A student sits on a freely rotating stool holding two weights, each of mass 3.05

Question

A student sits on a freely rotating stool holding two weights, each of mass 3.05 kg. When his arms are extended horizontally, the weights are 0.92 m from the axis of rotation and he rotates with an angular speed of 0.742 rad/s. The moment of inertia of the student plus stool is 3.05 kg m2 and is assumed to be constant. The student pulls the weights inward horizontally to a position 0.292 m from the rotation axis. a) Find the new angular speed of the student. differs from the correct answer by more than 100%, rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the weights inward Your response differs from the correct answer by more than 10%. Double check your calculations.) (before) ) (after)

Explanation / Answer

initial moment of inertia, Ii = (3.05) + 2(3.05 x 0.92^2)

= 8.213 kg m^2

final moment of inertia, If = (3.05) + 2(3.05 x 0.292^2)

= 3.57 kg m^2

wi = 0.742 rad/s

Applying angular momentum conservation,

Ii wi = If wf

wf = 1.71 rad/s

(B) Kbefore = Ii wi^2 /2 = 2.26 J  

Kafter = If wf^2 /2 = 5.22 J

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