The Spinning Skater's Drop · AI Generator #GEN-EF50D294

Physics · mechanics

Problem

A figure skater performs a dramatic move where she spins with arms extended, then suddenly pulls her arms inward while simultaneously dropping a small sequin from her costume. The skater initially spins at ω0=2.0  rad/s\omega_0 = 2.0\;\text{rad/s} with her arms extended. When she pulls her arms in, her moment of inertia decreases from I1=3.2  kg⋅m2I_1 = 3.2\;\text{kg}\cdot\text{m}^2 to I2=1.6  kg⋅m2I_2 = 1.6\;\text{kg}\cdot\text{m}^2. At the exact moment she begins pulling her arms in, a sequin detaches from her costume at a distance r=0.80  mr = 0.80\;\text{m} from her center of rotation. From the perspective of a stationary observer watching the performance, what is the speed of the sequin immediately after it detaches from the skater?

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