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 ?
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5Rotate a long bar in space and get close to c speed – voix Jun 30 '11 at 19:29
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Do you mean the rotation of a particle or mass. You state general relativity and rotating objects in the same sentence. – Fortunato Jun 30 '11 at 19:47
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@fortunato I mean rotation of a non-point mass. I dont know if the sentence is wrong. Could you please correct me ? – New Horizon Jun 30 '11 at 21:13
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@Marek's answer in @voix's linked-question seems to answer it for me. Good question all the same :-) – qftme Jun 30 '11 at 23:53
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so, if they spin a disk with diameter of 9,55cm to 60 000m rpm the edge will get speed of light. True? – Nov 26 '13 at 19:16
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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.
Snowhare
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I haven't studied general relativity, but it seems odd that an event horizon could rotate. Where does this limit come from? – Dan Jul 05 '11 at 00:15
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A nice explanation can be found on pages 16 and 17 of this article by M. Camernzind and A. Muller. In essence, it is the speed that the black hole frame drags. It can't exceed the speed of light at the event horizon or you would no longer have an event horizon. – Snowhare Jul 05 '11 at 14:43
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@BenjaminFranz Other than infalling bodies, necessarily slower than speed of light, what can increase the angular speed of a black hole. – babou Aug 23 '13 at 19:58
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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 $\frac{c}{2r\pi}$
