Name: 
 

rotational motion


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
When an object is moving with uniform circular motion, the object’s tangential speed
a.
is circular.
b.
is perpendicular to the plane of motion.
c.
is constant.
d.
is directed toward the center of motion.
 

 2. 
When an object is moving with uniform circular motion, the centripetal acceleration of the object
a.
is circular.
b.
is perpendicular to the plane of motion.
c.
is zero.
d.
is directed toward the center of motion.
 

 3. 
What term describes a change in the speed of an object in circular motion?
a.
tangential speed
c.
centripetal acceleration
b.
tangential acceleration
d.
centripetal force
 

 4. 
What is the term for the net force directed toward the center of an object’s circular path?
a.
circular force
c.
centripetal force
b.
centrifugal force
d.
orbital force
 

 5. 
Which of the following can be a centripetal force?
a.
friction
c.
tension
b.
gravity
d.
all of the above
 

 6. 
The centripetal force on an object in circular motion is
a.
perpendicular to the plane of the object’s motion.
b.
in the plane of the object’s motion and perpendicular to the tangential speed.
c.
in the plane of the object’s motion and in the same direction as the tangential speed.
d.
in the plane of the object’s motion and in the direction opposite the tangential speed.
 

 7. 
The centripetal force on an object in circular motion is
a.
in the same direction as the tangential speed.
b.
in the direction opposite the tangential speed.
c.
in the same direction as the centripetal acceleration.
d.
in the direction opposite the centripetal acceleration.
 
 
A child rides a bicycle in a circular path with a radius of 2.0 m. The tangential speed of the bicycle is 2.0 m/s. The combined mass of the bicycle and the child is 43 kg.
 

 8. 
What is the magnitude of the bicycle’s centripetal acceleration?
a.
1.0 m/s2
c.
4.0 m/s2
b.
2.0 m/s2
d.
8.0 m/s2
 

 9. 
What is the magnitude of the centripetal force on the bicycle?
a.
4.0 N
c.
86 N
b.
43 N
d.
3.7 kN
 

 10. 
What kind of force provides the centripetal force on the bicycle?
a.
gravitational force
c.
air resistance
b.
friction
d.
normal force
 

 11. 
When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?
a.
centripetal acceleration
c.
centrifugal force
b.
centripetal force
d.
inertia
 

 12. 
A ball is whirled on a string, then the string breaks. What causes the ball to move off in a straight line?
a.
centripetal acceleration
c.
centrifugal force
b.
centripetal force
d.
inertia
 

 13. 
Tides are caused by
a.
differences in the gravitational force of the sun at different points on Earth.
b.
differences in the gravitational force of the moon at different points on Earth.
c.
differences in Earth’s gravitational field strength at different points on Earth’s surface.
d.
fluctuations in the gravitational attraction between Earth and the moon.
 

 14. 
Why does an astronaut weigh less on the moon than on Earth?
a.
The astronaut has less mass on the moon.
b.
The astronaut is farther from Earth’s center when he or she is on the moon.
c.
The gravitational field strength is less on the moon’s surface than on Earth’s surface.
d.
The astronaut is continually in free fall because the moon orbits Earth.
 

 15. 
If you lift an apple from the ground to some point above the ground, the gravitational potential energy in the system increases. This potential energy is stored in
a.
the apple.
b.
Earth.
c.
both the apple and Earth.
d.
the gravitational field between Earth and the apple.
 

 16. 
An object’s tendency to resist acceleration is measured by the object’s
a.
gravitational mass.
c.
gravitational field strength.
b.
inertial mass.
d.
weight.
 

 17. 
The degree to which an object attracts other objects is measured by the object’s
a.
gravitational mass.
c.
gravitational field strength.
b.
inertial mass.
d.
weight.
 

 18. 
Which of the following confirms that gravitational mass and inertial mass are equivalent?
a.
Free-fall acceleration is the same throughout the universe.
b.
Free-fall acceleration is the same at all points where the gravitational field strength is the same.
c.
Newton’s second law is valid throughout the universe.
d.
An object’s weight can change with location, but the object’s mass remains constant.
 

