A student sits on a rotating stool holding two 3.0-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.0-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 in the objects horizontally to 0.30 m from the rotation axis. (a) Find the new angular speed of the student. (b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation / Answer

By using conservation of angular momentum,

There are no external forces acting on the system, so angular momentum is conserved

L1 = L2

I1w1 = I2w2

(3 + 2*3*1^2)*0.75 = (3 + 2*3*0.3^2)*w2

w2 = (3 + 2*3*1^2)*0.75/(3 + 2*3*0.3^2)

= 1.9 rad/s

By decreasing the moment of inertia, the student is able to spin faster

Rotational KE = 1/2 I w^2,

So, KE1 =1/2 I1 (w1)^2

= 1/2*(3 + 2*3*1^2)*0.75^2 (7)(0.75)^2

= 2.53 J

KE2 = 1/2 I2 (w2)^2

= 1/2*(3 + 2*3*0.3^2)*1.9^2

= 6.39 J

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