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Chapter 11: Q3P (page 320)
Question: A 140Kghoop rolls along a horizontal floor so that the hoop鈥檚 center of mass has a speed of 0.150 m/s.How much work must be done on the hoop to stop it?
Answer
Work needed to stop the hoop is -3.15j .
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A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (Figure). A toy train of mass mis placed on the track and, with the system initially at rest, the train鈥檚 electrical power is turned on. The train reaches speedwith respect to the track. What is the angular speed of the wheel if its mass isand its radius is(Treat the wheel as a hoop, and neglect the mass of the spokes and hub.)
Question: Figure gives the speed vversus time tfor 0.500 kg a object of radius 6.00 cmthat rolls smoothly down a 30 0ramp. The scale on the velocity axis is set by vs = 4.0 m/sWhat is the rotational inertia of the object?
A rhinoceros beetle rides the rim of a horizontal disk rotating counterclockwise like a merry-go-round. If the beetle then walks along the rim in the direction of the rotation, will the magnitudes of the following quantities (each measured about the rotation axis) increase, decrease, or remain the same (the disk is still rotating in the counterclockwise direction): (a) the angular momentum of the beetle鈥揹isk system, (b) the angular momentum and angular velocity of the beetle, and (c) the angular momentum and angular velocity of the disk? (d) What are your answers if the beetle walks in the direction opposite the rotation?
A bowler throws a bowling ball of radius along a lane. The ball (in figure) slides on the lane with initial speed and initial angular speed . The coefficient of kinetic friction between the ball and the lane is. The kinetic frictional forceacting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed has decreased enough and angular speed v has increased enough, the ball stops sliding and then rolls smoothly.
(a) What then is in terms ofV? During the sliding (b) What is the ball鈥檚 linear acceleration (c) What is the angular acceleration? (d) How long does the ball slide? (e) How far does the ball slide? (f) What is the linear speed of the ball when smooth rolling begins?
Forceacts on a particle with position vector. (a) What is the torque on the particle about the origin, in unit-vector notation? (b) What is the angle between the directions of and?
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