 19. 
In this text, which of the following symbols represents gravitational field strength?
a.
Fmc019-1.jpg
c.
g
b.
G
d.
Fmc019-2.jpg
 

 20. 
In this text, which of the following symbols represents the constant of universal gravitation?
a.
Fmc020-1.jpg
c.
g
b.
G
d.
Fmc020-2.jpg
 

 21. 
Which of the following equations expresses Newton’s law of universal gravitation?
a.
mc021-1.jpg
c.
mc021-3.jpg
b.
mc021-2.jpg
d.
mc021-4.jpg
 

 22. 
When calculating the gravitational force between two extended bodies, you should measure the distance
a.
from the closest points on each body.
b.
from the most distant points on each body.
c.
from the center of each body.
d.
from the center of one body to the closest point on the other body.
 

 23. 
The gravitational force between two masses is 36 N. What is the gravitational force if the distance between them is tripled? (G = 6.673 ´ 10mc023-1.jpg N·mmc023-2.jpg/kgmc023-3.jpg)
a.
4.0 N
c.
18 N
b.
9.0 N
d.
27 N
 

 24. 
Two small masses that are 10.0 cm apart attract each other with a force of 10.0 N. When they are 5.0 cm apart, these masses will attract each other with what force?
(G = 6.673 ´ 10mc024-1.jpg N·mmc024-2.jpg/kgmc024-3.jpg)
a.
5.0 N
c.
20.0 N
b.
2.5 N
d.
40.0 N
 

 25. 
Kepler developed his laws of planetary motion as he tried to reconcile
a.
Ptolemaic theory with Copernican theory.
b.
Ptolemaic theory with Copernicus’s data.
c.
Copernican theory with Tycho Brahe’s data.
d.
Copernican theory with his own data.
 

 26. 
Until the middle of the 16th century, most people believed ____ was at the center of the universe.
a.
Earth
c.
the sun
b.
the moon
d.
a black hole
 
 

nar002-1.jpg
 

 27. 
In the figure above, according to Kepler’s laws of planetary motion,
a.
Amc027-1.jpg = Amc027-2.jpg.
c.
if Dtmc027-5.jpg = Dtmc027-6.jpg, then the orbit is circular.
b.
Dtmc027-3.jpg > Dtmc027-4.jpg.
d.
if Dtmc027-7.jpg = Dtmc027-8.jpg, then Amc027-9.jpg = Amc027-10.jpg.
 

 28. 
Newton’s law of universal gravitation
a.
is equivalent to Kepler’s first law of planetary motion.
b.
can be used to derive Kepler’s third law of planetary motion.
c.
can be used to disprove Kepler’s laws of planetary motion.
d.
does not apply to Kepler’s laws of planetary motion.
 

 29. 
The equation for the speed of an object in circular orbit is mc029-1.jpg. What does m represent in this equation?
a.
the mass of the sun
c.
the mass of the central object
b.
the mass of Earth
d.
the mass of the orbiting object
 

 30. 
How would the speed of Earth’s orbit around the sun change if Earth’s distance from the sun increased by 4 times?
a.
It would increase by a factor of 2.
c.
It would decrease by a factor of 2.
b.
It would increase by a factor of 4.
d.
The speed would not change.
 

 31. 
How would the speed of Earth’s orbit around the sun change if Earth’s mass increased by 4 times?
a.
It would increase by a factor of 2.
c.
It would decrease by a factor of 2.
b.
It would increase by a factor of 4.
d.
The speed would not change.
 

 32. 
When an astronaut in orbit experiences apparent weightlessness,
a.
no forces act on the astronaut.
b.
no gravitational forces act on the astronaut.
c.
the net gravitational force on the astronaut is zero.
d.
the net gravitational force on the astronaut is not balanced by a normal force.
 

 33. 
Which of the following quantities measures the ability of a force to rotate or accelerate an object around an axis?
a.
axis of rotation
c.
tangential force
b.
lever arm
d.
torque
 

 34. 
Where should a force be applied on a lever arm to produce the most torque?
a.
closest to the axis of rotation
b.
farthest from the axis of rotation
c.
in the middle of the lever arm
d.
It doesn’t matter where the force is applied.
 

