Question

A boy sitting over a rotating stool has his arms folded. If he stretches his arms, his angular momentum about the axis of rotation

Answer 1

Consider in initial rotational energy(when the hands were out-stretched ) as:

Ei=L2i2Ii

Final rotational energy (when his hands are folded) as:

Ef=L2f2If

Now by COAM

Li=Lf

But

If<Ii

Because same mass is now nearer to the axis of rotation.

So

Ei<Ef

This implies positive work has been done on the system to make the final kinetic energy more.