Physics Articles

Article / Updated 10-06-2022

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 9.0 meters above his present position in order to be safe. Can he swing it? The principle of conservation of mechanical energy gives you the answer: At Tarzan’s maximum height at the end of the swing, his speed, v2, will be 0 meters/second, and assuming h1 = 0 meters — meaning that he started swinging from the same height as the tree branch he's swinging to — you can relate h2 to v1 like this: Solving for h2, this means that Tarzan will come up 0.4 meters short of the 9.0 meters he needs to be safe, so he needs some help.

Article / Updated 09-27-2022

Many people find Physics to be a difficult subject to approach. Well now, you have some tools to help you along the way. This handy list of physics equations organized by topic contains the most common equations you’ll run across:

Article / Updated 08-17-2022

General relativity was Einstein’s theory of gravity, published in 1915, which extended special relativity to take into account non-inertial frames of reference — areas that are accelerating with respect to each other. General relativity takes the form of field equations, describing the curvature of space-time and the distribution of matter throughout space-time. The effects of matter and space-time on each other are what we perceive as gravity. Einstein immediately realized that his theory of special relativity worked only when an object moved in a straight line at a constant speed. What about when one of the spaceships accelerated or traveled in a curve? Einstein came to realize the principle of equivalence, and it states that an accelerated system is completely physically equivalent to a system inside a gravitational field. As Einstein later related the discovery, he was sitting in a chair thinking about the problem when he realized that if someone fell from the roof of a house, he wouldn’t feel his own weight. This suddenly gave him an understanding of the equivalence principle. As with most of Einstein’s major insights, he introduced the idea as a thought experiment. If a group of scientists were in an accelerating spaceship and performed a series of experiments, they would get exactly the same results as if sitting still on a planet whose gravity provided that same acceleration, as shown in this figure. Einstein’s brilliance was that after he realized an idea applied to reality, he applied it uniformly to every physics situation he could think of. For example, if a beam of light entered an accelerating spaceship, then the beam would appear to curve slightly, as in the left picture of the following figure. The beam is trying to go straight, but the ship is accelerating, so the path, as viewed inside the ship, would be a curve. By the principle of equivalence, this meant that gravity should also bend light, as shown in the right picture of the figure above. When Einstein first realized this in 1907, he had no way to calculate the effect, other than to predict that it would probably be very small. Ultimately, though, this exact effect would be the one used to give general relativity its strongest support.

Article / Updated 08-17-2022

General relativity was Einstein’s theory of gravity, published in 1915, which extended special relativity to take into account non-inertial frames of reference — areas that are accelerating with respect to each other. General relativity takes the form of field equations, describing the curvature of space-time and the distribution of matter throughout space-time. The effects of matter and space-time on each other are what we perceive as gravity. The theory of the space-time continuum already existed, but under general relativity Einstein was able to describe gravity as the bending of space-time geometry. Einstein defined a set of field equations, which represented the way that gravity behaved in response to matter in space-time. These field equations could be used to represent the geometry of space-time that was at the heart of the theory of general relativity. As Einstein developed his general theory of relativity, he had to refine the accepted notion of the space-time continuum into a more precise mathematical framework. He also introduced another principle, the principle of covariance. This principle states that the laws of physics must take the same form in all coordinate systems. In other words, all space-time coordinates are treated the same by the laws of physics — in the form of Einstein’s field equations. This is similar to the relativity principle, which states that the laws of physics are the same for all observers moving at constant speeds. In fact, after general relativity was developed, it was clear that the principles of special relativity were a special case. Einstein’s basic principle was that no matter where you are — Toledo, Mount Everest, Jupiter, or the Andromeda galaxy — the same laws apply. This time, though, the laws were the field equations, and your motion could very definitely impact what solutions came out of the field equations. Applying the principle of covariance meant that the space-time coordinates in a gravitational field had to work exactly the same way as the space-time coordinates on a spaceship that was accelerating. If you’re accelerating through empty space (where the space-time field is flat, as in the left picture of this figure), the geometry of space-time would appear to curve. This meant that if there’s an object with mass generating a gravitational field, it had to curve the space-time field as well (as shown in the right picture of the figure). Without matter, space-time is flat (left), but it curves when matter is present (right). In other words, Einstein had succeeded in explaining the Newtonian mystery of where gravity came from! Gravity resulted from massive objects bending space-time geometry itself. Because space-time curved, the objects moving through space would follow the “straightest” path along the curve, which explains the motion of the planets. They follow a curved path around the sun because the sun bends space-time around it. Again, you can think of this by analogy. If you’re flying by plane on Earth, you follow a path that curves around the Earth. In fact, if you take a flat map and draw a straight line between the start and end points of a trip, that would not be the shortest path to follow. The shortest path is actually the one formed by a “great circle” that you’d get if you cut the Earth directly in half, with both points along the outside of the cut. Traveling from New York City to northern Australia involves flying up along southern Canada and Alaska — nowhere close to a straight line on the flat maps we’re used to. Similarly, the planets in the solar system follow the shortest paths — those that require the least amount of energy — and that results in the motion we observe. In 1911, Einstein had done enough work on general relativity to predict how much the light should curve in this situation, which should be visible to astronomers during an eclipse. When he published his complete theory of general relativity in 1915, Einstein had corrected a couple of errors and in 1919, an expedition set out to observe the deflection of light by the sun during an eclipse, in to the west African island of Principe. The expedition leader was British astronomer Arthur Eddington, a strong supporter of Einstein. Eddington returned to England with the pictures he needed, and his calculations showed that the deflection of light precisely matched Einstein’s predictions. General relativity had made a prediction that matched observation. Albert Einstein had successfully created a theory that explained the gravitational forces of the universe and had done so by applying a handful of basic principles. To the degree possible, the work had been confirmed, and most of the physics world agreed with it. Almost overnight, Einstein’s name became world famous. In 1921, Einstein traveled through the United States to a media circus that probably wasn’t matched until the Beatlemania of the 1960s.

Cheat Sheet / Updated 06-30-2022

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.

Cheat Sheet / Updated 06-28-2022

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.

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.

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.

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.

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.