 35. 
If you want to open a swinging door with the least amount of force, where should you push on the door?
a.
close to the hinges
c.
as far from the hinges as possible
b.
in the middle
d.
It does not matter where you push.
 

 36. 
If you cannot exert enough force to loosen a bolt with a wrench, which of the following should you do?
a.
Use a wrench with a longer handle.
b.
Tie a rope to the end of the wrench and pull on the rope.
c.
Use a wrench with a shorter handle.
d.
You should exert a force on the wrench closer to the bolt.
 

 37. 
Suppose a doorknob is placed at the center of a door. Compared with a door whose knob is located at the edge, what amount of force must be applied to this door to produce the torque exerted on the other door?
a.
one-half as much
c.
one-fourth as much
b.
two times as much
d.
four times as much
 

 38. 
A heavy bank-vault door is opened by the application of a force of 3.0 ´ 10mc038-1.jpg N directed perpendicular to the plane of the door at a distance of 0.80 m from the hinges. What is the torque?
a.
120 N·m
c.
300 N·m
b.
240 N·m
d.
360 N·m
 

 39. 
If the torque required to loosen a nut on a wheel has a magnitude of 40.0 N·m and the force exerted by a mechanic is 133 N, how far from the nut must the mechanic apply the force?
a.
1.20 m
c.
30.1 cm
b.
15.0 cm
d.
60.2 cm
 

 40. 
What kind of simple machine are you using if you pry a nail from a board with the back of a hammer?
a.
a wedge
c.
a lever
b.
a pulley
d.
a screw
 

 41. 
A girl pushes a box that has a mass of 450 N up an incline. If the girl exerts a force of 150 N along the incline, what is the mechanical advantage of the incline?
a.
0.33
c.
300
b.
3.0
d.
33%
 

 42. 
Which of the following is not a valid equation for mechanical advantage?
a.
mc042-1.jpg
c.
mc042-3.jpg
b.
mc042-2.jpg
d.
mc042-4.jpg
 

 43. 
An iron bar is used to lift a slab of cement. The force applied to lift the slab is 4.0 ´ 10mc043-1.jpg N. If the slab weighs 6400 N, what is the mechanical advantage of the bar?
a.
1.6
c.
6000
b.
16
d.
6.3%
 

 44. 
What is the efficiency of a machine that requires 1.00 ´ 10mc044-1.jpg J of input energy to do 35 J of work?
a.
2.9%
c.
35%
b.
29%
d.
65%
 

 45. 
A box weighing 210 N is pushed up an inclined plane that is 2.0 m long. A force of 140 N is required. If the box is lifted 1.0 m, what is the efficiency of the inclined plane?
a.
33%
c.
67%
b.
50%
d.
75%
 

 46. 
What quantity measures the output force of a machine relative to the input force?
a.
torque
c.
mechanical advantage
b.
leverage
d.
efficiency
 

 47. 
What quantity measures the work done by a machine relative to the work done on a machine?
a.
torque
c.
mechanical advantage
b.
leverage
d.
efficiency
 

Short Answer
 

 48. 
Explain how an object moving at a constant speed can have a nonzero acceleration.
 

 49. 
Two horses are side by side on a carousel. Which has a greater tangential speed—the one closer to the center or the one farther from the center? Explain your answer.
 

 50. 
What provides the centripetal force for a car driving on a circular track?
 

 51. 
What provides the centripetal force for a ball whirled on a string?
 

 52. 
Show how the equation for centripetal force can be derived by substituting the equation for centripetal acceleration into Newton’s second law.
 

 53. 
Is there an outward force in circular motion? Explain.
 

 54. 
A ball is whirled in a horizontal circular path on the end of a string. Predict the path of the ball when the string breaks. Explain your answer.
 

 55. 
A parent holds a child by the arms and spins around in a circle at a constant speed. If the parent spins fast enough, will the child’s feet leave the ground? Explain your answer.
 

 56. 
A tether ball is tied to a string and whirled in a horizontal circular path at a constant speed. What causes the ball and string to move away from the post?
 

