Question

# A student sits on a freely rotating stool holding two dumbbells, each of mass 2.91 kg...

A student sits on a freely rotating stool holding two dumbbells, each of mass 2.91 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.03 m from the axis of rotation and the student rotates with an angular speed of 0.758 rad/s. The moment of inertia of the student plus stool is 2.61 kg · m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.297 m from the rotation axis (Figure b).

Two figures depict a man holding a dumbbell in each hand while spinning on a rotating stool.

• In figure (a), the man's arms are fully extended so the dumbbells are far from his body. He is rotating with angular speed ωi.
• In figure (b), the man's arms are pulled in so the dumbbells are close to his body. He is rotating with angular speed ωf > ωi.

Two figures depict a man holding a dumbbell in each hand while spinning on a rotating stool.

(a) Find the new angular speed of the student.

(b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

 Kbefore = J Kafter = J

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