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Re: Relativity



1. To the observer translating relative to the
wheel, each part of the wheel is in a different reference frame.

No. There is only one "reference frame", that of the observer.

2. Special relativity does not really apply to a
any part of the rim of a rotating wheel because each piece is
accelerating, and NOT an inertial frame.

Special relativity certainly does apply to accelerated
particles in an inertial reference frame, and this is such
a case.

But it is an interesting problem. On first thought,
the path to the solution would seem to be to consider a non- rotating
wheel next to the rotating one ( or a non-rotating groove containing the
rotating ring with a very small clearance). Thus it would seem
that the shapes of the rotating and non-rotating wheels must vary in the
same way.

Now you're on to the solution ...

BUT there is the problem of simultaneity, like the problem of
something longer than the barn in one frame being momentarily enclosed by
the barn in another frame.

.... and you back away from it because it seems simple. Relax
and enjoy it; the solution to the problem is that it is not
a different problem.

Incidentally, is everyone familiar with the well-known result
for the Terrell rotated appearance of a translating sphere,
say an eight ball with numbers on front and rear?

Leigh