What it the maximum angular velocity that can possibly be attained by a rigid body?
I'm tempted to say c/r in which c is the speed of light and r is the maximum perpendicular distance from points on the body to the rotation axis. In practice the body will fly apart at a far lower angular velocity. To calculate it you'd need to know the body's mass distribution and the ultimate tensile stress of its material. To get some idea of the order of magnitude you could consider the easy case of a thin rod rotated about an axis through one of its ends and perpendicular to the rod. I make it about 300 rad per second for a steel rod 1 metre long.
Iranian engineers know the angular speed at which a rigid body explodes.
This means that the value depends on the rotational inertia of the body. Why is it that there is no fixed limit for the angular velocity for any body, like there is c for translational motion?
This sounds incredulous, but if I have a photon that can rotate about a fixed given axis, how fast would it rotate?
These are deep waters...
First off, why should there be?
That said, there is a problem with a rigid body in Newtonian mechanics in relativistic physics. A perfectly rigid body necessarily has an infinite speed of sound. The resolution is simple: There is no such thing as a perfectly rigid body in reality. It is a useful abstraction that is approximately valid at low rotation speeds, where "low" means the velocity at every point on the body relative to the center of mass is much, much smaller than speed of light.
Elementary particles are point masses.
On the flip side, why should there not be?
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