A student sits on a freely rotating stool holding two dumbbells, each of mass 2.

Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 2.93 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 0.99 m from the axis of rotation and the student rotates with an angular speed of 0.746 rad/s. The moment of inertia of the student plus stool is 2.77 kg · m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.299 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

Angular momentum is conserved

I . w = ( 2.77 + (2 . 2.93 . 0.99^2)) . 0.746 = 6.35 kgm^2/s

I (new) . w(new) = 6.35 = (2.77 + (2 . 2.93 . 0.299^2)) . w(new)

(a) w(new) = 1.93 rad/s

b) Kinetic Energy before = 1/2 . I . w^2 = 0.5*(( 2.77 + (2 . 2.93 . 0.99^2))*0.746^2 = 2.369 J

Kinetic energy after = 1/2 . I . w^2 = 0.5*((2.77 + (2 . 2.93 . 0.299^2))*1.93^2 = 6.134 J

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