Question

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. $\frac{I\omega }{I+m{R}^2}$
• 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 $\frac{I\omega -mvR}{I+m{R}^2}$

Let clockwise be positive

Initial angular Momentum $=Iw+m(-V)R$

$=Iw-mVR$

Let finally . common angular

velocity = $w^1$(clockwise)

So, Final angular Momentum $=(I+m{R}^2)w^1$

By,angular Momentum conservation :-

$Iw-mVR=(I+m{R}^2)w^1$

$w^1=\frac{Iw-mvR}{I+m{R}^2}$

option (C)