Big Spinning Ball Question (Confused)

[obiwanjabroni]

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!

 

[pervect]

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).

 

[Entropia]

Hi there! That's a really interesting question. So, if I understand correctly, you're asking about the forces involved when a large, rigid ball is rotating at a very high speed, with different points on the surface moving at different velocities.

In this scenario, there would definitely be shearing forces acting on the ball. Shearing force is a type of force that occurs when different parts of an object are moving at different speeds or in different directions. In this case, the ball's surface would experience shearing forces because the points closer to the center of rotation would be moving at a slower speed than those further away from the center.

As for how a point on the surface with a greater radius and a point with a lesser radius would "see" each other, it would depend on the specific speed and direction of rotation. However, in general, the points on the surface would experience a relative motion and would likely appear to be moving in opposite directions to each other.

I hope this helps answer your question! Physics can definitely be confusing at times, but it's always fun to think about these types of scenarios and how the laws of motion and forces come into play. Keep exploring and asking questions!