A ballet dancer spins about a vertical axis at 1 rps with her arms stretched and with her arms folded, her moment of inertia about the axis decreases by 40%. Calculate the new rate of revolution

Ballerina Revolution Calculation

Formula: \( I_1 \omega_1 = I_2 \omega_2 \)

Given: \( \omega_1 = 1 \, \text{rps} \), \( I_2 = 0.6 I_1 \) (40% decrease)

Calculation: \( I_1 \cdot 1 = 0.6 I_1 \cdot \omega_2 \)

\( \omega_2 = \frac{I_1}{0.6 I_1} = \frac{1}{0.6} \approx 1.6667 \, \text{rps} \)

Result: 1.67 rps