Spinning disk and relativity

Factual Questions
1

Say I’m looking down on a spinning disk. From my perspective it’s spinning clockwise, and the edge of the disk is moving at .5c.

What would I see? On one hand, when you spin a disk it looks the same. On the other hand, the circumference should appear to be shortened. But the diameter should still be the same. :confused:

2

In the theory of special relativity it is impossible to accelerate a rigid body whilst maintaining its rigidity (this creates paradoxes): thus you cannot spin a rigid disk from a speed of 0 to a relativistic speed. The disk will inevitably deform. As NardoPolo says, according to special relativity, the radius will remain the same, but the circumference will shrink. See this page and this page for a little more detail.

The actual solution brings in rather complex calculations involving general relativity, which I don’t have to hand and can’t find online (and I’m not sure if anyone has done).

3

Addendum: I said “according to special relativity, the radius will remain the same, but the circumference will shrink.” This is due to a limitation in the special theory of relativity, and does not describe the actual behaviour.

4

You can view an applet of a spinning wheel here: http://physics.berea.edu/~king/Teaching/ModPhys/Relativity/animations.htm#length

A non-relativistic wheel on the left is compared to a wheel spinning at 87% the speed of light on the right side of the page. Below that is an applet showing a spacetime wheel diagram.

As already pointed out, there are no rigid materials. Information on the position and movement of different areas on a physical object can only be transmitted at less than the speed of light.

5

Fine, so it’s not rigid. Which way would it flex? The rim of the wheel would compress (circumferentially), but so would the distance around the circumference itself.

If we took a 10º wedge out of the disk, the remaining 350º would compress. But so would the 10º section of nothing.

Refusal your second link is helpful. I especially liked the statements:

Yet I’m still scratching my head. What is the contradiction?