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Figure 8-27
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8 Rotational Motion For more problems, go to Additional Problems, Appendix B
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91 Basketball A basketball is rolled down the court
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A regulation basketball has a diameter of 241 cm, a mass of 060 kg, and a moment of inertia of 58 10 3 kg m2 The basketball s initial velocity is 25 m/s a What is its initial angular velocity b The ball rolls a total of 12 m How many revolutions does it make c What is its total angular displacement
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97 The second hand on a watch is 12 mm long What
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is the velocity of its tip
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98 Lumber You buy a 244-m-long piece of 10 cm
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10 cm lumber Your friend buys a piece of the same size and cuts it into two lengths, each 122 m long, as shown in Figure 8-29 You each carry your lumber on your shoulders a Which load is easier to lift Why b Both you and your friend apply a torque with your hands to keep the lumber from rotating Which load is easier to keep from rotating Why
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92 The basketball in the previous problem stops rolling
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after traveling 12 m a If its acceleration was constant, what was its angular acceleration b What torque was acting on it as it was slowing down
244 m
93 A cylinder with a 50 m diameter, as shown in
Figure 8-28, is at rest on a surface A rope is wrapped around the cylinder and pulled The cylinder rolls without slipping a After the rope has been pulled a distance of 250 m at a constant speed, how far has the center of mass of the cylinder moved b If the rope was pulled a distance of 250 m in 125 s, how fast was the center of mass of the cylinder moving c What is the angular velocity of the cylinder
122 m 122 m
Figure 8-29
99 Surfboard Harris and Paul carry a surfboard that
is 243 m long and weighs 143 N Paul lifts one end with a force of 57 N a What force must Harris exert b What part of the board should Harris lift
100 A steel beam that is 650 m long weighs 325 N
50 m
It rests on two supports, 300 m apart, with equal amounts of the beam extending from each end Suki, who weighs 575 N, stands on the beam in the center and then walks toward one end How close to the end can she come before the beam begins to tip
Figure 8-28
Thinking Critically
101 Apply Concepts Consider a point on the edge of
a rotating wheel a Under what conditions can the centripetal acceleration be zero b Under what conditions can the tangential (linear) acceleration be zero c Can the tangential acceleration be nonzero while the centripetal acceleration is zero Explain d Can the centripetal acceleration be nonzero while the tangential acceleration is zero Explain
94 Hard Drive A hard drive on a modern computer
spins at 7200 rpm (revolutions per minute) If the drive is designed to start from rest and reach operating speed in 15 s, what is the angular acceleration of the disk
95 Speedometers Most speedometers in automobiles
measure the angular velocity of the transmission and convert it to speed How will increasing the diameter of the tires affect the reading of the speedometer
96 A box is dragged across the floor using a rope that is
a distance h above the floor The coefficient of friction is 035 The box is 050 m high and 025 m wide Find the force that just tips the box
physicsppcom/chapter_test
102 Apply Concepts When you apply the brakes in a
car, the front end dips Why
8 Assessment
103 Analyze and Conclude A banner is suspended
from a horizontal, pivoted pole, as shown in Figure 8-30 The pole is 210 m long and weighs 175 N The banner, which weighs 105 N, is suspended 180 m from the pivot point or axis of rotation What is the tension in the cable supporting the pole
105 Analyze and Conclude Gerald and Evelyn carry
the following objects up a flight of stairs: a large mirror, a dresser, and a television Evelyn is at the front end, and Gerald is at the bottom end Assume that both Evelyn and Gerald exert only upward forces a Draw a free-body diagram showing Gerald and Evelyn exerting the same force on the mirror b Draw a free-body diagram showing Gerald exerting more force on the bottom of the dresser
Cable
Axis of rotation 105 m 180 m 210 m
Center of mass
c Where would the center of mass of the television have to be so that Gerald carries all the weight
250
Writing in Physics
106 Astronomers know that if a satellite is too close to
a planet, it will be torn apart by tidal forces That is, the difference in the gravitational force on the part of the satellite nearest the planet and the part farthest from the planet is stronger than the forces holding the satellite together Do research on the Roche limit and determine how close the Moon would have to orbit Earth to be at the Roche limit
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