Question

if a gymnast rotates once each second while sailing through the air and contracts to reduce her rotational inertia to one - third of what it was, how many rotations per second will result? express your answer in rotations per second to one significant figure.

Explanation:

Step1: Recall the law of conservation of angular momentum

$L = I\omega$, where $L$ is angular momentum, $I$ is rotational - inertia and $\omega$ is angular velocity. Initially, $L_1=I_1\omega_1$, and finally $L_2 = I_2\omega_2$. Since there is no external torque, $L_1 = L_2$, so $I_1\omega_1=I_2\omega_2$.

Step2: Substitute the given relationship between rotational inertias

We know that $I_2=\frac{1}{3}I_1$ and $\omega_1 = 1$ rotation per second. Substituting into $I_1\omega_1=I_2\omega_2$, we get $I_1\times1=\frac{1}{3}I_1\times\omega_2$.

Step3: Solve for $\omega_2$

Dividing both sides of the equation $I_1=\frac{1}{3}I_1\omega_2$ by $\frac{1}{3}I_1$ (assuming $I_1
eq0$), we find $\omega_2 = 3$ rotations per second.

Answer:

3