Q. Two wheels $A$ and $B$ are mounted on the same axle. Moment of inertia of $A$ is 6 $kgm^{2}$ and it is rotating at 600 rpm when $B$ is at rest. What is moment of inertia of $B$, if their combined speed is 400 rpm?
A) $8\ kg\ m^{2}$
B) $4\ kg\ m^{2}$
C) $3\ kg\ m^{2}$
D) $5\ kg\ m^{2}$
Explanation
(c) Applying the principle of conservation of angular momentum,
$\left( I_{1} + I_{2} \right)\omega = I_{1}\omega_{1} + I_{2}\omega_{2}$
$\left( 6 + I_{2} \right)\frac{400}{60} \times 2\pi = 6 \times \frac{600}{60} \times 2\pi + I_{2} \times 0$
Which gives, $I_{2} = 3\ kg\ m^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.