Question

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a woman is sitting on a spinning piano stool with her arms folded. ignore any friction in the spinning stool. when she extends her arms outward, which of the following is true?
her angular speed decreases, and her angular momentum remains constant.
her angular speed decreases, and her angular momentum increases.
her angular speed increases, and her angular momentum remains constant.
her angular speed increases, and her angular momentum decreases.

Explanation:

When there is no external torque (friction is ignored), the angular momentum \(L = I\omega\) (where \(I\) is the moment of inertia and \(\omega\) is the angular speed) is conserved. When the woman extends her arms outward, her moment of inertia \(I\) increases. Since \(L = I\omega\) is constant (\(L_1 = L_2\), so \(I_1\omega_1=I_2\omega_2\)), if \(I_2>I_1\), then \(\omega_2 <\omega_1\) (angular speed decreases).

Answer:

Her angular speed decreases, and her angular momentum remains constant.