A student sits on a freely rotating stool holding two dumbbells, each of mass 3.

Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.08 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.09 m from the axis of rotation and the student rotates with an angular speed of 0.755 rad/s. The moment of inertia of the student plus stool is 2.55 kg · m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.302 m from the rotation axis (Figure b).

(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 dumbbells inward.

Explanation / Answer

a) in this process, angular momentum will not change .

initial = final angular momentum

Ii wi = If wf

Ii = 2.55 + (2 x 3.08 x 1.09^2 ) = 9.87 kg m^2

If = 2.55 + (2 x 3.08 x 0.302^2) = 3.11 kg m^2

9.87 x 0.755 = 3.11 x wf

wf = 2.39 rad/s

b) Ki = Ii wi^2 /2 = 9.87 x 0.755^2 /2 = 2.81 J

Kf = If wf^2 /2 = 3.11 x 2.39^2 /2 = 8.88 J

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