I spent a long time trying to solve this however I still don't have an answer. The prof who gave me the question said that I should think of it like Newtonian mechanics and then solve it with relativity. I'm assuming that means $KE=I\omega^2/2$. I and omega depend on R, which changes due to length contraction. I tried 3 different thing and got 3 different answers. One of them was 0, the other 1/2mv^4 and infinity.
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See Rotate a long bar in space and get close to (or even beyond) the speed of light $c$ – sammy gerbil Jun 18 '18 at 18:03
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What is the energy if the mass of the disk is concentrated at the rim, so that $I=mR^2$? ... Maybe you got the correct answer. Ask your prof to explain his solution. – sammy gerbil Jun 18 '18 at 18:17
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See also https://physics.stackexchange.com/q/201492/25301 – Kyle Kanos Jun 19 '18 at 09:42