Question

The moment of inertia of a rigid body in terms of its angular momentum $L$ and kinetic energy $K$ is

• A. $\frac{L^{2}}{K}$
• B. $\frac{L^{2}}{2 K}$
• C. $\frac{L}{2 K^{2}}$
• D. $\frac{L}{2 K}$

Answer 1

Answer: (B)

Angular momentum of a rigid body about a fixed axis is given by
$L=I\omega $
Where $I$ is moment of inertia and $\omega $ is angular velocity about that axis.
Kinetic energy of body is given by
$K=\frac{1}{2} \, I\omega ^{2}$
$\therefore $ $K=\frac{1}{2 I}\left(I \omega \right)^{2}=\frac{L^{2}}{2 I}$
$\Rightarrow $ $I=\frac{L^{2}}{2 K}$