Ballet Dancer and Angular Velocity – Rankers Physics

Angular Momentum and Conservation of Angular Momentum: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Angular Momentum and Conservation of Angular Momentum. Understanding the underlying formula is key to arriving at the correct answer below:

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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