Invariant spacetime - distance - Circular Motion
This is a question that I thought up a few years ago when I was taking mechanics. I asked the professor but didn't really get a straight answer.
Imagine a record spinning at relativistic speeds. In the lab frame, the circumference of the record should decrease according to the Lorentz contraction. However the radius of the record should remain fixed since it is orthogonal to the direction of motion. So does the shape of the record appear distorted since the circumference is smaller but the radius is the same? What would it look like?
I have a feeling the answer is obvious and/or well known since it would seem to be similar to the situation of relativistic particles traveling around a circular accelerator but I can't think of how it can be solved.