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Chapter 12: Q. 21 (page 331)
The axle in FIGURE EX12.21 is half the distance
to the rim. What is the net torque about the axle? II
sd
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A 12-cm-diameter CD has a mass of 21g. What is the CD's moment of inertia for rotation about a perpendicular axis (a) through its center and (b) through the edge of the disk?
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鈥檚 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鈥檚 speed at point b?
c. What is the satellite鈥檚 speed at point c?
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?
A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in Figure P12.60. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?
A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg, 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 66 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. What is her new angular velocity, in rev/s?
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