A student sits on a freely rotating stool holding two weights, each of mass 2.93

Question

A student sits on a freely rotating stool holding two weights, each of mass 2.93 kg. When his arms are extended horizontally, the weights are 1.03 m from the axis of rotation and he rotates with an angular speed of 0.754 rad/s. The moment of inertia of the student plus stool is 2.93 kg·m2 and is assumed to be constant. The student pulls the weights inward horizontally to a position 0.291 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

Itotal   = 2mr2 + 3 kg m2

Ii       = 2*2.93*1.032 + 2.93 kg m2

Ii = 8.98 kg m2

Ki = ½ Iiwi2

Ki = ½ 8.98(0.754)2

Ki =2.55J

If = 2*2.93*0.2912 + 2.93 kg m2

If = 4.64 kg m2

Angular momentum is conserved

Li       = Lf             

Iiwi    = Ifwf

8.98(.754) = 4.64(wf)

wf = 1.46 rad / sec

Kf = ½ Ifwf2

Kf = ½ 4.64(1.46)2

Kf = 4.84 J

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