If angular momentum is conserved in a system, whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? explain.

 Answer: suppose that moment of inertia decreases to I', then angular speed will increase to ⍵', such that I⍵ = I'⍵'

Then K.E of rotation of the body = 1/2 I'(I/I' ⍵)^2

= 1/2 (I^2 / I')⍵^2

As I'<I, it follows that the K.E. of rotation of the body will increase when its moment of inertia decreases i.e kinetic energy of rotation will not be conserved.