giles@ucf-cs.UUCP (11/11/83)
I have been informed that the Coriolis force only acts upon moving objects, and that this signficantly alters my conclusions. I main- tain, however, that the Coriolis force is just one aspect of a more general pseudo-force which is the result of a planetary surface being a non-inertial frame. Hopefully, the following gedanken experiment will at least make my argument sound reasonable. (Translation -- I don't want to have to submit a more rigorous proof: it will run into hundreds of lines.) ====================================================================== Imagine that you are at the south pole, inside of a large, transparent geodesic dome. Directly over the pole is a large concrete basin, with mercury inside of it. Floating upon the mercury is a large concrete raft. Finally, above the basin is hanging a Foucault pendulum. //////////////////////////////////// ------------------------------------ | | | | | | | | | | | | / \ < > pendulum bob \_/ ==============+ ------------------------- +============== //////////////| | concrete raft | |////////////// //////////////| ------------------------- |////////////// //////////////=============================////////////// ///////////////////////////////////////////////////////// At 6:00, you enter the dome and paint a large black line on the con- crete raft in the direction of the sun (if it summer, at A. Centuri in winter...). You then start the pendulum bob such that its ground trace is over the black line. Being a lazy person, you leave the dome until noon. When you come back, the sun has moved through the sky by 90 degrees. When you look at the ground trace of the pendulum bob, you see that it is still pointed at the sun. What about the black line on the concrete raft? I claim that the earth has rotated underneath this raft, and so the black line is still pointed at the sun! When you come back at 18:00, the same thing has occurred. When you come back at midnight, the same thing has occurred. ..... -------------------------------------------------------------------- Because of the severe case of frostbite you recieved in Antartica, you decide to visit Kenya. While there, you take your trusty con- crete raft and Foucault pendulum to the summit of Mount Kenya (??). At day break, you paint a line on your concrete raft toward some landmark, and start the swing of the pendulum bob as described above. At noon, the pendulum bob has not changed the direction it is swinging in. What about the concrete raft? Once again, I claim that the forces acting on the raft are identical to those acting on the pendulum, so it has not rotated either. The next day, you come in and find the same thing..... ---------------------------------------------------------------------- Finally, you go home and in your back yard set up your trusty concrete raft and Foucault pendulum. What happens? ====================================================================== Clearly, these are distinct physical systems. One is moving, dynamic. The other is stationary, static. Yet they have the same response. The best analogy I can think of for this force is in general relativity, using differential geometry. When you try to translate a vector from one point in space to another, an extra term must be added due to the curvature of space. In Euclidean space, this term is identically zero. But on the surface of a sphere, it definity is not. I claim that this is what is known as the Coriolis force, and that for a moving body the vector could be its velocity. For a stationary body it could be any arbitrary reference direction. After all, by Newton's laws of motion if a body is initially at rest it will tend to remain at rest. Hopefully, this has cleared up some questions concerning what I meant by the Coriolis force/ pseudo-forces in my original article. Bruce Giles decvax!ucf-cs!giles (UUCP) UCF, Dept of Math, Orlando Fl 32816 (Snail)