question_answer

The moments of inertia of two rotating bodies A and B are \[{{I}_{A}}\] and \[{{I}_{B}}({{I}_{A}}>{{I}_{B}})\]and their angular momenta are equal. Which one has a greater kinetic energy?

Answer:

                Angular momentum,                 \[L=I\omega \]                 K.E. of rotation,                 \[K=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}\frac{{{I}^{2}}{{\omega }^{2}}}{I}=\frac{1}{2}\frac{{{L}^{2}}}{I}\]                 For constant L,  \[K\propto \frac{1}{I}\]                 As           \[{{I}_{A}}>{{I}_{B}}\]                 \[\therefore \]  \[{{K}_{A}}<{{K}_{B}}\] or \[{{K}_{B}}>{{K}_{A.}}\] So body B has a greater rotational K.E.