conservation of angular momentum

Question

A figure skater with arms extended has a moment of inertia of 4 kg·m² and rotates at 2 rad/s. When she pulls her arms in, her moment of inertia becomes 2 kg·m². What is her new angular velocity?

RankGuru · Accepted Answer

1. **Conservation Law**: If net external torque is zero, $L = I \omega$ remains constant.
2. **Equation**: $I_1 \omega_1 = I_2 \omega_2$.
3. **Application**:
   - $4 	imes 2 = 2 	imes \omega_2$.
   - $8 = 2 \omega_2$.
4. **Result**: $\omega_2 = 4$ rad/s.
5. **Concept**: By pulling arms in, the mass is distributed closer to the axis, reducing $I$ and forcing $\omega$ to increase to keep $L$ conserved.

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conservation of angular momentum

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