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relativity




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


agreed


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.

One can apply special relativity to accelerations, if you use the idea of
instantaneously co-moving reference frames. One hears from time to time
that special relativity can not handle accelerations (this is sometimes
given as a psuedo-solution to the twin paradox), but that idea is simply not
true. Certainly an accelration involves a sequence of instantaneously
co-moving reference frames (that are all inertial) so you can not cope with
just a single Lorentz transformation, but one can still do it.
Accelerations due to rotations are no different, for example, handling them
properly in special relativity resolves the factor of two in Thomas
precession.

Joel