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Chapter 12: Q. 34 (page 331)
A 500g, 8-cm-diameter can is filled with uniform, dense food. It rolls across the floor at 1.0 m/s. What is the can's kinetic energy?
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The marble rolls down the track shown in FIGURE P12.75 and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?
35. II An 8.0-cm-diameter, 400g solid sphere is released from rest at the top of a 2.1-m-long, incline. It rolls, without slipping, to the bottom.
a. What is the sphere's angular velocity at the bottom of the incline?
b. What fraction of its kinetic energy is rotational?
The earth’s rotation axis, which is tilted 23.5 from the plane of the earth’s orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earth’s rotation axis traces out a 23.5 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge, which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written Ω=𝜏/ω. Although we derived this equation for a specific situation, it’s a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?
A thin, uniform rod of length L and mass M is placed vertically on a horizontal table. If tilted ever so slightly, the rod will fall over.
a. What is the speed of the center of mass just as the rod hits the table if there’s so much friction that the bottom tip of the rod does not slide?
b. What is the speed of the center of mass just as the rod hits the table if the table is frictionless?
The 20-cm-diameter disk in FIGURE EX12.20 can rotate on an axle through its center. What is the net torque about the axle?
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