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

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
$K=\frac{1}{2}I{\omega }^2$
$\therefore$ $K=\frac{1}{2I}{\left(I\omega \right)}^2=\frac{L^2}{2I}$
$\Rightarrow$ $I=\frac{L^2}{2K}$