1. 6 Circular Motion, Orbits, and Gravity
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5. Reading Quiz For uniform circular motion, the acceleration
is parallel to the velocity.
is directed toward the center of the circle.
is larger for a larger orbit at the same speed.
is always due to gravity.
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6. Answer For uniform circular motion, the acceleration
is parallel to the velocity.
is directed toward the center of the circle.
is larger for a larger orbit at the same speed.
is always due to gravity.
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7. Reading Quiz
When a car turns a corner on a level road, which force provides the necessary centripetal acceleration?
Friction
Tension
Normal force
Gravity
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8. Answer
When a car turns a corner on a level road, which force provides the necessary centripetal acceleration?
Friction
Tension
Normal force
Gravity
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9. Reading Quiz
Newton’s law of gravity describes the gravitational force between
the earth and the moon.
a person and the earth.
the earth and the sun.
all of the above.
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10. Answer
Newton’s law of gravity describes the gravitational force between
the earth and the moon.
a person and the earth.
the earth and the sun.
all of the above.
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11. Checking Understanding
4. When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because
the speed is changing.
the direction is changing.
the speed and the direction are changing.
the ball is not accelerating.
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12. Answer
4. When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because
the speed is changing.
the direction is changing.
the speed and the direction are changing.
the ball is not accelerating.
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13. Checking Understanding
5. When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of the ball?
Tangent to the circle, in the direction of the ball’s motion
Leftward, using the right hand rule.
Rightward, using the right hand rule
Toward the center of the circle
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14. Answer
5. When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of the ball?
Tangent to the circle, in the direction of the ball’s motion
Leftward, using the right hand rule.
Rightward, using the right hand rule
Toward the center of the circle
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15. Checking Understanding: Circular Motion Dynamics
6. For the ball on the end of a string moving in a vertical circle:
What force is producing the centripetal acceleration of the ball?
gravity
air resistance
normal force
tension in the string
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16. Answer
6. For the ball on the end of a string moving in a vertical circle:
What force is producing the centripetal acceleration of the ball?
gravity
air resistance
normal force
tension in the string
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17. Checking Understanding: Circular Motion Dynamics
7. For the ball on the end of a string moving in a vertical circle: What is the direction of the net force on the ball?
tangent to the circle
toward the center of the circle
outward in the last direction it moved
there is no net force
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18. Answer
7. For the ball on the end of a string moving in a vertical circle: What is the direction of the net force on the ball?
tangent to the circle
toward the center of the circle
outward in the last direction it moved
there is no net force
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19. Checking Understanding: Circular Motion Dynamics
8. When the ball reaches the break in the circle, which path will it follow?
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20. Answer
8. When the ball reaches the break in the circle, which path will it follow? C.
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21. Forces in Circular Motion
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22. Checking Understanding: Gravity on Other Worlds
9. A 60 kg person stands on each of the following planets. Where would her weight be the lowest? A B C
Same everywhere
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23. Answer
9. A 60 kg person stands on each of the following planets. Where would her weight be the lowest? A B C
Same everywhere
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24. Summary
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25. Additional Questions 10. A coin sits on a rotating turntable.
At the time shown in the figure, which arrow gives the direction of the coin’s velocity?
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26. Answer 10. A coin sits on a rotating turntable.
At the time shown in the figure, which arrow gives the direction of the coin’s velocity? A
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27. Additional Questions 11. A coin sits on a rotating turntable.
At the time shown in the figure, which arrow gives the direction of the frictional force on the coin?
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28. Answer 11. A coin sits on a rotating turntable.
At the time shown in the figure, which arrow gives the direction of the frictional force on the coin? D
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29. Additional Questions 12. A coin sits on a rotating turntable.
At the instant shown, suppose the frictional force disappeared. In what direction would the coin move?
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30. Answer 12. A coin sits on a rotating turntable.
At the instant shown, suppose the frictional force disappeared. In what direction would the coin move? A
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31. 8 Equilibrium and Elasticity
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32. Slide 8-3

33. Checking Understanding
13. An object is in equilibrium if
Fnet = 0.
net = 0.
either A or B.
both A and B.    
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34. Answer 13. An object is in equilibrium if Fnet = 0. net = 0.
either A or B.
both A and B.    
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35. Checking Understanding
14. What does the scale read?
500 N
1000 N
2000 N
4000 N
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36. Answer 14. What does the scale read? 500 N 1000 N 2000 N 4000 N
F1r1 = F2r2
1000N 1m = 2000 N 0.5 m
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37. Balance
Base of support
Gravity acts at the center of gravity.
Line of action
This force exerts no torque about her toes.
For an object to balance, its center of gravity must reside over its base of support. That way gravity does not exert a torque.
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38. The Spring Force Fsp = k ∆x
The magnitude of the spring force is proportional to the displacement of its end:
Fsp = k ∆x
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39. Hooke’s Law (Fsp)x = –k ∆x
The spring force is directed oppositely to the displacement. We can then write Hooke’s law as
(Fsp)x = –k ∆x
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40. Checking Understanding
15. Which spring has the largest spring constant?
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41. Answer
15. Which spring has the largest spring constant? A
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42. Checking Understanding
16. The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude?
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43. Answer
16. The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude? The force is determined by the displacement from the spring’s equilibrium length, which is not given.
D. Not enough information to tell.
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44. The Springiness of Materials: Young’s Modulus
The force exerted by a stretched or compressed rod has the same form as Hooke’s law:
F = DL L YA
Y is Young’s modulus, which depends on the material that the rod is made of.
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45. Beyond the Elastic Limit
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46. Summary
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47. 7 Rotational Motion
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48. Slide 7-3

