A person, with outstretched arms, is spinning on a rotating...

A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which of the following is true about his kinetic energy $K$ and angular momentum $L ?$ (a) Both $\mathrm{K}$ and $L$ increase (b) Both $\mathrm{K}$ and $L$ remain unchanged (c) $\mathrm{N}$ remains constant, $L$ increases (d) $\lambda$ increases but $L$ remains constant

A person, with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which of the following is true about his kinetic energy $K$ and angular momentum $L ?$
(a) Both $\mathrm{K}$ and $L$ increase
(b) Both $\mathrm{K}$ and $L$ remain unchanged
(c) $\mathrm{N}$ remains constant, $L$ increases
(d) $\lambda$ increases but $L$ remains constant

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Key Concepts

Angular Momentum Conservation

This principle states that in the absence of external torques, the total angular momentum of a system remains constant. When the person on the stool brings his arms inward, there is no external torque acting on him, hence his angular momentum is conserved even though his moment of inertia changes.

Moment of Inertia

Moment of inertia quantifies how mass is distributed relative to the axis of rotation. With arms extended, the moment of inertia is higher, and when the arms are brought closer to the body, this value decreases. This change is critical as it dictates how the angular velocity must adjust to conserve angular momentum.

Rotational Kinetic Energy

Rotational kinetic energy depends on both the moment of inertia and the square of the angular velocity. When a person pulls their arms inwards, although angular momentum is conserved, the decrease in moment of inertia causes an increase in angular velocity, which in turn raises the kinetic energy of the system.

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