Suppose an object is rotating. It has an angular momentum defined as the product

Question

Suppose an object is rotating. It has an angular momentum defined as the product of the moment of inertia times the angular velocity. As long as no net external torque acts on the object, its angular momentum will stay the same. But what if the moment of inertia changes? In order to keep the same angular momentum, the angular velocity will adjust.

Suppose a figure skater is spinning with an initial angular speed of 3.10 rad/s. She then pulls her arms in, reducing her moment of inertia from a value of 1.88 kg·m/s to a value of 0.880 kg·m/s. What is her angular speed after pulling in her arms?

Explanation / Answer

given,

initial angular velocity = 3.1 rad/sec

initial moment of inertia = 1.88 kg .m^2

final moment of inertia = 0.88 kg m^2

by conservation of momentum

initial momentum = final momentum

1.88 * 3.1 = 0.88 * v

v = 6.62 rad/sec

angular speed after pulling arms = 6.62 rad/sec

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