Halliday D., Resnick R., Walker J. Fundamentals of physics. Test Bank
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37. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter
has an acceleration given by a =(4.0m/s
2
)
ˆ
i − (3.0m/s
2
)
ˆ
j. The torque, relative to the origin,
acting on it at the end of 2 .0 s is:
A. 0
B. (−18 N · m)
ˆ
k
C. (+24 N · m)
ˆ
k
D. (−144 N · m)
ˆ
k
E. (+144 N · m)
ˆ
k
ans: B
38. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer
radius, are each free to rotate about a fixed axis through its center. Assume the hoop is
connected to the rotation axis by light spokes. With the objects starting from rest, identical
forces are simultaneously applied to the rims, as shown. Rank the objects according to their
angular momenta after a given time t, least to greatest.
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disk
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sphere
•
A. all tie
B. disk, hoop, sphere
C. hoop, disk, sphere
D. hoop, sphere, disk
E. hoop, disk, sphere
ans: A
39. A single force acts on a particle P. Rank each of the orientations of the force shown below
according to the magnitude of the time rate of change of the particle’s angular momentum
about the point O, least to greatest.
•
O
•
P
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1
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4
A. 1, 2, 3, 4
B. 1 and 2 tie, then 3, 4
C. 1 and 2 tie, then 4, 3
D. 1 and 2 tie, then 3 and 4 tie
E. All are the same
ans: C
Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM 171
40. A pulley with radius R is free to rotate on a horizontal fixed axis through its center. A string
passes over the pulley. Mass m
1
is attached to one end and mass m
2
is attached to the other.
The portion of the string attached to m
1
has tension T
1
and the portion attached to m
2
has
tension T
2
. The magnitude of the total external torque, about the pulley center, acting on the
masses and pulley, considered as a system, is given by:
A. |m
1
− m
2
|gR
B. (m
1
+ m
2
)gR
C. |m
1
− m
2
|gR +(T
1
+ T
2
)R
D. (m
1
+ m
2
)gR +(T
1
− T
2
)R
E. |m
1
− m
2
|gR +(T
2
− T
1
)R
ans: A
41. An ice skater with rotational inertia I
0
is spinning with angular speed ω
0
. She pulls her arms
in, thereby increasing her angular speed to 4ω
0
. Her rotational inertia is then:
A. I
0
B. I
0
/2
C. 2I
0
D. I
0
/4
E. 4I
0
ans: D
42. A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends
his arms:
A. his angular velocity increases
B. his angular velocity remains the same
C. his rotational inertia decreases
D. his rotational kinetic energy increases
E. his angular momentum remains the same
ans: E
43. A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating
turntable. The effect of the weights is to double the rotational inertia of the system. As he is
rotating, the man opens his hands and drops the two weights. They fall outside the turntable.
Then:
A. his angular velocity doubles
B. his angular velocity remains about the same
C. his angular velocity is halved
D. the direction of his angular momentum vector changes
E. his rotational kinetic energy increases
ans: B
172 Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM
44. A uniform sphere of radius R rotates ab out a diameter with an angular momentum of magnitude
L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2.
