I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
Short answer, yes.
Long answer, there is always a limit, but what sets the limit differs by what you are spinning.
A black hole, which can't 'fly apart' as far as we know, can't rotate any faster than the angular velocity that would make its event horizon rotate at the speed of light. That is a limit set by relativity.
Objects other than black holes have limits set by the binding forces holding them together.
For example, a neutron star is held together by gravitation. If you spin it fast enough (fast enough in this case being a few thousand times per second) it will simply 'come apart' when the gravitation is roughly balanced by the rotation (the surface is moving at a substantial fraction of the speed of light at that point).
For objects held together by electromagnetism (ordinary matter), I believe the record is currently held by micrometer sized graphite flakes spinning at 60,000,000 rpm (as of Oct 2010). The group at the University of Maryland that did it said that the theoretical limit for graphene was about 1,000 times that fast.
Even an atomic nucleus (held together by the Strong Nuclear Force) will come apart if spun hard enough.
The maximum rotational velocity of a solid body is governed by the allowable material stresses. These forces reach a point which tears the body apart long before the tangential velocities at the rim approach any significant fraction of the speed of light.
There is a ratio that describes allowable max rotational speed of a disk in terms of strength of material it is built out of. Been a while and I forget the name of the guy this was named after, but a Google search should turn something up for you.
If you could construct a disk of sufficient material strength, such that you only had to worry about relativity, then the limit would be when the tangential velocity at the rim = c. Thus, the rotational angular velocity, in radians, of a disk of radius r, would be $c/(2rPi)$
protected by Community♦ Dec 30 '13 at 13:50
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