The Inclined Plane on Wikipedia

For those who live under a giant rock: Wikipedia is a user-created web-based encyclopedia. In conversation, I usually refer to it as a compendium of “common knowledge,” realizing of course that many elements of common knowledge are not common, and that many elements are flat wrong. Case in point: the Wikipedia entry on the inclined plane. (I refer to the article as it appeared on Sunday afternoon, 28 October 2007. The section on which I comment is reproduced in its entirety below, including the figure and text.)

The inclined plane is treated in detail in virtually every first-year physics course on the planet. I suspect that nearly everyone who took physics in college remembers it. We use it to teach students the quantitative aspects of Newton’s second law in two-dimensions, and to introduce friction. The Wikipedia article, although somewhat brief, touches on both of these. If I were grading the entry as an answer to a exam question, it would earn 3 out of 5 points, meaning that it gets some things correct, but that it also reveals major errors of fact or reasoning unacceptable for a first-year physics student.

Coulomb’s Law and the Direction of the Force

Coulomb’s law presents a unique challenge to physics students struggling to understand how magnitude and direction can coexist in the same quantity–a vector. The difficulty with Coulomb’s law is that electric charge, a property of certain subatomic particles, comes in two types, arbitrarily called positive and negative. For example, the electron carries a negative electric charge, and the proton a positive electric charge. (They have the same magnitude, or amount, of charge.) Because charge can be positive or negative, Coulomb’s law often produces answers that are easily misinterpreted with regard to the direction of the force.

Fun With Orbits, Or How to Slow Down by Speeding Up

Orbits are cool. Let’s see how, shall we?

When a satellite orbits the Earth in a perfect circle, it experiences a centripetal acceleration that depends on its orbital speed v (a constant) and its orbital radius r (also constant):

A centripetal acceleration changes only your direction of motion.  A tangential acceleration changes your speed.  In your car, your steering wheel produces a centripetal acceleration, and your gas and brake pedals produce a tangential acceleration.

The centripetal acceleration experienced by an orbiting satellite is due to the Earth’s gravitational field:

where G is the universal gravitational constant and M is the mass of the Earth. (If you’re going to build a universe, you must decide how strong the force of gravity will be. You do this by setting the value of G. In our universe, and perhaps others, G has the value 6.673 x 10^-11 in SI units.)

Intelligent Observers

An interesting concept in special relativity is the intelligent observer. An “intelligent” observer is one who takes account of the finite speed of light to reason from calculations as opposed to what she sees. A simple example illustrates the concept.