A person sits on a freely spinning lab stool (no friction). When this person extends her arms,
A) her moment of inertia decreases and her angular velocity increases.
B) her moment of inertia decreases and her angular velocity decreases.
C) her moment of inertia increases and her angular velocity increases.
D) her moment of inertia increases and her angular velocity decreases.
E) her moment of inertia increases and her angular velocity remains the same.

Question

Quizplus · Accepted Answer

When the person extends her arms, her moment of inertia increases because the mass is farther away from the axis of rotation. However, her angular momentum must be conserved, so her angular velocity must decrease to compensate for the increase in moment of inertia. This can be seen in the equation L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity. If I increases, ω must decrease to maintain the same value of L.

A Person Sits on a Freely Spinning Lab Stool (No