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Suppose a typical case of a girl dancing and after sometime changing her $I$ (moment of inertia to rotate) faster, my doubt is in this case there is a non-zero difference in initial and final total KE (in this case only rotational KE), why does it so?

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The kinetic energy increases for the dancer after pulling her arms in (for example). That would decrease her moment of inertia, but from conservation of angular momentum, increase her angular velocity $\omega$.

$$K.E. = \frac{1}{2}I\omega^2$$

so the kinetic energy has increased.

The energy has come from the work she has to do to pull her arms in, i.e. the girl has done the work needed to increase her rotational kinetic energy.

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  • $\begingroup$ Thanks understood :) $\endgroup$
    – Orion_Pax
    Nov 27 '21 at 11:17

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