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 2.95 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 0.98 m from the axis of rotation and the student rotates with an angular speed of 0.749 rad/s. The moment of inertia of the student plus stool is 2.53 kg·m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.296 m from the rotation axis (Figure b). of (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 Kbefore Kafter-

Explanation / Answer

we will conserve L ( angular momentum = Iw)

I1w1 = I2w2

( 2.53 + 2x 2.95 x 0.98^2) 0.749 rad/ s= ( 2.53 + 2x 2.95 x 0.296^2) w2

6.139 = 3.04 w2

w2= 2 rad/sec appprx

KE before = 1/2 I w^2= 2.3 J apprx

KE after = 0.5 I2 w2^2= 6.1 J apprx

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