Rigid body angular velocity limit

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SUMMARY

The discussion centers on the limitations of rigid body rotation in the context of special relativity. It establishes that a rigid body, such as a sphere, cannot exceed a maximum radial size defined by the equation r < A/c, where A is the angular velocity and c is the speed of light. Additionally, increasing the angular velocity beyond this limit results in the loss of rigidity, as the speed of sound in any material is significantly less than c. The concept of "Born Rigidity" is introduced, highlighting that no object can maintain this form of rigidity while rotating under relativistic conditions.

PREREQUISITES
  • Understanding of angular velocity and tangential velocity
  • Familiarity with the principles of special relativity
  • Knowledge of material properties, specifically the speed of sound in various materials
  • Concept of "Born Rigidity" in physics
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  • Research the implications of special relativity on rigid body dynamics
  • Study the mathematical formulation of Born Rigidity
  • Explore the speed of sound in different materials and its relation to relativistic effects
  • Examine case studies of rigid body motion in relativistic physics
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Physicists, engineers, and students interested in the intersection of mechanics and relativity, particularly those studying the behavior of materials under extreme rotational conditions.

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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?
 
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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,
 

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