Question

A physics teacher sits on a rotating stool to demonstrate the conversion of angular motion. with her arms stretched, she rotates at 0.75 rev/s. When teacher's arms are tucked in close in her chest, she rotates at 1.50 rev/s. What is the ratio of her moment of inertia with outstretched arms to the moment of inertia with arms tucked in to her chest?

Answer 1

Let's write the law of conservation of angular momentum:

$$L_{i}=L_{f},$$ $$I_{str.}\omega_{str.}=I_{tuck.}\omega_{tuck.},$$ $$\dfrac{I_{str.}}{I_{tuck.}}=\dfrac{\omega_{tuck.}}{\omega_{str.}}=\dfrac{1.50\ \dfrac{rev}{s}}{0.75\ \dfrac{rev}{s}}=2.$$

Answer:

$\dfrac{I_{str.}}{I_{tuck.}}=2.$