasty sandwich. Friction may seem like an enemy to the hearty physics follower, but it’s also your friend.
Physics
You can use physics to determine how gravity affects the acceleration of an object as it moves along an inclined plane. When you’re on or near the surface of the Earth, the pull of gravity is constant. It’s a constant force directed straight down with magnitude equal to mg, where m is the mass of the object being pulled by gravity, and g is the magnitude of the acceleration due to gravity:
g = 9.
In physics terms, impulse tells you how much the momentum of an object will change when a force is applied for a certain amount of time. Say, for example, that you’re shooting pool. Instinctively, you know how hard to tap each ball to get the results you want. The nine ball in the corner pocket? No problem — tap it and there it goes.
In physics, when two objects are in contact with each other and are also moving, you get what’s called kinetic friction. The force due to kinetic friction has its own coefficient, called the coefficient of kinetic friction,
Say that a gold ingot with a mass of 1,000 kilograms has a coefficient of kinetic friction of 0.
Physics
Mass, velocity, and radius are all related when you calculate centripetal force. In fact, when you know this information, you can use physics equations to calculate how much force is required to keep an object moving in a circle at the same speed.
You always have to accelerate an object toward the center of the circle to keep it moving in circular motion.
Physics
In physics, the sign of an object’s acceleration depends on its direction. If you slow down to a complete stop in a car, for example, and your original velocity was positive and your final velocity was 0, so your acceleration is negative because a positive velocity came down to 0. However, if you slow down to a complete stop in a car and your original velocity was negative and your final velocity was 0, then your acceleration would be positive because a negative velocity increased to 0.
Physics
In physics, when the net force acting on an object is elastic (such as on a vertical or horizontal spring), the object can undergo a simple oscillatory motion called simple harmonic motion.
An oscillatory motion is one that undergoes repeated cycles.
The force that tries to restore the object to its resting position is proportional to the displacement of the object.
When two surfaces aren’t moving but are pressing together, they have the chance to interlock on the microscopic level. When this happens, it creates static friction. In physics, the coefficient of static friction is
You experience static friction when you push something that starts at rest. This is the friction that you have to overcome to get something to slide.
The force of friction comes from the surface characteristics of materials that come into contact. How does physics predict those characteristics theoretically? It doesn’t. Detailed knowledge of surfaces that come into contact is something people have to measure themselves (or they can check a table of information after someone else has done all the work).
In physics, when you rotate an extended object, such as a rod, disk, or cube, which has its mass distributed through space, you have to take into account where the force is applied. Enter torque. Torque is a measure of the ability of a force to cause rotation. In physics terms, the torque exerted on an object depends on the force itself (its magnitude and direction) and where you exert the force.
Physics
In physics, the principle of conservation of momentum states that when you have an isolated system with no external forces, the initial total momentum of objects before a collision equals the final total momentum of the objects after the collision. In other words,
You may have a hard time dealing with the physics of impulses because of the short times and the irregular forces.
You can use the components of vectors to add vectors together using a grid. Doing so reduces the problem of adding vectors to a simple combination of adding numbers together, which is very useful when you solve physics problems.
Use vector coordinates to make handling vectors easy.
Take a look at the vector addition problem A + B in the above figure.
In physics terms, acceleration, a, is the amount by which your velocity changes in a given amount of time. Given the initial and final velocities, vi and vf, and the initial and final times over which your speed changes, ti and tf, you can write the equation like this: In terms of units, the equation looks like this:Distance per time squared?
Picture a small child on a spinning playground ride, such as a merry-go-round, and she’s yelling that she wants to get off. You have to stop the spinning ride, but it’s going to take some effort. Why? Because it has angular momentum. In physics, you can calculate angular momentum in the same way that you calculate linear momentum — just substitute moment of inertia for mass, and angular velocity for velocity.
Physics
In physics, you can apply Newton’s first and second laws to calculate the centripetal acceleration of an orbiting object. Newton’s first law says that when there are no net forces, an object in motion will continue to move uniformly in a straight line. For an object to move in a circle, a force has to cause the change in direction — this force is called the centripetal force.
Physics
In physics, if you want to find the change in an object’s kinetic energy, you have to consider only the work done by the net force acting on the object. In other words, you convert only the work done by the net force into kinetic energy.
For example, when you play tug-of-war against your equally strong friends, you pull against each other but nothing moves.
Physics
Displacement is the distance between an object’s initial position and its final position and is usually measured or defined along a straight line. Since this is a calculation that measures distance, the standard unit is the meter (m).
