A man stands on a rotating platform with his arms stretched...

A man stands on a rotating platform with his arms stretched holding a $5 \mathrm{~kg}$ weight in each hand. The angular speed of the platform is $1.2$ rev $\mathrm{s}^{-1}$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $6 \mathrm{~kg} \mathrm{~m}^{2}$. If the man brings his arms close to his chest with the distance of each weight from the axis changing from $100 \mathrm{~cm}$ to $20 \mathrm{~cm}$. The new angular speed of the platform is (a) 2 rev $s^{-1}$ (b) 3 rev $s^{-1}$ (c) $5 \mathrm{rev} \mathrm{s}^{-1}$ (d) 6 rev $\mathrm{s}^{-1}$

A man stands on a rotating platform with his arms stretched holding a $5 \mathrm{~kg}$ weight in each hand. The angular speed of the platform is $1.2$ rev $\mathrm{s}^{-1}$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $6 \mathrm{~kg} \mathrm{~m}^{2}$. If the man brings his arms close to his chest with the distance of each weight from the axis changing from $100 \mathrm{~cm}$ to $20 \mathrm{~cm}$. The new angular speed of the platform is
(a) 2 rev $s^{-1}$
(b) 3 rev $s^{-1}$
(c) $5 \mathrm{rev} \mathrm{s}^{-1}$
(d) 6 rev $\mathrm{s}^{-1}$

Key Concepts

Moment of Inertia

The moment of inertia quantifies how much a body resists rotational acceleration about a particular axis and depends on the distribution of the body's mass relative to that axis. When mass is moved closer to the axis, the moment of inertia decreases, which affects the rotational behavior of the system.

Conservation of Angular Momentum

This principle states that if no external torques act on a system, the total angular momentum remains constant. When the distribution of mass changes, such as pulling weights closer to the axis of rotation, the moment of inertia changes, leading to an inverse change in angular speed to maintain the same angular momentum.

Angular Speed

Angular speed is the rate at which an object rotates around an axis. In rotational systems with conserved angular momentum, changes in the moment of inertia will result in a compensatory adjustment in angular speed, so that the product of the moment of inertia and the angular speed remains constant.

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