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A student sits on a freely rotating stool holding two dumbells....find the new a

ID: 2032233 • Letter: A

Question

A student sits on a freely rotating stool holding two dumbells....find the new angular speed of the student.

A student sits on a freely rotating stool holding two dumbbells, each of mass 2.99 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 0.755 rad/s. The moment of inertia of the student plus stool is 2.51 kg m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.295 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. Kbefore Katter-

Explanation / Answer

a) m = 2.99 kg, r = 0.99 m, w = 0.755 rad/s, I = 2.51 kg.m2, r1 = 0.295 m

I ' = I + 2 m r2 = 2.51 + (2 * 2.99 * 0.992) = 8.37 kg.m2

I" = I + 2 m r12 = 2.51 + (2 * 2.99 * 0.2952) = 3.03 kg.m2

new angular speed w1 = I ' * w / I " = 8.37 * 0.755 / 3.03

new angular speed = 2.08 rad /s

b) KEbefore = 1/2 * I' * w2

= 1/2 * 8.37 * 0.7552= 2.38 J

KEafter = 1/2 I" * w12

= 1/2 * 3.03 * 2.082 = 6.55 J