A student sits on a rotating stool holding two 2.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg·m2 and is assumed to be constant. The student then pulls the objects horizontally to 0.40 m from the rotation axis.

(a) Find the new angular speed of the student.
(b) Find the kinetic energy of the student system before and after the objects are pulled in.

Explanation / Answer

Iw needs to remain constant (angular momentum) (3+2*1)*0.75=3.75 (3+2*.4)*w=3.75 3.75/(3+2*.4)=0.986=w 1/2*I*w^2=KE 1/2*5*.75^2=1.41 (KE before) 1/2*(3+2*.4)*.986^2=1.85 (KE after)

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