A student sits on a rotating stool holdingtwo 5 kg objects. When his arms are ex

Question

A student sits on a rotating stool holdingtwo 5 kg objects. When his arms are extendedhorizontally, the objects are 0.9 m from the axis of rotation,and he rotates with angular speed of 0.66 rad/sec. The moment of inertiaof the student plus the stool is 8 kg.m2 and is assumed to be constant. The student then pulls theobjects horizontally to a radius 0.31 m from the rotationaxis.

Calculate the change in kinetic energy of the system.Ignore the difference in the moment of inertia contributed by thetwo different arm shapes.

Explanation / Answer

Let w be the final angular velocity. Equating angular momentum before and after: (2 * 5 * 0.9^2 + 8)0.66 = (2 * 5 * 0.31^2 + 8)w w = (2 * 5 * 0.9^2 + 8)0.66 / (2 * 5 * 0.31^2 + 8) = 1.186 rad/s. The change in KE is: (1/2)[ (2 * 5 * 0.31^2 + 8)1.186^2 - (2 * 5 * 0.9^2 + 8)0.66^2] = 5.591 J.

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