Question

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

• A. Decrease
• B. Increase
• C. Be halved
• D. Not change

Answer 1

Answer: (B)

When no external force acts on a body its angular momentum remains conserved.
From law of conservation of angular momentum, we have
$J=I\omega =$ constant
Where $I$ is moment of inertia of the body and $\omega$ is angular velocity .
Also $I=\frac{1}{2}M{R}^2$ (for disc) where $M$ is mass and $R$ is radius of disc.
$\therefore J=\frac{1}{2}M{R}^2\omega =$ constant
Since, man moves towards the center of the disc, distance of mass distribution $R$ decreases hence, so $\omega$ increases.