Some Physics Essays, Examples, and Worked Problems

This page contains a number of  essays, worked problems, and examples.  Each deals with a particular topic or item; things that deal with general principles and fundamental methods (such as an introduction to Lagrangian mechanics) are on the basic stuff page.

 Proof that an orbit around a massive body takes the shape of a conic section.  This is a bit dry, I'm afraid, and is unrelated to relativity, but none the less I found it really cool to finally work out the details of this one. NewtonianOrbit Shapes Might it be possible to use quantum entanglement to communicate faster than light?  This frivolous little tale considers one possible consequence. The CCentipede No relativity website is complete without a derivation of the Lorentz transforms!  So, here's mine. LorentzTransforms The Twins, moving linearly, neglecting acceleration.  This is the classic special relativity "paradox".  What makes my treatment different from the 500 other discussions you can find on the web or in textbooks?  I don't compute gamma, I don't use a Lorentz transform anywhere in it. TheLinear Twins The Twins, moving linearly ... not neglecting acceleration. The traveler accelerates at 1g for the first half of the trip and decelerates at 1g for the second half of the trip.  Treated from Earth's PoV, from the MCRF of the traveler, and from the porthole view.  I don't know how educational this one is but it's certainly entertaining.  What hair! TheAcceleratingTwins What does an astronaut see, looking through a telescope at a distance planet, when a spaceship first starts to accelerate toward that planet?  Not what I expected, that's for sure. Porthole View,Looking Forward An orbiting clock, neglecting gravitational effects (i.e., a clock moving in a circle).  Everybody knows this one, so what's the point?  Well, I do it from the clock's point of view, too. The RevolvingClock The Twins again, but now they're going in circles:  Counter-orbiting space ships.  Each time they pass each other, A observes B's clock is running slow, yet somehow it never really falls behind.  So, it must catch up again.  But when? The RevolvingTwins When time runs backwards:  A spaceship orbits around a distant planet.  How fast is time passing on Earth, as viewed from the MCRF of the spaceship?  The answer is strange, indeed! The RevolvingAstronaut The Sagnac effect is often claimed to be difficult to explain, requiring very messy mathematics.  Sometimes it's said to admit no explanation with special relativity.  Actually it's a rather simple effect, and no math more advanced than a Lorentz transform is needed. The SagnacEffect It's well known that the gas around some supernovas appears to be moving away from the star faster than C.  It's just a trick of the light, but working out the details is a little messy. SuperluminalShells Space is weird just outside the event horizon of a black hole.  In Schwarzschild coordinates things seem to "stick" just before they get to the horizon.  This is a somewhat naive discussion of that behavior. StickyBlack Holes A few items having to do with magnetism, including derivation of the field of a dipole. Magnetism

Page created on 11/16/06, from pieces extracted from the old front page; last updated 1/7/07