42. An obiect's moment ot'inertia is 2.0 kg m3. Its angular velocity is increasing at the rate of4.0 radfs. What is the net torque on the object? 43. A 200 g, 20 cm diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1800 rpm in 4 s? 120 rpm 44. What is the magnitude of the angular momentum of the 720 g bar rotated at 120 rpm about its center with a length of2 m? 45. A uniform bar has length 0.8 In. The bar begins to rotate from rest about the axis passing '2 N through the left end. What will the magnitude ofthe angular momentum be 6 seconds after 02 the motion has begun? A a N 46. In the gure above, a piece ofelay starting from rest falls from rest a height h and sticks to a wheel that is free to rotate on a low-friction axle at location A. Several different possible locations for the collision are shown, each with the same momentum of the clay just before it hits and sticks. a. In which case will the device rotate fastest? Explain. b. [n which case will the device not rotate at all? Explain If we increase the mass of the clay, how will that affect the rotation of the device? Explain 57 d. If the clay is going faster just before it sticks to the ball, how will that affect the rotation of the device? Explain 34. What is the angular momentum of a 0.25 kg mass rotating on the end of a piece of rope in a circle of radius 0.75m at an angular speed of 12.5 rad/s? 35. A bowling ball has a mass of 5.5 kg and a radius of 12.0 cm. It is released so that it rolls down the alley at a rate of 12 rev/s. Find the magnitude of its angular momentum. 36. A figure skater rotates on ice at a rate of 3.5 rad/s with her arms extended horizontally. When she lowers her arms to her side, she speeds up to 7.5 rad/s. Find the ratio of her moment of inertia in the first case to that in the second case. 37. A disk has a mass of 3.5 kg and radius of 15 cm is rotating with an angular speed of 94.2 rad/s when a second non- rotating disk of 5.0 kg, mounted on the same shaft is dropped onto it. If the second disk has a diameter of 18 cm and a mass of 5.0 kg, what is the common final angular speed of the system? 38. If the total angular momentum of a system of particles is zero, are all the particles at rest? Explain. 39. If the total angular momentum of a system is constant, does this mean that no net force acts on the system? Explain 40. A student whose mass is 60 kg is standing on the edge of a circular merry-go- round facing inward. The merry-go- round has a mass of 100 kg and a radius of 2.0 m and spins at a rate of 2 rad/s. The student walks slowly from the outer edge toward the center and stops at a distance of 0.50m from the center. Calculate the magnitude of the angular velocity of the system. (treat merry go round as a solid disk/cylinder) 41. A figure skater spinning at 3.4 rad/sec with a moment of inertia of 3.2 Kgm puts his arms out so that his new moment of inertia is 4.5 Kgm'. What is his new angular speed