On 27/7/2007 3:51 PM, Michel Jullian wrote: > > ----- Original Message ----- > From: "Harry Veeder" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Friday, July 27, 2007 8:27 PM > Subject: Re: [Vo]:Re: The Earth and the Wheel > > >> On 27/7/2007 5:02 AM, Michel Jullian wrote: >> >> Thanks for the comments. >> >> Harry, a few comments in your text below: >> >> "Consider a wheel located on Earth's equator (see fig. below). >> Initially a brake prevents the wheel from turning so the wheel is not >> turning relative to the ground. Next the brake is released and assuming the >> axel [axle] of the wheel is frictionless and since the Earth is slowly >> turning the wheel will begin [continue] to slowly turn about its own centre >> at the same rate as the Earth's rotation. >> >> "continue" is consistent with the account you give below. > > Not only, the wheel was already turning in the inertial frame when the brakes > were on wasn't it? So it continues to turn, it doesn't begin.
The "brake on" means it is locked and cannot turn wrt to the ground. The locked wheel is already to turning about the inertial frame tied to the earth's axis of rotation, but the wheel only begins to turn about its own centre when the brake is off. > >> For someone standing beside the wheel it might appear as if the brake were >> still applied. However, if the wheel is turning about its own centre the >> periphery of the wheel is subject to an associated centrifugal force. The >> person beside the wheel would deny this unless they knew the brake was >> released." [no, the centrifugal force is a fictitious force associated to >> the motion of the non-inertial frame of reference (here the ground-bound >> frame, or that bound to the bottom of the wheel, which is the same) wrt to >> an inertial frame of reference (here the Earth center+distant stars frame). >> This motion, whichever way you look at it, is a simple rotation at 1 turn >> per day around the Earth axis, at one Earth radius distance] >> >> Pointing out that it is a "fictitious" force does not invalidate what I am >> saying. > > But the rest of the comment does, unless I misunderstand what you are saying > which is quite possible. > >> Of course the hub of the wheel continues to rotate about the Earth's axis >> of rotation. However, please entertain my assertion as a testable >> conjecture. >> If the wheel with the brake off is really rotating about its own >> centre then the tension in the spokes should differ from the tension in the >> spokes >> when the brake on. > > I am afraid the tension will be strictly identical whether the brakes are on > or off, since the wheel has the same absolute motion in both cases. > > Michel > Here is another way looking at it. For the sake of balance, imagine a wheel is setup on opposite sides of the equator. One wheel has the brake on and the other has the brake off. If you could stop the Earth rotating, the wheel that has the brake on will continue to remain at rest wrt to the ground but the other wheel will continue to turn once per day wrt to the ground. The two motions differ, but the difference is masked by the rotation of the Earth. Do you agree? Harry