How to find displacement
In physics, you find displacement by calculating the distance between an object’s initial position and its final position.
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.
Physics
In physics, you can use the impulse-momentum theorem to calculate force based on impulse and momentum. For example, you can relate the impulse with which you hit an object to its consequent change in momentum. According to the theorem:
How about using the equation the next time you hit a pool ball? You line up the shot that the game depends on.
Physics
You can use the Stefan-Boltzmann constant to measure the amount of heat that is emitted by a blackbody. Physicists have determined that a blackbody is an object that absorbs 100 percent of the radiant energy striking it, and if it’s in equilibrium with its surroundings, it emits all the radiant energy as well.
Physics
When you launch a projectile into the air, you can use physics to determine how long it will remain airborne. Because the force of gravity only acts downward — that is, in the vertical direction — you can treat the vertical and horizontal components of the flight path separately. As a result, you can calculate things like the time the projectile will be airborne before it strikes the ground.
Physics
In physics, you can calculate power based on force and speed. Because work equals force times distance, you can write the equation for power the following way, assuming that the force acts along the direction of travel:
where s is the distance traveled. However, the object’s speed, v, is just s divided by t, so the equation breaks down to
That’s an interesting result — power equals force times speed?
Sometimes, it isn’t just the amount of work you do but the rate at which you do work that’s important. In physics, the concept of power gives you an idea of how much work you can expect in a certain amount of time.
Power in physics is the amount of work done divided by the time it takes, or the rate of work. Here’s what that looks like in equation form:
Assume you have two speedboats of equal mass, and you want to know which one will get you up to a speed of 120 miles per hour faster.
You can use physics to calculate the amount of force needed to offset torque and maintain rotational equilibrium. For example, say the manager at the hardware store you work at asks you to help hang a flag over the top of the store. The store is extra-proud of the flag because it’s an extra-big one (to check it out, see the figure).
If you put a lot of work into rotating an object, the object starts spinning. And when an object is spinning, all its pieces are moving, which tells a physicist that it has kinetic energy. For spinning objects, you have to convert from the linear concept of kinetic energy to the rotational concept of kinetic energy.
In physics, one major player in the linear-force game is work; in equation form, work equals force times distance, or W = Fs. Work has a rotational analog. To relate a linear force acting for a certain distance with the idea of rotational work, you relate force to torque (its angular equivalent) and distance to angle.
Physics
In a physics equation, given a constant acceleration and the change in velocity of an object, you can figure out both the time involved and the distance traveled. For instance, imagine you’re a drag racer. Your acceleration is 26.6 meters per second2, and your final speed is 146.3 meters per second. Now find the total distance traveled.
Physics
Using principles of physics, if you push a partially open door in the same direction as you push a closed door, you create a different torque because of the non-right angle between your force and the door.
You produce a useful angle of a lever arm by exerting force in the proper direction.
Take a look at diagram A in the figure to see a person obstinately trying to open a door by pushing along the door toward the hinge.
Physics
When a collision between two objects is elastic, kinetic energy is conserved. In physics, the most basic way to look at elastic collisions is to examine how the collisions work along a straight line. If you run your bumper car into a friend’s bumper car along a straight line, you bounce off and kinetic energy is conserved.
Physics
If you apply force at an angle instead of parallel to the direction of motion, you have to supply more force to perform the same amount of work. You can use physics to calculate how much work is required, for example, when you drag an object using a tow rope, as the figure shows.
More force is required to do the same amount of work if you pull at a larger angle.
Physics
Using physics, you can calculate the work required to move an object over a given distance. Motion is needed for work to be done. For work to be done, a net force has to move an object through a displacement. Work is a product of force and displacement.
To do work on this gold ingot, you have to push with enough force to overcome friction and cause the ingot to move.
Physics
In physics, if a force on an object has a component in the same direction as the motion, the work that force does on the object is positive. If a force on an object has a component in the opposite direction to the motion, the work done by that force on the object is negative.
Consider this example: You’ve just gone out and bought the biggest television your house can handle.
Physics
Using physics, you can calculate what happens when you swerve. For example, you may be in a car or on a walk when you suddenly accelerate in a particular direction. In this case, just like displacement and velocity, acceleration, a, is a vector.
Assume that you’ve just managed to hit a groundball in a softball game and you’re running to first base.
Physics
In space, gravity supplies the centripetal force that causes satellites (like the moon) to orbit larger bodies (like the Earth). Thanks to physics, if you know the mass and altitude of a satellite in orbit around the Earth, you can calculate how quickly it needs to travel to maintain that orbit.
