Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 2.96 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 0.91 m from the axis of rotation and the student rotates with an angular speed of 0.741 rad/s. The moment of inertia of the student plus stool is 2.67 kg. m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.304 m from the rotation axis (Figure b). 00; f 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 = Kafter = Need Help? Read It Watch It

Answer 1

F F2 3 0.304² Initial moment of inestia 2.67 +2mn² T; = 2.67+ 2x2.96x0.92 Ij = 7.57 kom? Final moment of inostia Is = 2.67 + 2x2.96% 0. 3.22 kg m² initial ongular speed wi= 0.741 rodis using angular momentum conservation Li Is Wi f 7.57xo.741=3.22 Wf wf = 1.74 radis - = If we - (b) К. I; w? before = 1/2 x 7.570.742 2.08 J Kasser = 2 Is up? = 1/2 * 3.22 x 1.74 - 4.87 J