Part 1 of 2 .
Moment of inertia of Student with Stool ; Is = 4 kg-m2
When there are 2 objects of 4 kg each at radius 0.7m, it will add moment of inertia of the system; so, total moment of inertia will be
I1 = Is + 2* 4 * (0.7)2 = 4 + 8* 0.49 = 7.92 kg-m2
Angular speed ω1 = 0.69 rad/s
When arms are pulled and objects are at 0.29 m distance, total moment of inertia will be
I2 = Is + 2* 4 * (0.29)2 = 4 + 8* 0.0841 = 4.6728 kg-m2
As the angular momentum is conserved , we will have
I1ω1 = I2ω2 ; where ω2 is Angular speed in second case
ω2 = I1ω1 /I2 = 7.92 * 0.69 / 4.6728 = 1.17 rad/s
Part 2 of 2
Change in Kinetic energy will be given as
(1/2) I2ω22 - (1/2) I1ω12
= (1/2) * 4.6728 * 1.172 - (1/2) * 7.92 * 0.692
= 1.31 J
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