A ballet dancer spins about a vertical axis at 90 rpm with arms outstretched. With the arms folded. the moment of inertia about the same axis of rotation changes to 75%. Calculate the new speed of rotation.
(Ans: 120 rpm)
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Given:
Angular velocity = 90 rpm
Moment of inertia = 75 %
To find:
The new speed.
Solution:
By the law of conservation of angular momentum,
3 / 4 ( Inertia ) New angular velocity = Inertia * Angular velocity
Substituting,
And cancelling Inertia on both sides,
We get,
3 / 4 New angular velocity = 90
New angular velocity = 90 * 4 / 3
New angular velocity = 120 rpm
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