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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 center, then the angular velocity of the disc:

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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 center, then the angular velocity of the disc:

AFMCAFMC 2002

Solution:

If $M$ is mass of disc, $R$ is radius then moment of inertia is
image
$I=\frac{1}{2} M R^{2}$
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.