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  4. A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its center. At some instant of time a viscous fluid of mass m is dropped at the center and is allowed to spread out and finally fall. The angular velocity during this period

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Q. A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its center. At some instant of time a viscous fluid of mass $m$ is dropped at the center and is allowed to spread out and finally fall. The angular velocity during this period

AIIMSAIIMS 2005System of Particles and Rotational Motion

Solution:

From law of conservation of angular momentum if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is $J=I \omega=$ constant Hence, if $I$ decreases, $\omega$ increases and viceversa. When liquid is dropped, mass increases hence $I$ increases $\left(I=m r^{2}\right)$. So, $\omega$ decreases, but as soon as the liquid starts falling $\omega$ increases again.