A particular satellite can have only one speed when in orbit around a particular body at a given distance because the force of gravity doesn’t change.
Physics
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 = –kxThe minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring.
Physics
In physics, velocity, which is the rate of change of position (or speed in a particular direction), is a vector. Imagine that you just hit a ground ball on the baseball diamond and you’re running along the first-base line, or the s vector, 90 feet at a 45-degree angle to the positive x-axis. But as you run, it occurs to you to ask, “Will my velocity enable me to evade the first baseman?
Physics
In physics, you can apply Hooke’s law, along with the concept of simple harmonic motion, to find the angular frequency of a mass on a spring. And because you can relate angular frequency and the mass on the spring, you can find the displacement, velocity, and acceleration of the mass.Hooke’s law says thatF = –kxwhere F is the force exerted by the spring, k is the spring constant, and x is displacement from equilibrium.
Physics
In physics, displacement, which is a change in position, has a magnitude and a direction associated with it. When you have a change of position in a particular direction and of a particular distance, these are given by the magnitude and direction of the displacement vector.
Instead of writing displacement as s, you should write it as s, a vector (if you’re writing on paper, you can put an arrow over the s to signify its vector status).
Physics
Starting with the physics equation for the force of gravity, you can plug in the mass and radius of the Earth to calculate the force of gravity near the surface of the Earth.
The equation for the force of gravity is
and it holds true no matter how far apart two masses are.
The gravitational force between a mass and the Earth is the object’s weight.
Physics
You can use physics to calculate the kinetic energy of an object. When you start pushing or pulling a stationary object with a constant force, it starts to move if the force you exert is greater than the net forces resisting the movement, such as friction and gravity. If the object starts to move at some speed, it will acquire kinetic energy.
Physics
In physics, latent heat is the heat per kilogram that you have to add or remove to make an object change its state; in other words, latent heat is the heat needed to make a phase change happen. Its units are joules per kilogram (J/kg) in the MKS (meter-kilogram-second) system.
Physicists recognize three types of latent heat, corresponding to the changes of phase between solid, liquid, and gas:
The latent heat of fusion, Lf.
Physics
According to the laws of physics, when a projectile flies into the air, its trajectory is shaped by Earth’s gravitational pull. Because the force of gravity only acts downward — that is, in the vertical direction — you can treat the vertical and horizontal components separately. As a result, you can calculate how far the projectile can travel straight up in the air.
Physics
In physics, when you calculate an object’s moment of inertia, you need to consider not only the mass of the object but also how the mass is distributed. For example, if two disks have the same mass but one has all the mass around the rim and the other is solid, then the disks would have different moments of inertia.
Physics
When a satellite travels in a geosynchronous orbit around the Earth, it needs to travel at a certain orbiting radius and period to maintain this orbit. Because the radius and period are related, you can use physics to calculate one if you know the other.
The period of a satellite is the time it takes it to make one full orbit around an object.
Physics
In physics, a substance’s specific gravity is the ratio of that substance’s density to the density of water at 4 degrees Celsius. Because the density of water at 4 degrees Celsius is 1,000 kg/m3, that ratio is easy to find. For example, the density of gold is 19,300 kg/m3, so its specific gravity is the following:
Specific gravity has no units because it’s a ratio of density divided by density, so all units cancel out.
Physics
You can use physics to calculate the amount of torque needed to accelerate (or decelerate) the speed of a spinning disc. Without the ability to change the speed of a disc, it would be impossible for you to watch a movie on your DVD player.
Here’s an interesting fact about DVD players: They actually change the angular speed of the DVD to keep the section of the DVD under the laser head moving at constant linear speed.
Physics
In physics, when you go from linear motion to rotational motion, you need to change the equations that you use to calculate your results. Here are the angular equivalents (or analogs) for the linear motion equations:
In all these equations, t stands for time,
f means final, and i means initial. In the linear equations, v is velocity, s is displacement, and a is acceleration.
Using physics, you can convert linear force to angular torque. For example, say that you’re whirling a ball in a circle on the end of a string, as shown in the figure. You apply a tangential force (along the circle) to the ball, making it speed up (keep in mind that this force is not directed toward the center of the circle, as when you have a centripetal force).
Physics
When an object falls, its gravitational potential energy is changed to kinetic energy. You can use this relationship to calculate the speed of the object’s descent. Gravitational potential energy for a mass m at height h near the surface of the Earth is mgh more than the potential energy would be at height 0. (It’s up to you where you choose height 0.
