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Consider a case where a person stands on top of a rotating disk. The disc is given to rotate at a constant rate. There are two possible movements of the man:

  1. He moves away from the center: In this case moment of inertia increases and hence the angular velocity decreases. The net mechanical energy of the system decreases.
  2. He moves towards the center: In this case the moment of inertia decreases, thereby causing an increase in the angular velocity. The net mechanical energy increases.

In both the cases, the man expends some energy to move outwards and inwards. So how is it that the energy of the system increases in one case while decreases in the other? Which forces perform some positive work so as to cause an increase in the energy of the system?

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You assumption that energy changes is incorrect. In both cases the rotational energy is conserved.

Rotational energy is given by $E_{rot}=\frac{1}{2}I\omega^2$.

As no work is done on the system the energy of the system must be conserved.

We then see that as the man walks out $I$ increases and $\omega$ decreases and visa versa as he walks in just as you had. But the energy remains constant.

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  • $\begingroup$ I don't mean to prove you wrong, but there several solutions, contrary to yours, in books which are mainstream. One example is H. C. Verma's Concepts of Physics. You could Google it too. $\endgroup$
    – user117913
    Commented Dec 14, 2014 at 15:47

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