Question

A cockroach is moving with a velocity $v$ in anticlock 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. $\frac{I\omega }{I+m{R}^2}$
• B. $\frac{I\omega +mvR}{I+m{R}^2}$
• C. $\frac{I\omega -mvR}{I+m{R}^2}$
• D. $\frac{I\omega -mvR}{I}$

Answer 1

The correct option is C $\frac{I\omega -mvR}{I+m{R}^2}$

Total angular momentum is conserved.
$\Rightarrow {\omega }^{\prime }=\frac{I\omega -mvR}{(I+m{R}^2)}$.