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

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Q. 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:

BHUBHU 2004

Solution:

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.