Physics
In physics, collisions can be defined as either elastic or inelastic. When bodies collide in the real world, they sometimes squash and deform to some degree. The energy to perform the deformation comes from the objects’ original kinetic energy. In other cases, friction turns some of the kinetic energy into heat.
Physics
In physics, when a wheel is spinning, it has not only an angular speed but also a direction. Here’s what the angular velocity vector tells you:
The size of the angular velocity vector tells you the angular speed.
The direction of the vector tells you the axis of the rotation, as well as whether the rotation is clockwise or counterclockwise.
In physics, when you break a vector into its parts, those parts are called its components. For example, in the vector (4, 1), the x-axis (horizontal) component is 4, and the y-axis (vertical) component is 1. Typically, a physics problem gives you an angle and a magnitude to define a vector; you have to find the components yourself using a little trigonometry.
Physics
In physics, sometimes you have to find the angle and magnitude of a vector rather than the components. To find the magnitude, you use the Pythagorean theorem. And to find
you use the inverse tangent function (or inverse sine or cosine).
For example, assume you’re looking for a hotel that’s 20 miles due east and then 20 miles due north.
Physics
You can use the principle of conservation of momentum to measure characteristics of motion such as velocity. Say, for example, that you’re out on a physics expedition and you happen to pass by a frozen lake where a hockey game is taking place. You measure the speed of one player as 11.0 meters per second just as he collides, rather brutally for a pick-up game, with another player initially at rest.
Physics
In physics, the principle of conservation of momentum comes in handy when you can’t measure velocity with a simple stopwatch. Say, for example, that you accept a consulting job from an ammunition manufacturer that wants to measure the muzzle velocity of its new bullets. No employee has been able to measure the velocity yet, because no stopwatch is fast enough.
Physics
When you talk about the expansion of a solid in any one dimension under the influence of heat, you’re talking about linear expansion. Thanks to physics, you can measure how much a solid will expand based on how much its temperature changes.
The figure shows an image of this phenomenon.
Linear expansion usually takes place when you apply heat to solids.
Physics
Thanks to physics, you know that when you increase the temperature of a solid or liquid, its volume will expand. If a solid or liquid undergoes a small temperature change of just a few degrees, you can say that its volume will change in a way proportionate to the temperature change.
As long as the temperature differences involved are small, the fraction by which a solid expands,
is proportionalto the change in temperature,
With volume expansion, the constant involved is called the coefficient of volume expansion.
You don’t come across vector subtraction very often in physics problems, but it does pop up. To subtract two vectors, you put their feet (or tails, the non-pointy parts) together; then draw the resultant vector, which is the difference of the two vectors, from the head of the vector you’re subtracting to the head of the vector you’re subtracting it from.
Physics
In physics, when you have a process where no heat flows from or to the system, it’s called an adiabatic process. The first figure shows an example of an adiabatic process: a cylinder surrounded by an insulating material. The insulation prevents heat from flowing into or out of the system, so any change in the system is adiabatic.
Physics
In physics, when you have a process where the pressure stays constant, it’s called isobaric (baric means “pressure”). The first figure shows an example of an isobaric system, where a cylinder with a piston is being lifted by a quantity of gas as the gas gets hotter. The volume of the gas is changing, but the weighted piston keeps the pressure constant.
Physics
In physics, when the temperature remains constant as other quantities change, you have what is called an isothermal system. The remarkable apparatus in the first figure shows an example of an isothermal system.
An isothermal system maintains a constant temperature amidst other changes.
It’s specially designed to keep the temperature of the enclosed gas constant, even as the piston rises.
Physics
In physics, when the pressure in a system changes but the volume is constant, you have what is called an isochoric process. An example of this would be a simple closed container, which can’t change its volume.
An isochoric system features a constant volume as other quantities vary.
In the first figure, someone has neglectfully tossed a spray can onto a fire.
Physics
In physics, if a fluid is flowing at a certain speed at a certain point in a system of pipes, you can predict what its speed will be at another point by using the equation of continuity. Because the mass of the fluid is neither created nor destroyed, if mass moves away from one place at a certain rate, it must therefore move to the neighboring place at the same rate.
Physics
In physics, to take angles (or direction) into account when measuring force, you need to do a little vector addition. Take a look at the following figure. Here, the mass m isn’t moving, and you’re applying a force F to hold it stationary. Here’s the question: What force is the pulley’s support exerting, and in which direction, to keep the pulley where it is?
