# Rigid body angular velocity limit

1. Apr 24, 2012

### bob900

Suppose a rigid body (say a sphere) ofis rotating with angular velocity A. Any point at a distance r from the axis of rotation has tangential velocity v=A*r and that v must be less than c. Does this mean that :

1. The rigid body can only be a certain maximum (radial) size r, where r<A/c?
2. If you try to increase its angular velocity, it will no longer stay rigid?

2. Apr 24, 2012

### pervect

Staff Emeritus
The speed of sound in an ideal rigid body would be infinite, which is not compatible with relativity, which limits the speed of sound to something less than 'c'.

For any sort of normal matter, (say steel, or even buckytubes, the strongest material known) the speed of sound is much less than c You'd also find that you couldn't build anything strong enough to even approach a tangential velocity of 'c' with available materials.

You can create a notion of rigidity that is compatible with special relativity called "Born Rigidity", however it turns out that you can't make something that's Born rigid rotate at all while still satisfying the defining conditions.

See for instance http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html and the references therin,