question_answer

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

Answer:

                Here \[L=I\omega =\]constant Rotational K.E. is given by \[K=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}\frac{{{I}^{2}}{{\omega }^{2}}}{I}=\frac{1}{2}.\frac{{{L}^{2}}}{I}\] For constant L, \[K\propto \frac{1}{I}\] So when the moment of inertia decreases, the rotational K.E. increases. Hence rotational K.E. is not conserved.