The magnitude of its new angular momentum is:
A. L/4
B. L/2
C. L
D. 2L
E. 4L
ans: C
45. When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic
energy:
A. must increase
B. must decrease
C. must remain the same
D. may increase or decrease depending on his initial angular velocity
E. may increase or decrease depending on his angular acceleration
ans: B
46. When a woman on a frictionless rotating turntable extends her arms out horizontally, her
angular momentum:
A. must increase
B. must decrease
C. must remain the same
D. may increase or decrease depending on her initial angular velocity
E. tilts away from the vertical
ans: C
47. Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational
inertia I and is spinning with angular velocity ω. The second disc has rotational inertia 2I
and is spinning in the same direction as the first disc with angular velocity 2ω as shown. The
two disks are slowly forced toward each other along the shaft until they couple and have a final
common angular velocity of:
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2ω
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A. 5ω/3
B. ω
√
3
C. ω
0
7/3
D. ω
E. 3ω
ans: A
Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM 173
48. A wheel with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia,
is rotating with angular speed ω
0
. A nonrotating wheel with rotational inertia 2 I is suddenly
dropped onto the same shaft as shown. The resultant combination of the two wheels and shaft
will rotate at:
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A. ω
0
/2
B. 2ω
0
C. ω
0
/3
D. 3ω
0
E. ω
0
/4
ans: C
49. A phonograph record is dropped onto a freely spinning turntable. Then:
A. neither angular momentum nor mechanical energy is conserved because of the frictional
forces between record and turntable
B. the frictional force between record and turntable increases the total angular momentum
C. the frictional force between record and turntable decreases the total angular momentum
D. the total angular momentum remains constant
E. the sum of the angular momentum and rotational kinetic energy remains constant
ans: D
50. A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-
round is at rest, a child with mass m runs with speed v along a line tangent to the rim and
jumps on. The angular velocity of the merry-go-round is then:
A. mv/I
B. v/R
C. mRv/I
D. 2mRv/I
E. mRv/(mR
2
+ I)
ans: E
174 Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM
51. A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg · m
2
.It
is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When
the child reaches the rim the angular velocity of the merry-go-round is:
A. 0.62 rad/s
B. 0.73 rad/s
C. 0.80 rad/s
D. 0.89 rad/s
E. 1.1 rad/s
ans: A
52. Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of
equal length. The lighter bob is drawn aside and then released so that it collides with the other
bob on reaching the vertical position. The collision is elastic. What quantities are conserved
in the collision?
A. Both kinetic energy and angular momentum of the system
B. Only kinetic energy
C. Only angular momentum
D. Angular speed of lighter bob
E. None of the above
ans: A
53. A particle, held by a string whose other end is attached to a fixed p oint C, moves in a circle
on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle
about the point C:
A. increases
B. decreases
C. does not change
D. changes direction but not magnitude
E. none of these
ans: C
54. A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table
as shown. As the string is slowly pulled through a small hole in the table:
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pull
A. the angular momentum of the block remains constant
B. the angular momentum of the block decreases
C. the kinetic energy of the block remains constant
D. the kinetic energy of the block decreases
E. none of the above
ans: A
Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM 175
Chapter 12: EQUILIBRIUM AND ELASTICITY
1. A net torque applied to a rigid object always tends to produce:
A. linear acceleration
B. rotational equilibrium
C. angular acceleration
D. rotational inertia
E. none of these
ans: C
2. The conditions that the net force and the net torque both vanish:
A. hold for every rigid body in equilibrium
B. hold only for elastic solid bodies in equilibrium
C. hold for every solid body
D. are always sufficient to calculate the forces on a solid object in equilibrium
E. are sufficient to calculate the forces on a solid object in equilibrium only if the object is
elastic
ans: A
3. For an object in equilibrium the net torque acting on it vanishes only if each torque is calculated
about:
A. the center of mass
B. the center of gravity
C. the geometrical center
D. the point of application of the force
E. the same point
ans: E
4. For a body to be in equilibrium under the combined action of several forces:
A. all the forces must be applied at the same point
B. all of the forces form pairs of equal and opposite forces
C. the sum of the components of all the forces in any direction must equal zero
D. any two of these forces must be balanced by a third force
E. the lines of action of all the forces must pass through the center of gravity of the body
ans: C
5. For a body to be in equilibrium under the combined action of several forces:
A. all the forces must be applied at the same point
B. all of the forces form pairs of equal and opposite forces
C. any two of these forces must be balanced by a third force
D. the sum of the torques about any point must equal zero
E. the lines of action of all the forces must pass through the center of gravity of the body
ans: D
176 Chapter 12: EQUILIBRIUM AND ELASTICITY
6. To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting
on the particles of the body can be replaced by a single force acting at:
A. the center of mass
B. the geometrical center
C. the center of gravity
D. a point on the boundary
E. none of the above
ans: C
7. The center of gravity coincides with the center of mass:
A. always
B. never
C. if the center of mass is at the geometrical center of the body
D. if the acceleration due to gravity is uniform over the body
E. if the body has a uniform distribution of mass
ans: D
8. The location of which of the following points within an object might depend on the orientation
of the object?
