Question:
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
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
Updated On: Sep 3, 2024
- $2I$
- $3I$
- $I/2$
- $I/3$
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The Correct Option is A
Solution and Explanation
Here, angular momentum is conserved.
Initial angular momentum = Final angular momentum
$I \times 20 = I' \times 10$, where $I'$ is new moment of inertia
$\therefore I' = 2I$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.