A child is standing with folded hands at the centre of a...

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child now stretches his arms so that the moment of inertia of the system becomes doubled. The kinetic energy of the system now is: (a) $2 K$ (b) $\mathrm{K} / 2$ (c) $K / 4$ (d) $4 K$

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child now stretches his arms so that the moment of inertia of the system becomes doubled. The kinetic energy of the system now is:
(a) $2 K$
(b) $\mathrm{K} / 2$
(c) $K / 4$
(d) $4 K$

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Key Concepts

Conservation of Angular Momentum

This principle states that if no external torques act on a system, the total angular momentum remains constant. In problems involving rotational motion, changes in the distribution of mass (and thus the moment of inertia) lead to compensatory changes in the angular velocity to ensure angular momentum is conserved.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. When the mass distribution changes, such as by extending or retracting arms, the moment of inertia changes, affecting the angular velocity while conserving angular momentum.

Rotational Kinetic Energy

The kinetic energy in a rotating system is given by the formula K = (1/2)I?², where I is the moment of inertia and ? is the angular velocity. Changes in the moment of inertia and angular velocity due to conserved angular momentum directly affect the rotational kinetic energy of the system.

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