Question

A body is rotating with angular momentum L. If $I$ is its moment of inertia about the axis of rotation, its kinetic energy of rotation is

• A. $\frac{1}{2}I{{L}^{2}}$
• B. $\frac{1}{2}IL$
• C. $\frac{1}{2}{{I}^{2}}L$
• D. $\frac{1}{2}\frac{{{L}^{2}}}{I}$

Answer 1

Answer: (D)

$\frac{1}{2}\frac{{{L}^{2}}}{I}$

Answer 2

We know that $L=I\omega$ Kinetic energy of a body with angular momentum $KE=\frac{1}{2}I{{\omega }^{2}}$ $KE=\frac{1}{2}\times I\times {{\left( \frac{L}{I} \right)}^{2}}$ $KE=\frac{{{L}^{2}}}{2I}$