Re: does circumference contract with velocity?

David wrote:
If I have a disk that has a rotational velocity V at its outer
edge, does someone who is at rest with respect to the center of the
disk conclude that some sort of length contraction occurs because of V
and therefore the rotating disk has a smaller circumference than the
same disk when it is not rotating?

Normally when one says "the circumference of this disk", they mean a measurement made _simultaneously_ around the entire edge of the disk. For an inertial observer (e.g. of the inertial frame in which the center is at rest) this is easy; for a rotating observer on the disk itself this is impossible -- there is no single self-consistent definition of simultaneity for a rotating system.

So you _must_ change your notion of what "circumference" means for a rotating disk.

If instead of a solid disk you imagine a "disk" made up of thin radial fibers with increasing widths such that together they make up the disk when not rotating, then as the set of fibers starts rotating, small gaps will appear between the fibers, getting larger as the tangential velocity increases. Of course in practice this is immeasurably small, and for practical materials the fibers will be torn apart long before either an appreciable fraction of c is achieved or the gaps are observable.


Tom Roberts
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