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*Let there be a body rotating about its axis, with a moment of inertia I and an angular velcity w.*

The angular momentum of the system is L = Iw.

Now, if the radius of the body change, its moment of inertia will also change. Let the new moment of inertia be I`, such that, I`= kI.

But the angular momentum of the system will remain constant.

So, the angular velcity must change. So, w`=w/k.

But, initially, the energy of the system was purely kinetic and was given by

E=1/2 Iw

The new energy is given by, I`= 1/2 I`w`

So, E`= E/k.

So the new energy of the system is either more {0<k<1} of less {k>1} than the previous energy!

The angular momentum of the system is L = Iw.

Now, if the radius of the body change, its moment of inertia will also change. Let the new moment of inertia be I`, such that, I`= kI.

But the angular momentum of the system will remain constant.

So, the angular velcity must change. So, w`=w/k.

But, initially, the energy of the system was purely kinetic and was given by

E=1/2 Iw

^{2}.The new energy is given by, I`= 1/2 I`w`

^{2}= 1/2 kI (w/k)^{2}So, E`= E/k.

So the new energy of the system is either more {0<k<1} of less {k>1} than the previous energy!

What am I doing wrong?