014 (part 1 of 2) 10.0 points A student sits on a rotating stool holding two 1.6

Question

014 (part 1 of 2) 10.0 points A student sits on a rotating stool holding two 1.6 kg masses. When his arms are extended horizontally, the masses are 0.74 m from the axis of rotation, and he rotates with an angu lar velocity of 1.8 rad/sec. The student then pulls the weights horizontally to a shorter dis- tance 0.39 m from the rotation axis and his angular velocity increases to u2 angular velocity increases to w. For simplicity, assume the student himself plus the stool he sits on have constant com- bined monent of inertia Is 4.9 kg m2

Explanation / Answer

Using the conservation of angular momentum.

Is*Wi + I*Wi = Is*Wf + I'*Wf

4.9*1.8 + 2(1.6*0.74^2)1.8=(4.9+ 3.2*(0.39^2)*Wf

Then Wf=2.2 rad s^-1

Increase enrgy = 0.5 (Ii*Wi^2 - If*Wf^2)

=0.5((4.9+3.2(0.74^2)1.8^2 -(4.9+3.2(0.39^2)2.2^2

=l21.55-26.10l*0.5

=2.55j

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