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 ω. If the cockroach stops, the angular velocity of the disc will be

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 ω. If the cockroach stops, the angular velocity of the disc will be

(a) $\frac{I \omega }{I + m R^2}$

(b) $\frac{I \omega + m v R}{I + m R^2}$

(c) $\frac{I \omega – m v R}{I + m R^2}$

(d) $\frac{I \omega + m v R}{I }$

Ans: (c)

Sol: On Applying conservation of Angular momentum

$I_1 \omega_1 = I_2 \omega_2$

$I \omega – m v R = ( I + m R^2 )\omega_2$

$\omega_2 = \frac{I \omega – m v R}{I + m R^2}$