speed A student sits on e rotating stool holding two 2.2-kg objects. When his ar

Question

speed A student sits on e rotating stool holding two 2.2-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 of o.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 in the objects horizontally to 0.42 m from the rotation axis (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student before and after the objects are pulled in. before after

Explanation / Answer

Initial moment of inertia is that of the student & stoolplus the two masses:

   Ii = 3.0 + 2.2*1.02 + 2.2*1.02 = 7.4 kgm2

Final moment of inertia is same idea, but the masses arecloser:

   If = 3.0 + 2.2*0.422 + 2.2*0.422 = 3.77 kgm2

Now, since angular momentum is conserved:

    Ii i =   If f        

      7.4 * 0.75   = 3.77 *       or   final = 1.47 rad/s

initial KE = (1/2) I 2 = (1/2) * 7.4 * 0.752 = 2.08J

final KE = (1/2) I 2 = (1/2) * 3.77 * 1.472 = 4.07J

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