Question

A skater rotating about a vertical axis pulls her arms inward. Ignoring all frictional effects, which of the following statements are true? Denote the magnitude of her angular velocity by $\omega$, the magnitude of her angular momentum by $L$, and her kinetic energy by $E_k$.

• A. $L$ is constant, $E_k$ increases
• B. $L$ is constant, $\omega$ increases
• C. $L$ and $E_k$ are both constant
• D. $L$ and $\omega$ both constant

Answer 1

Answer: (A), (B)

The correct options are
A $L$ is constant, $E_k$ increases
B $L$ is constant, $\omega$ increases

In the absence of any external torque, $L=Iw=constant$

Thus folding her arms inwards will decrease moment of inertia which according to the conservation of L, will increase $w$.

Now $E_k=\frac{1}{2}I{w}^2$

Thus increasing $w$ will also increase $E_k$.