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} $