Q. A cockroach is moving with velocity $v$ in anticlockwise direction on the rim of a disc of radius $R$ of mass $m$. The moment of inertia of the disc about the axis is $I$ and it is rotating in clockwise direction with an angular velocity $\omega$. If the cockroach stops, the angular velocity of the disc will be
A) $\frac{I\omega}{I + mR^{2}}$
B) $\frac{I\omega + mvR}{I + mR^{2}}$
C) $\frac{I\omega - mvR}{I + mR^{2}\ }$
D) $\frac{I\omega - mvR}{I}$
Explanation
(c) $L_{1} = L_{2}$
$I\omega - mvR = \left( I + mR^{2} \right)\omega^{'} \Rightarrow \omega^{'} = \frac{I\omega - mvR}{(I + mR^{2})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.