Physics
Thanks to the work of a 19th-century engineer named Sadi Carnot, you can apply the law of conservation of energy to measure the heat efficiency of an engine.
Given the amount of work a heat engine does and its efficiency, you can calculate how much heat goes in and how much comes out (along with a little help from the law of conservation of energy, which ties work, heat in, and heat out together).
Physics
Different materials (such as glass, steel, copper, and bubble gum) conduct heat at different rates, so the thermal conductivity constant depends on the material in question. Lucky for you, physicists have measured the constants for various materials already. This table shows some of these values.
Here’s an example of how conductivity affects heat transfer.
Physics
Newton’s first law says that an object remains in uniform motion unless acted on by a net force. When a net force is applied, the object accelerates. Newton’s second law details the relationship between net force, the mass, and the acceleration:
The acceleration of an object is in the direction of the net force.
Newton’s third law of motion is famous, especially in wrestling and drivers’ ed circles, but you may not recognize it in all its physics glory: “Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.”
The more popular version of this, which you’ve probably heard many times, is “For every action, there’s an equal and opposite reaction.
In physics, Newton’s laws explain what happens with forces and motion, and his first law states, “An object continues in a state of rest, or in a state of motion at a constant velocity along a straight line, unless compelled to change that state by a net force.” Translation? If you don’t apply a net, or unbalanced, force to an object at rest or in motion, it will stay at rest or in that same motion along a straight line.
Sir Isaac Newton came up with one of the heavyweight laws in physics for you: the law of universal gravitation. This law says that every mass exerts an attractive force on every other mass. If the two masses are m1 and m2 and the distance between them is r, the magnitude of the force (F) is
This equation allows you to figure the gravitational force between any two masses.
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.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.
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.
Physics
Thanks to the principle of conservation of mechanical energy, you can use physics to determine the final height of a moving object. At this very moment, for example, suppose Tarzan is swinging on a vine over a crocodile-infested river at a speed of 13.0 meters/second. He needs to reach the opposite river bank 9.
Physics
In physics, you can use the ideal gas law to predict the pressure of an ideal gas if you know how much gas you have, its temperature, and the volume you’ve enclosed it in.
For an ideal gas (at constant volume), pressure is directly proportional to temperature.
Here’s how the various factors affect pressure:
Temperature.
Physics
In physics, you can connect the impulse you give to an object — like striking a pool ball with a cue — with the object’s change in momentum; all you need is a little algebra and a process called the impulse-momentum theorem.
What makes the connection easy is that you can play with the equations for impulse and momentum to simplify them so you can relate the two topics.
In physics, just as you can use formulas to calculate linear velocity, acceleration, displacement, and motion, you can also use equivalent formulas for angular (rotational) movement.
You can think of the angle, theta, in rotational motion just as you think of the displacement, s, in linear motion. This is great, because it means you have an angular counterpart for many of the linear motion equations.
In physics, a handy way of visualizing the flow of a fluid is through streamlines. You draw a fluid’s streamline so that a tangent to the streamline at any point is parallel to the fluid’s velocity at that point. In other words, a streamline follows the fluid flow.
A streamline shows the directions of flow.
You can see an example in the figure, where the streamline is the darker line in the middle of the fluid flow.
To keep like measurements together, physicists and mathematicians have grouped them into measurement systems. The most common measurement system you see in introductory physics is the meter-kilogram-second (MKS) system, referred to as SI (short for Système International d’Unités, the International System of Units), but you may also come across the foot-pound-second (FPS) system.
In physics, fluid flow has all kinds of aspects — steady or unsteady, compressible or incompressible, viscous or nonviscous, and rotational or irrotational, to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Note that fluid flow can get very complex when it becomes turbulent.
Physics
In physics, if you know the kinetic and potential energies that act on an object, then you can calculate the mechanical energy of the object. Imagine a roller coaster car traveling along a straight stretch of track. The car has mechanical energy because of its motion: kinetic energy. Imagine that the track has a hill and that the car has just enough energy to get to the top before it descends the other side, back down to a straight and level track (see the figure).
Physics
In physics, tracking simple harmonic motion can require time and patience when you have to figure out how the motion of an object changes over time.
Imagine that one day you come up with a brilliant idea for an experimental apparatus. You decide to shine a spotlight on a ball bouncing on a spring, casting a shadow on a moving piece of photographic film.
Physics
Thanks to physics, we know that convection can be either natural, where heat rises on its own, or forced, where you control the movement of the heat.
