I am thinking on a object, e.g. ball or planet that starts rotating with increasing speed. Let's assume that his speed get's closer to the speed of light, what happens to this object? There are several forces acting. But I always get caught thinking that it will get heavier and heavier because of the additional energy which is needed to accelerate it. Is that all? Or anything else interesting happens?
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$\begingroup$ I assume by "his speed" you mean the velocity on the most outer part? using rotation is oftenly tried approach "to overcome" the speed barrier so you will find lots of explanation on that. One fundamental problem with this is you would need a physically impossible object. $\endgroup$– BortFeb 12, 2016 at 12:36
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$\begingroup$ @Bort I see, so it is really more complicated that I thought. $\endgroup$– DerbFeb 12, 2016 at 12:40
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$\begingroup$ its not impossible to do, far from that, but there is always this danger that you try do "break" relativity theory by breaking physics somewhere else. One further example that I think is in many textbooks is a ski driver that drives over a gap. At first it will seem that the result (does he make it over the gap?) depends on the frame of reference (due to length contraction), but the resolution in the end is that you cannot assume the ski to be a rigid body, because a rigid body has sound velocity of infinity which is larger than $c$ $\endgroup$– BortFeb 12, 2016 at 12:45
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1$\begingroup$ As a rotating body approaches the speed of light, the molecular attractions tend to break under the stress from the centrifugal force.You might want to look up for a video by veritasium on youtube, where they have addressed this very problem. $\endgroup$– AbhinavFeb 12, 2016 at 12:48
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$\begingroup$ @Abhinav Yes, this conflict situation is interesting for me. Thanks for the keywords for youtube. :-) $\endgroup$– DerbFeb 12, 2016 at 12:51
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2 Answers
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Note that "c" means linear velocity, not angular. Then, you would refer to tangential velocity.
If an object rotated at relativistic (tangential) velocity, then each "shell" will have a different space and time compression. By contraction of the tangent lengthes, the perceived length of large circles would be smaller than $2\pi r$, leaning to 0 lenght at equator as the tangential speed approach c.
Appart from that, yes you would need more and more energy to accelerate it, and also the material coherency of the object is unlikely to resist to centrifugal force !
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$\begingroup$ So an object rotating at the speed of light would be a point particle or infinitely small line? $\endgroup$ Jun 12, 2016 at 3:16
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$\begingroup$ c - 7.83088611035e-62 (to reach the planck length) would be very fast though. $\endgroup$ Jun 12, 2016 at 3:22
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A phenomenon which has been observed in stars and planets is that when the body rotates faster and faster, the object becomes more and more elongated, thus some points in the object are farther away from the rotation axis, increasing the relative moment of inertia and requiring more torque to accelerate the body by the same amount.
This effect has also been observed in everyday objects and in everyday devices. For example, the governors on steam engines exhibit this effect. When it spins slowly, the weights are almost all the way in. When it rotates faster, the weights swing outward and are further away from the shaft, requiring more torque to maintain constant angular acceleration.
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