Question

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 ·
m^{2} 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
*ω*_{i}. - In figure (b), the man's arms are pulled in so the dumbbells
are close to his body. He is rotating with angular speed
*ω*_{f}>*ω*_{i}.

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.

rad/s

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

K_{before} |
= J |

K_{after} |
= J |

Answer #1

A student sits on a freely rotating stool holding two dumbbells,
each of mass 2.98 kg. When his arms are extended horizontally, the
dumbbells are 0.94 m from the axis of rotation and the student
rotates with an angular speed of 0.752 rad/s. The moment of inertia
of the student plus stool is 2.79 kg · m2 and is assumed to be
constant. The student pulls the dumbbells inward horizontally to a
position 0.308 m from the rotation axis.
(a)...

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