If a person standing on a rotating disc stretches out his hands, the angular speed will

When a person standing on a rotating disc stretches out his hands, his angular speed decreases. This is because of the law of conservation of angular momentum, where the angular momentum of a system remains the same if no external torque acts on it.

Angular momentum is the product of the moment of inertia and angular velocity. If he stretches his arms out to his sides, the person increases his moment of inertia, as the mass distribution moves farther from the axis of rotation. In order to conserve angular momentum, the angular velocity-or angular speed-must decrease correspondingly.

This principle is often seen in figure skating or gymnastics. A spinning skater can raise his speed by retracting his arms so that he reduces his moment of inertia and increases his angular velocity. He slows down if he stretches out his arms.

This principle also applies to many real-world circumstances, such as athletes using body movements to control rotational speed or space probes adjusting the orientation of their trajectory in space. In such a case, by extending their arms, the moment of inertia is increased, leading to a decrease in angular velocity to keep angular momentum constant.

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