question_answer

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

Answer:

                Here, \[\text{L}=l\omega \]= constant \[\therefore \]  K.E. of rotation,                \[K=\frac{1}{2}I{{\omega }^{2}}\]                                                                 \[K=\frac{1}{2I}{{I}^{2}}{{\omega }^{2}}=\frac{{{L}^{2}}}{2I}\] As L is constant,                                                \[\therefore \]  \[K\propto 1/I\] When moment of inertia (I) decreases, K.E of rotation (K) increases. Thus K.E. of rotation is not conserved.