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  4. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of 20 rad/s. When she stretches her arms fully, the spinning speed decrease as 10 rad/s. If I is the initial moment of inertia of the dancer, the new moment of inertia is

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Q. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of $20 \,rad/s$. When she stretches her arms fully, the spinning speed decrease as $10\, rad/s$. If $I$ is the initial moment of inertia of the dancer, the new moment of inertia is

System of Particles and Rotational Motion

Solution:

Here, angular momentum is conserved.
Initial angular momentum = Final angular momentum
$I \times 20 = I' \times 10$, where $I'$ is new moment of inertia
$\therefore I' = 2I$