A ballet dancer of mass 80 kg and a wingspan of 80cm is executing a spin. She then folds her arms and brings them to within 20 cm from the central axis of her body. If she was initially making 3 rotations per second, how many does she make now?

Explanation

To solve this problem, we use the principle of conservation of angular momentum, which states that the initial angular momentum must equal the final angular momentum in the absence of external torques. Mathematically, this is represented as:I1ω1 = I2ω2where I is the moment of inertia and ω is the angular velocity. The moment of inertia for a rotating body like a dancer is proportional to the square of the radius (r), so I = mr2. When the dancer folds her arms, the radius decreases from 80 cm to 20 cm, a factor of 4 reduction. Consequently, the angular velocity increases by the square of this factor, that is, 42 = 16 times. Thus, the new angular velocity is 3 rotations per second × 16 = 48 rotations per second.Options A (35 rotations per second), C (15 rotations per second), and D (6 rotations per second) provide incorrect results because they fail to apply the correct factor of increase in angular velocity based on the reduction in radius.