A "C"avalcade of Physics Vocabulary Quiz

Answer: Take the average of the objects' positions, weighted by their masses.

The center of mass of a group of objects is a point located at the mass-weighted average position of those objects. It's very useful in determining the motion of the system, which can often be very complicated (think, for example, of buckshot fired from a shotgun). Instead of individually calculating the momentum of each object, you can find the momentum of the system by multiplying its total mass by the velocity of the center of mass -- only one calculation! Similarly, the total force on the system can be calculated from the total mass and the center of mass's acceleration.

We can also calculate the center of mass of a continuous system -- such as a sports car or a figure skater -- using an integral to calculate the average, rather than a sum. (An integral allows you to add up infinitesimally small pieces.) An athlete's center of mass changes depending on his or her posture, and need not be located within the body at all -- making possible maneuvers like the Fosbury Flop. High jumpers can thus clear the bar without ever bringing their centers of mass above it, simply by bending their bodies to keep those centers low!

Answer: The charge of a proton

Charge is quantized, which means that it only comes in certain allowed values -- namely multiples of the proton charge. (An electron has negative one times the proton charge; neutrons and neutrinos have zero times the proton charge.) This realization was one of numerous world-changing physics discoveries of the twentieth century; it is not coincidental that the word "quantized" resembles the phrase "quantum mechanics."

Quarks, the tiny particles that make up protons and neutrons, carry charge in units of 2/3 the proton charge (e.g. the up quark) and of 1/3 the proton charge (e.g. the down quark). However, quarks cannot be observed by themselves in nature. They obey a rule called "confinement": they can never appear without the company of other quarks, in "composite" particles called hadrons. Quarks cannot even be isolated as free particles in the lab, although with the right tools you can look at an individual quark inside a hadron.

Answer: The speed of light

Clocking in at about 300 million meters per second, the speed of light in a vacuum shows up everywhere. Maxwell's equations, which sum up all of classical electrodynamics in only four lines, show that traveling electromagnetic waves must move at the speed of light. This insight not only changed our understanding of light (showing that it is a traveling electromagnetic field), but also inspired Einstein's theory of relativity. He realized that, if Maxwell was right, any measurement of the speed of light had to give the same result, no matter how fast the observer was moving -- and this simple premise gave rise to all the strange length-contracting, time-dilating effects we associate with relativity today.

In a material -- like water or glass -- light doesn't travel quite as fast. Repeatedly absorbed and re-emitted by the atoms of the material, its apparent speed is reduced by a factor n, the index of refraction. This fact makes possible one of the cooler "c" phenomena: "Čerenkov radiation." Since the effective speed of light is reduced in a medium, an energetic charged particle can actually move faster in that medium than light can, producing an optical shock wave. It's like a sonic boom -- but with light! This is what produces the eerie blue glow associated with nuclear reactors.

Answer: The Big Bang theory

The cosmic microwave background (CMB) consists of light (in the microwave part of the spectrum) that permeates the universe, coming from all directions and astoundingly identical in every place one looks. (The differences between CMB photons from one region and from another are tiny: less than one part in 100,000.) The existence of the CMB was predicted by Big Bang theorists in the 1940s and experimentally confirmed in the 1960s.

According to this theory, the universe was once very small and very hot, a plasma of quarks, gluons, photons and electrons all interacting with one another. As it cooled, these fundamental particles began to combine: quarks gave way to hadrons (such as protons and neutrons), which formed the nuclei of light atoms (like helium or lithium), and after about 379,000 years the universe was cool enough for these nuclei to capture electrons -- becoming neutral atoms of the type we're so familiar with today. At that moment, the universe changed from opaque to transparent: photons could, and often did, travel indefinitely without striking or being absorbed by other particles. The CMB photons we see today have been traveling from that moment until their interception by our telescopes; their energies obey a classic black-body spectrum, showing that they began as thermal radiation. Since they began their journey, the expansion of the universe has cooled them to a characteristic temperature of 2.7 Kelvin, and the tiny differences between one part of the night sky and the next offer crucial clues as to the structure of the early universe.

Answer: The force goes as one divided by the distance squared.

Coulomb's law states that the electrical force E between two charges, q1 and q2, separated by a distance r, is F=k(q1*q2)/r^2, where k is a constant dictated by the material that separates the charges. Thus, if you move the charges closer together so that their separation is reduced by half, the force is multiplied by four; if you double the separation between the charges, the force between them is only a quarter of what it was.

You may notice that Coulomb's law is very similar to the expression for the gravitational force between two masses m1 and m2: F = G(m1*m2)/r^2. These are both examples of inverse square laws (so named because they depend on the inverse square of the distance). We do not know why both electrical and gravitational forces have this inverse square dependence, but we're lucky that they do: for an inverse cube law, bound states (like a proton and electron in an atom, or like the Earth in orbit around the Sun) would not be possible!