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50. Reading Quiz 17. Moment of inertia is
the rotational equivalent of mass.
the point at which all forces appear to act.
the time at which inertia occurs.
an alternative term for moment arm.
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51. Answer 17. Moment of inertia is the rotational equivalent of mass.
the point at which all forces appear to act.
the time at which inertia occurs.
an alternative term for moment arm.
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52. Reading Quiz
18. Which factor does the torque on an object not depend on?
The magnitude of the applied force.
The object’s angular velocity.
The angle at which the force is applied.
The distance from the axis to the point at which the force is applied.
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53. Answer 18. Which factor does the torque on an object not depend on?
The magnitude of the applied force.
The object’s angular velocity.
The angle at which the force is applied.
The distance from the axis to the point at which the force is applied.
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54. Reading Quiz
19. Which statement about an object’s center of gravity is NOT true
If an object is free to rotate about a pivot, the center of gravity will come to rest below the pivot.
The center of gravity coincides with the geometric center of the object.
The torque due to gravity can be calculated by considering the object’s weight as acting at the center of gravity.
For objects small compared to the earth, the center of gravity and the center of mass are essentially the same.
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55. Answer
19. Which statement about an object’s center of gravity is NOT true?
If an object is free to rotate about a pivot, the center of gravity will come to rest below the pivot.
The center of gravity coincides with the geometric center of the object.
The torque due to gravity can be calculated by considering the object’s weight as acting at the center of gravity.
For objects small compared to the earth, the center of gravity and the center of mass are essentially the same.
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56. Reading Quiz 20. A net torque applied to an object causes
a linear acceleration of the object.
the object to rotate at a constant rate.
the angular velocity of the object to change.
the moment of inertia of the object to change.
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57. Answer 20. A net torque applied to an object causes
a linear acceleration of the object.
the object to rotate at a constant rate.
the angular velocity of the object to change.
the moment of inertia of the object to change.
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58. Checking Understanding
21. Two coins rotate on a turntable. Coin B is twice as far from the axis as coin A.
The angular velocity of A is twice that of B.
The angular velocity of A equals that of B.
The angular velocity of A is half that of B.
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59. Answer
21. Two coins rotate on a turntable. Coin B is twice as far from the axis as coin A.
The angular velocity of A is twice that of B.
The angular velocity of A equals that of B.
The angular velocity of A is half that of B.
All points on the turntable rotate through the same angle in the same time.
All points have the same period.
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60. Checking Understanding
22. Two coins rotate on a turntable. Coin B is twice as far from the axis as coin A.
The speed of A is twice that of B.
The speed of A equals that of B.
The speed of A is half that of B.
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61. Answer
22. Two coins rotate on a turntable. Coin B is twice as far from the axis as coin A.
The speed of A is twice that of B.
The speed of A equals that of B.
The speed of A is half that of B.
Twice the radius means twice the speed
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62. Angular Acceleration
Angular acceleration α measures how rapidly the angular velocity is changing:
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63. Linear and Circular Motion Compared
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64. Linear and Circular Kinematics Compared
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65. Sign of the Angular Acceleration
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66. Centripetal and Tangential Acceleration
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67. Checking Understanding
23. The four forces shown have the same strength. Which force would be most effective in opening the door?
Force F1
Force F2
Force F3
Force F4
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68. Answer
23. The four forces shown have the same strength. Which force would be most effective in opening the door?
Force F1
Force F2
Force F3
Force F4
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69. Interpreting Torque
Torque is due to the component of the force perpendicular to the radial line.
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70. Newton’s Second Law for Rotation
I = moment of inertia. Objects with larger moments of inertia are harder to get rotating.
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71. Checking Understanding
24. Suppose you make a new kind of compact disc that is the same thickness as a current disc but twice the diameter By what factor will the moment of inertia change?
Increase 2x
Increase 4x
Increase 8x
Increase 16x

72. Answer
24. Suppose you make a new kind of compact disc that is the same thickness as a current disc but twice the diameter By what factor will the moment of inertia change?
Increase 2x
Increase 4x
Increase 8x
Increase 16x
For a disc, I = ½ m r2
The mass increases x4 since the volume of a disc = pr2h so a doubling of the radius results in a quadrupling of the mass.
Furthermore, the radius increases x2 which is has to be squared resulting in another quadrupling of the moment of inertia.

73. Checking Understanding
25. Two children carry a lightweight 1.8 m long horizontal pole with a water bucket hanging from it. The older child supports twice as much weight as the younger child. How far is the bucket from the older child?
0.3 m
0.6 m
0.9 m
1.2 m

74. Answer
25. Two children carry a lightweight 1.8 m long horizontal pole with a water bucket hanging from it. The older child supports twice as much weight as the younger child. How far is the bucket from the older child?
0.3 m
0.6 m
0.9 m
1.2 m
St = Foro - Fyry = 0
Fo = 2Fy
2Fyro = Fyry
2ro = ry

75. Checking Understanding
26. In the gyroscope pictured, which direction is the angular momentum? Notice it is turning so the front edge is moving upward.
upward
downward
leftward
rightward

76. Answer
26. In the gyroscope pictured, which direction is the angular momentum? Notice it is turning so the front edge is moving upward.
upward
downward
leftward
rightward

77. Rotational and Linear Dynamics Compared
Angular velocity w Velocity v
Angular momentum L = I w Momentum p = m v
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78. Summary
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