Q. A round disc of moment of inertia $I_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_{1}$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is
A) $\frac{I_{2}\omega}{I_{1} + I_{2}}$
B) $\omega$
C) $\frac{I_{1}\omega}{I_{1} + I_{2}}$
D) $\frac{\left( I_{1} + I_{2} \right)\omega}{I_{1}}$
Explanation
(c) The angular momentum of a disc of moment of inertia $I_{1}$ and rotating about its axis with angular velocity $\omega$ is
$L_{1} = I_{1}\omega$
When a round disc of moment of inertia $I_{2}$ is placed on first disc, then angular momentum of the combination is
$L_{2} = (I_{1} + I_{2})\omega'$
In the absence of any external torque, angular momentum remains conserved, $ie$.,
$L_{1} = L_{2}$
$I_{1}\omega = (I_{1} + I_{2})\omega'$
$\Rightarrow$ $\omega^{'} = \frac{I_{1}\omega}{I_{1} + I_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.