Conservation Of Angular Momentum

Question

A skater decreases moment of inertia from 4 to 1 kg·m². Initial ω = 3 rad/s. Final ω?

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1. **Conservation Law**: If no external torque acts on a system, the total angular momentum $\vec{L}$ remains constant.
2. **Mathematical Form**: $L = I_1 \omega_1 = I_2 \omega_2$.
3. **Scenario Analysis**: By pulling her arms in, the skater decreases $I$. To keep $L$ constant, $\omega$ must increase.
4. **Calculation**:
   - $4 	ext{ kg·m}^2 	imes 3 	ext{ rad/s} = 1 	ext{ kg·m}^2 	imes \omega_2 $
   - $12 = 1 	imes \omega_2 \implies \omega_2 = 12 	ext{ rad/s}$.
5. **Significance**: This explains how spinning objects speed up when they become more compact.

Conservation Of Angular Momentum

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