Chapter 12: Q. 36 (page 331)
A solid sphere of radius R is placed at a height of 30 cm on a slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius be released on the same slope in order to equal the sphere's speed at the bottom?
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A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain.
b. What is the satellite’s speed at point b?
c. What is the satellite’s speed at point c?
A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the top’s precession frequency in rpm?
A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a frictionless groove in the surface of the turntable. What is the turntable’s rotation angular velocity when the block reaches the outer edge?
The two blocks in FIGURE CP12.86 are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.50 N m. If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?
A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very
bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
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