Answer to Question #250772 in Physics for prettygirl

Question

The moment of inertia of a dancer is 7. 0 𝑘𝑔 𝑚 when she performs 48 rotations per minute with both arms outstretched. The moment of inertia reduces to 2. 2 𝑘𝑔 𝑚 when she wraps her arms around her body. Calculate the new number of rotations per second

Answer 1

To calculate the new number of rotations per second, apply conservation of angular momentum:

$$I_1\omega_1=I_2\omega_2,\\\space\\ I_1n_1=I_2n_2,\\\space\\ n_2=n_1\frac{I_1}{I_2}=48·\frac{7}{2.2}=153\text{ rpm}.$$