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Chapter 12: Q. 19 (page 331)
In FIGURE EX12.19, what magnitude force provides net torque about the axle?
The magnitude of the force is
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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?
The axle in FIGURE EX12.21 is half the distance
to the rim. What is the net torque about the axle? II
The earth鈥檚 rotation axis, which is tilted 23.5颅 from the plane of the earth鈥檚 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鈥檚 rotation axis traces out a 23.5颅 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 惟=饾湉/蠅. Although we derived this equation for a specific situation, it鈥檚 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?
Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation
about a perpendicular axis through the center.
An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60rpm to 90 rpm in 10s .
a. What is the tangential acceleration of the pedal?
b. What length of chain passes over the top of the sprocket during this interval?
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