 57. 
What provides the centripetal force for the moon’s orbit around Earth?
 

 58. 
Describe briefly how the moon causes tides on Earth.
 

 59. 
Discuss the following statement: “A satellite is continually in free fall.”
 

 60. 
What is the significance of the word universal in Newton’s law of universal gravitation?
 

 61. 
Compare the gravitational force the sun exerts on Earth to the gravitational force Earth exerts on the sun.
 
 
Earth exerts a 1.0 N gravitational force on an apple.
 

 62. 
Does the apple accelerate toward Earth, or does Earth accelerate toward the apple? Explain your answer.
 

 63. 
What is the magnitude of the gravitational force the apple exerts on Earth?
 

 64. 
What is Earth’s weight in the apple’s gravitational field?
 

 65. 
Briefly, how did Ptolemy describe the motion of the planets?
 

 66. 
Briefly, how did Copernicus describe the motion of the planets?
 

 67. 
What is Kepler’s first law of planetary motion?
 

 68. 
What is Kepler’s second law of planetary motion?
 

 69. 
State Kepler’s third law of planetary motion, both in words and symbolically.
 
 

nar002-1.jpg
 

 70. 
What law does the diagram shown above illustrate?
 

 71. 
How did Newton use Kepler’s laws?
 

 72. 
On what variable factors do the period and speed of an object in circular orbit depend?
 

 73. 
Are astronauts in orbit weightless? Explain your answer.
 

 74. 
How will an object move if it is acted on by a nonzero net torque and a net force of zero?
 

 75. 
According to the sign conventions used in the text, in what direction will an object rotate if the sign of the net torque on the object is negative?
 
 

nar004-1.jpg
 

 76. 
Identify the simple machine in the figure shown above.
 
 

nar005-1.jpg
 

 77. 
Identify the simple machine in the figure shown above.
 
 

nar006-1.jpg
 

 78. 
Identify the simple machine in the figure shown above.
 
 

nar007-1.jpg
 

 79. 
Identify the simple machine in the figure shown above.
 
 

nar008-1.jpg
 

 80. 
Identify the simple machine in the figure shown above.
 

 81. 
Explain how the operation of a simple machine alters the applied force and the distance moved.
 

 82. 
How does the use of a machine alter the work done on the object?
 

 83. 
When a machine increases the force acting on an object, what happens to the distance the object moves?
 

 84. 
When a machine decreases the force acting on an object, what happens to the distance the object moves?
 

Problem
 
 
A 35 kg child moves with uniform circular motion while riding a horse on a carousel. The horse is 3.2 m from the carousel’s axis of rotation and has a tangential speed of 2.6 m/s.
 

 85. 
What is the child’s centripetal acceleration?
 

 86. 
What is the centripetal force on the child?
 
 
A car on a roller coaster loaded with passengers has a mass of 2.0 ´ 10nar010-1.jpg kg. At the lowest point of the track, the radius of curvature of the track is 24 m and the roller car has a tangential speed of 17 m/s.
 

 87. 
What is the centripetal acceleration of the roller car at the lowest point on the track?
 

 88. 
What centripetal force is exerted on the roller car at the lowest point?
 

 89. 
A 5.0 kg ball is whirled on a 1.2 m string so that the ball moves in uniform circular motion in a horizontal plane. The tension in the string is 25 N, and the string is at a 30° angle below the horizontal plane. What is the tangential speed of the ball?
 

 90. 
A satellite in a circular orbit experiences a centripetal acceleration of 8.62 m/spr090-1.jpg. The tangential speed of the satellite is 7.65 ´ 10pr090-2.jpg m/s. What is the altitude of the satellite? (rpr090-3.jpg = 6.38 ´ 10pr090-4.jpg m)
 

 91. 
A 61.5 kg student sits at a desk 1.25 m away from a 70.0 kg student. What is the magnitude of the gravitational force between the two students? (G = 6.673 ´ 10pr091-1.jpg N·mpr091-2.jpg/kgpr091-3.jpg)
 

 92. 
Two trucks with equal mass are attracted to each other with a gravitational force of 6.7 ´ 10pr092-1.jpg N. The trucks are separated by a distance of 3.0 m. What is the mass of one of the trucks? (G = 6.673 ´ 10pr092-2.jpg N·mpr092-3.jpg/kgpr092-4.jpg)
 

 93. 
Show how the constant of proportionality in Kepler’s third law can be found by equating gravitational force and the centripetal force in a circular orbit.
 
