What is the rotational kinetic energyof a point body moving in a circle?

Question

The correct answer is l square/2i which I donot get

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Answer 1 · 2018-04-07T02:46:34

See below

The kinetic energy is #K = 1/2mv^2#

Now, the magnitude #L# of the angular momentum about the center of the circle is #mvr#. Thus #v = L/(mr)#

So

#K = 1/2 m (L/(mr))^2 = 1/2 L^2/(mr^2)#

Writing #I=mr^2# for a point particles gives us

#K = L^2/(2I)#