Question

A skater is doing skating with his arms stretched out, as soon he brings his arm closed to his body, his rotation speed increases significantly. Explain this phenomenon in the light of law of conservation of angular momentum.

Answer 1

According to law of conservation of angular momentum,

The angular momentum of a system around is conserved if there is no net external torque is acting on it.

Similarly, we can consider the angular mopmentum is conserved for the skater as no net external torque is acting on him.

we know, angular mpmentum [Where I= moment of inertia of the skater with respect to the axis of rotation and = angular velocity ]

Let, and be the angular momentum of the skater when his arms are stretched and when he brings his arms closer to his body respectively.

By angular momentum conservation law,

Hence, [The primed quantities refer to the situation when he pulls his arms closer]

Now, we know moment of inertia [r= distance of masses from axis of rotation]

As the skater draws his arms closer to his body, r becomes smaller and hence moment of inertia becomes smaller; i.e.

must be greater than . . [As, ]

If the shater brings his arms closer, his rotation speed increases significantly.