 
A new planet is discovered orbiting a star with a mass 3.5 ´ 10nar011-1.jpg kg at a distance of 1.2 ´ 10nar011-2.jpg m. Assume that the orbit is circular.
 

 94. 
What is the orbital speed of the planet? (G = 6.673 ´ 10pr094-1.jpg N·mpr094-2.jpg/kgpr094-3.jpg)
 

 95. 
What is the orbital period of the planet? (G = 6.673 ´ 10pr095-1.jpg N·mpr095-2.jpg/kgpr095-3.jpg)
 

 96. 
A new moon is discovered orbiting Neptune with an orbital speed of 9.3 ´ 10pr096-1.jpg m/s. Neptune’s mass is 1.0 ´ 10pr096-2.jpg kg. What is the radius of the new moon’s orbit? What is the orbital period? Assume that the orbit is circular. (G = 6.673 ´ 10pr096-3.jpg N·mpr096-4.jpg/kgpr096-5.jpg)
 

 97. 
Earth’s mean distance from the sun is 1.50 ´ 10pr097-1.jpg m. The length of one Earth year is 3.16 ´ 10pr097-2.jpg s. Use this data to calculate the mass of the sun. (G = 6.673 ´ 10pr097-3.jpg N·mpr097-4.jpg/kgpr097-5.jpg)
 

 98. 
A planet has twice the mass of Earth. How much larger would the radius of the planet have to be for the gravitational field strength, g, at the planet’s surface to be the same as on Earth’s surface?
 

 99. 
A bucket filled with water has a mass of 23 kg and is attached to a rope wound around a cylinder with a radius of 0.050 m at the top of a well. What torque does the weight of the water and bucket produce on the cylinder? (g = 9.81 m/spr099-1.jpg)
 

 100. 
A force of 4.0 N is applied to a door at an angle of 60.0° and a distance of 0.30 m from the hinge. What is the torque produced?
 

 101. 
To warm up before a game, a baseball pitcher tosses a 0.15 kg ball by rotating his forearm, which is 0.32 m in length, to accelerate the ball. The ball starts at rest and is thrown at a speed of 12 m/s in 0.40 s. While the ball is in the pitcher’s hand, what torque is applied to the ball to produce the final tangential speed?
 

 102. 
A child with a weight of 4.50 ´ 10pr102-1.jpg N sits on a seesaw 0.60 m from the axis of rotation. How far from the axis of rotation on the other side should a child with a weight of 6.00 ´ 10pr102-2.jpg N sit so the seesaw will remain balanced?
 
 

nar012-1.jpg
 

 103. 
A 4.0 m board with a mass of 19 kg is pivoted at its center of gravity. A helium balloon attached 0.23 m from the left end of the board produces an upward force of 7.0 N. A 3.5 kg book is placed 0.73 m from the left end of the board, and another book of 1.3 kg is placed 0.75 m from the right end of the board. Find the torque on the board and the direction of rotation.
 

 104. 
A force of 255 N is needed to pull a nail from a wall, using a claw hammer. If the resistance force of the nail is 3650 N, what is the mechanical advantage of the hammer?
 

 105. 
A boy can raise a rock that weighs 95 N by using a lever and applying a force of 15 N. What is the mechanical advantage of the lever?
 

 106. 
A force of 1250 N is needed to move a crate weighing 3270 N up a ramp that is 4.55 m long. If the elevated end of the ramp is 0.750 m high, what is the efficiency of the ramp?
 

 107. 
What is the efficiency of a machine that requires 135 J of input energy to do 87.5 J of work?
 

 108. 
How much energy would be required to do 675 J of work with a machine that was 35% efficient?
 



 
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