A student sits on a freely rotating stool holding two weights, each of mass 3.08

Question

A student sits on a freely rotating stool holding two weights, each of mass 3.08 kg. When his arms are extended horizontally, the weights are 0.90 m from the axis of rotation and he rotates with an angular speed of 0.741 rad/s. The moment of inertia of the student plus stool is 3.08 kg·m2 and is assumed to be constant. The student pulls the weights inward horizontally to a position 0.295 m from the rotation axis.

(a) Find the new angular speed of the student.
______ rad/s
(b) Find the kinetic energy of the rotating system before and after he pulls the weights inward.
______J (before)
______J (after)

Explanation / Answer

(a) Here, angular momentum is conserved

I . w = ( 3.08 + (2 . 3.08 . 0.90^2)) . 0.741 = 5.98 kgm^2/s

Again,

I (new) . w(new) = 5.98 = (3.08 + (2 . 3.08 . 0.295^2)) . w(new)

=> 5.98 = 3.62.w(new)

=> w(new) = 1.65 rad/s

(b) Initial K.E. = 1/2 .I . w^2 = 0.5*8.07*0.741^2 = 2.21 J

Final K.E. = 1/2 .I(new) . w(new)^2 = 0.5*3.62*1.65^2 = 4.93 J

Please note that here, the KE after is greater than the KE before, because the student does work pulling the weights inwards.

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