Answer: Cross product

Enter any electromagnetism classroom during a test, and you'll see students waving their right hands in the air, contorting their fingers into various positions and focusing oddly on the location of their thumbs. No, this isn't some strange ritual for luck: they're calculating the cross product between two vectors.

A vector is a size combined with a direction in three-dimensional space (the velocity of a car, for example, or the force of gravity), and computing the interaction between two vectors requires certain mathematical tools.

The cross product, which results in a vector perpendicular to the first two, with a magnitude equal to the product of the magnitudes of the two vectors with the sine of the angle between them, is one such method.

The right-hand rule is used to decide which direction the result is pointing in. (That's a matter of convention, of course; you can use a left-hand rule. In order to be consistent, however, you'll have to adopt left-handed coordinate systems and ignore all those textbook pictures of right hands, every time.

After a hundred years of convention and tradition behind the right-hand rule, it must be said that, for ease of use in cross products, the right hands rule.)

Answer: 1.4 times the mass of the sun

Since stars have a lot of mass, the gravitational force -- which tends to make the star collapse -- has a very strong effect. During the bulk of a star's lifetime, nuclear fusion (the energy-producing process going on at its core) releases enough energy to stave off collapse. The star goes through various stages, each characterized by a different fuel for the nuclear reaction, but at the end there is no fuel left for any reaction that can counteract gravity, and the star begins to collapse. A white dwarf star -- the final destination of about 97% of stars -- is made mainly of carbon atoms and is supported by electron degeneracy pressure, a quantum effect that prevents two electrons from occupying the same space and state.

On a voyage from India to England, physicist Subrahmanyan Chandrasekhar realized that electron degeneracy pressure is not infinite, and can only go so far to prevent gravitational collapse. A white dwarf below 1.4 solar masses can be supported by this pressure; above that mass, it cannot be. A Type Ia supernova is thought to occur when the mass is just above the Chandrasekhar limit: gravitational collapse raises the temperature inside the star until it triggers nuclear fusion among the carbon nuclei. These runaway fusion reactions occur throughout the star, generating so much energy that the whole thing explodes. This is one exciting physics term!

Answer: Centripetal force

A "centripetal" force is literally center-seeking, tending to accelerate the object inward; if the force were removed, the object would simply travel in a straight line tangent to its original, circular path. Any force can be a centripetal force if it drives uniform circular motion. For example, gravity is the centripetal force for a satellite's motion around the Earth; tension provides the centripetal force for a ball being swung on the end of a string; and the force of friction, acting centripetally, is what guides cars and trains around curves.

By contrast, "centrifugal" (center-fleeing) forces are fictitious forces. Instead of expressing real physical interactions between objects, they are artifacts of the reference frame in which they are observed: a rotating frame, rather than an inertial one. To a person in a car rounding a bend, it certainly feels as if there's a mysterious force pressing them outward -- but there is no mystery to an observer outside the car, who sees that the person is continuing to move straight ahead while the car (their reference frame) is turning. The person seems to move outward relative to the car, but really it's the car that's moving inward!

Answer: The force does no net work when an object is moved so that it returns to its starting point.

When a force -- like gravity, or the electric force, or a child pulling a toy wagon -- moves an object across some distance, it does work equal to the change in the system's energy between the object's final position and its initial one. Sometimes, the amount of work depends on the particular path that the object travels. For example, it generally takes less work to move along the bank of a river than to fight against the current in the water. When one is dealing solely with conservative forces, however, the work done does NOT depend on the path: the object could travel the most meandering route imaginable, and still the system would return to its original energy when the object returned to its starting position. Processes driven by conservative forces are reversible.

Conservation of energy and momentum, a vital principle, is quite general and also applies to the actions of nonconservative forces (like friction). Forces that push systems to equilibrium -- spring forces, for example -- are called restoring forces.

Answer: As a result of a measurement

The most famous example of this situation is the tragic situation of Schrödinger's cat (another "c" word!), which he actually proposed in order to illustrate the problems with the concept of wave function collapse! Erwin Schrödinger wondered what would happen if an imaginary cat were placed in a box where a poison gas would be released (or confined) according to a quantum mechanical process. Until the process was observed, it would be impossible to tell whether the cat was alive or dead; the cat would, in some sense, exist in a combination of "live" states and "dead" ones, with some probability of each. Not until the box was opened and the cat observed would it be positively and one hundred percent alive (or dead).

In actuality, quantum mechanical principles do not translate well to large systems (such as cats), for reasons that are still under investigation -- so Schrödinger's imaginary feline can rest easy. However, smaller systems -- such as a single electron or the nucleus of an atom -- do behave in probabilistic ways, aptly described by a wave function. The interpretation of this behavior is still a matter of hot debate among physicists, with those of the Copenhagen school arguing for measurement as a special (but often ill-defined) process that collapses wave functions, while those of other schools substitute other strange-seeming principles (such as decoherence between multiple paths, all of which are traversed).

I hope that the superposition of your enjoyment states for this quiz has been heavily weighted towards the pleasurable end of the spectrum. In other words, I hope you had as much fun as I did! Thank you for playing.