Question

A circular disc is rotating with angular velocity $\omega$ If a man standing at the edge of the disc walks towards its center, then the angular velocity of the disc:

• A. is not changed
• B. be halved
• C. decreases
• D. increases

Answer 1

Answer: (D)

If $M$ is mass of disc, $R$ is radius then moment of inertia is

$I=\frac{1}{2}M{R}^2$
From law of conservation of angular momentum
$J=I\omega =\text{ constant }$
where, $\omega$ is angular velocity.
Hence, if $I$ decreases $\omega$ increases and vice versa.
$J=\frac{1}{2}M{R}^2\omega =$ constant
When man standing at the edge of the disc walks towards its center, $R$ decreases, hence angular velocity increases.