Ballet Dancer and Angular Velocity – Rankers Physics
Topic: Rotational Motion
Subtopic: Angular Momentum and Conservation of Angular Momentum

Ballet Dancer and Angular Velocity

Assertion (A): A ballet dancer increases or decreases the angular velocity of spin, about the vertical axis by pulling in or extending out her limbs.
Reason (R): \(L = I\omega\) which is constant about rotational axis where symbols have their usual meaning.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true: A ballet dancer changes her moment of inertia \(I\) by adjusting her body posture. Reason (R) is true: Angular momentum \(L = I\omega\) is conserved in the absence of external torque. Therefore, as \(I\) changes, \(\omega\) must change inversely to keep \(L\) constant. R is the correct explanation of A.

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