You may have heard the maxim “heat rises,” which is all about convection. However, a more accurate statement is that “hot fluid rises.” In substances where convection is free to take place — that is, in gases and liquids — hotter material naturally ends up on top and cooler material ends up on the bottom because of the higher buoyancy of the hotter material.
Radiation is one way to transfer heat. You experience radiation personally whenever you get out of the shower soaking wet in the dead of winter and bask in the warmth of the heat lamp in your bathroom. Why? Because of a little physics, of course. The heat lamp, which you see in the figure, beams out heat to you and keeps you warm through radiation.
Physics
In physics, Archimedes’s principle says that any fluid exerts a buoyant force on an object wholly or partially submerged in it, and the magnitude of the buoyant force equals the weight of the fluid displaced by the object. An object that’s less dense than water floats because the water it displaces weighs more than the object does.
Physics
Conduction transfers heat through material directly, through contact. Thanks to physics, we know that conduction is affected by temperature difference, the area of conduction, the distance the heat must travel, and the amount of time that passes.
Take a look at the metal pot in the figure and its metal handle; the pot has been boiling for 15 minutes.
Physics
In physics calculations, acceleration — just like displacement and velocity — can be positive or negative. The sign of the acceleration tells you whether you’re speeding up or slowing down (depending on which direction you’re traveling).
For example, say that you’re driving at 75 miles per hour, and you see those flashing red lights in the rearview mirror.
Physics
In physics, Pascal’s principle says that given a fluid in a totally enclosed system, a change in pressure at one point in the fluid is transmitted to all points in the fluid, as well as to the enclosing walls. In other words, if you have a fluid enclosed in a pipe (with no air bubbles) and change the pressure in the fluid at one end of the pipe, the pressure changes all throughout the pipe to match.
Physics
Because Bernoulli’s equation relates pressure, fluid speed, and height, you can use this important physics equation to find the difference in fluid pressure between two points. All you need to know is the fluid’s speed and height at those two points.
Bernoulli’s equation relates a moving fluid’s pressure, density, speed, and height from Point 1 to Point 2 in this way:
Here are what the variables stand for in this equation (where the subscripts indicate whether you’re talking about Point 1 or Point 2):
The equation assumes that you’re working with the steady flow of an incompressible, irrotational, nonviscous fluid.
Physics
Thanks to the principle of conservation of mechanical energy, you can use physics to calculate the final speed of an object that starts from rest.
“Serving as a roller coaster test pilot is a tough gig,” you say as you strap yourself into the Physics Park’s new Bullet Blaster III coaster. “But someone has to do it.
Physics
In physics, you can use Boyle’s and Charles’s laws to express the ideal gas law in different ways. For example, you can express the relationship between the pressure and volume of an ideal gas before and after one of those quantities changes at a constant temperature like this:
PfVf = PiVi
This equation, called Boyle’s law, says that all other factors being the same, the product of pressure and volume (PV) will be conserved.
Physics
In physics, no force can be exerted without an equal and opposite force (even if some of that opposing force comes from making an object accelerate). A rope and pulley can act together to change the direction of the force you apply, but not for free. In order to change the direction of your force from –F (that is, downward) to +F (upward on the mass), the pulley’s support has to respond with a force of 2F.
Physics
In physics, you can examine certain properties of molecules of an ideal gas as they zip around. For instance, you can calculate the average kinetic energy (and speed) of each molecule with a very simple equation:
where k is Boltzmann’s constant,
and T is the temperature in kelvins. And because you can determine the mass of each molecule if you know which gas you’re dealing with, you can figure out the molecules’ speeds at various temperatures.
Physics
In physics, you can apply the zeroth law of thermodynamics to compare the temperatures of multiple objects. Two objects are in thermal equilibrium if heat can pass between them but no heat is actually doing so. For example, if you and the swimming pool you’re in are at the same temperature, no heat is flowing from you to it or from it to you (although the possibility is there).
In physics, when you have a vector, you have to keep in mind two quantities: its direction and its magnitude. Quantities that have only a magnitude are called scalars. If you give a scalar magnitude a direction, you create a vector.
Visually, you see vectors drawn as arrows, which is perfect because an arrow has both a clear direction and a clear magnitude (the length of the arrow).
Physics
Thanks to physics, we know that phase changes occur when materials change state, going from liquid to solid (as when water freezes), solid to liquid (as when rocks melt into lava), liquid to gas (as when you boil water for tea), and so on. When the material in question changes to a new state — liquid, solid, or gas (you can also factor in a fourth state: plasma, a superheated gas-like state) — some heat goes into or comes out of the process without changing the temperature.
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