Q. What is moment of inertia in terms of angular momentum ($L$) and kinetic energy ($K$)?
A) $\frac{L^{2}}{K}$
B) $\frac{L^{2}}{2K}$
C) $\frac{L}{{2K}^{2}}$
D) $\frac{L}{2K}$
Explanation
(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
$K = \frac{1}{2}\ I\omega^{2}$
$\therefore$ $K = \frac{1}{2l}(I\omega)^{2} = \frac{L^{2}}{2l}$
$\Rightarrow$ $I = \frac{L^{2}}{2K}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.