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)

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