(b) On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman's moment of inertia about the axis of rotation is 5.00 kg-m² and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any

(II) A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s . Its total moment of inertia is 1360 kg.m2 Four people standing on the ground, each of mass 65 kg, suddenly step onto the edgeof the merry-go-round. (a) What is the angular velocity of the merry-go-round now? (b) What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?

(II) Figure 11–35 shows two masses connected by a cord passing over a pulley of radius R, and moment of inertia I. Mass MA slides on a frictionless surface, and Mg hangs freely. Determine a formula for (a) the angular momentum of the system about the pulley axis, as a function of the speed v of mass MA or Mg, and (b) the accelera- MA tion of the masses. MB FIGURE 11-35 Problem 41.