Hi, so a friend and I had a question a few days ago and we don't know what will happen. So, let's say that there's an infinitely rigid ball that's very large (so it doesn't deform and so that the tangential velocity at different radii are noticeably different). Now, let's say this ball were rotating such that a point on the surface of the sphere were moving at 0.9999. What kind of forces would be on the ball? Would it just be shearing forces to different "slices" of the ball? How would a point on the surface with a greater radii and a point on the surface with lesser radii see each other? Thanks in advance!
I've only seen the non-relativistic case analyzed for the forces (stresses), and that for a cylinder, not a sphere. In that (non-relativistic cylinder) case, you have both radial stresses, and tangential stresses both of which are in the form of tensions. see for instance http://arxiv.org/abs/physics/0211004 There is also a bare statement of the above results at http://www.dow.com/sal/design/guide/flat-disks.htm for the classical rotating cylinder, mainly of interest because it is concicise which appears to duplicate the above (non-relativistic) results. The radial stress term goes to zero as r->R, but there is still a large tangential stress. The quantity v, "Poisson's ratio" is about .28 for steel. Steel, of course, would never be strong enough to rotate at such relativistic velocities (but no material known to man would be strong enough either).