A. Its center of mass
B. Its center of gravity
C. Its geometrical center
D. Its center of momentum
E. None of the above
ans: B
9. A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its
geometrical center, is:
A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above
ans: B
10. A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its
geometrical center, is:
A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above
ans: A
Chapter 12: EQUILIBRIUM AND ELASTICITY 177
11. A cube balanced with one edge in contact with a table top and with its center of gravity directly
above the edge is in equilibrium with respect to rotation about the edge and in
equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.
A. stable, stable
B. stable, unstable
C. unstable, stable
D. unstable, unstable
E. unstable, neutral
ans: C
12. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force
F
1
is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force
F
2
(not
shown) is applied perpendicularly at the 100-cm end of the stick. The forces are horizontal. If
the stick does not move, the force exerted by the pivot on the stick:
0cm 20 cm 40 cm 60 cm 80 cm
•
100 cm
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pivot
A. must be zero
B. must be in the same direction as
F
1
and have magnitude |
F
2
| − |
F
1
|
C. must be directed opposite to
F
1
and have magnitude |
F
2
| − |
F
1
|
D. must be in the same direction as
F
1
and have magnitude |
F
2
| + |
F
1
|
E. must be directed opposite to
F
1
and have magnitude |
F
2
| + |
F
1
|
ans: E
13. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force
F
1
is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force
F
2
(not
shown) is applied perpendicularly at the 60-cm mark. The forces are horizontal. If the stick
does not move, the force exerted by the pivot on the stick:
0cm 20 cm 40 cm 60 cm 80 cm
•
100 cm
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F
1
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pivot
A. must be zero
B. must be in the same direction as
F
1
and have magnitude |
F
2
| − |
F
1
|
C. must be directed opposite to
F
1
and have magnitude |
F
2
| − |
F
1
|
D. must be in the same direction as
F
1
and have magnitude |
F
2
| + |
F
1
|
E. must be directed opposite to
F
1
and have magnitude |
F
2
| + |
F
1
|
ans: B
178 Chapter 12: EQUILIBRIUM AND ELASTICITY
14. Three identical uniform rods are each acted on by two or more forces, all perpendicular to
the rods and all equal in magnitude. Which of the rods could be in static equilibrium if an
additional force is applied at the center of mass of the rod?
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A. Only 1
B. Only 2
C. Only 3
D. Only 1 and 2
E. All three
ans: C
15. A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.
The magnitude of the tension force of each of the two supporting ropes is:
A. 60 N
B. 94 N
C. 120 N
D. 190 N
E. 260 N
ans: B
16. The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a
rope (AE) and friction between the rod and the wall. To use a single equation to find the
force exerted on the rod by the rope at which point should you place the reference point for
computing torque?
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•
A
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B
•
C
•
D
•
E
ans: C
Chapter 12: EQUILIBRIUM AND ELASTICITY 179
17. A picture P of weight W is hung by two strings as shown. The magnitude of the tension force
of each string is T . The total upward pull of the strings on the picture is:
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θθ
TT
A. 2W cos θ
B. T sin θ
C. T cos θ
D. 2T sin θ
E. 2T cos θ
ans: D
18. A picture can be hung on a wall with string in three di fferent ways, as shown. The magnitude
of the tension force of the string is:
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••
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III
A. least in I
B. greatest in I
C. greatest in II
D. least in III
E. greatest in III
ans: E
19. A uniform plank is supported by two equal 120-N forces at X and Y, as shown. The support
at X is then moved to Z (half-way to the plank center). The supporting forces at Y and Z are
then:
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XYZ
•
A. F
Y
= 240 N, F
Z
= 120 N
B. F
Y
= 200 N, F
Z
=40N
C. F
Y
=40N,F
Z
= 200 N
D. F
Y
=80N,F
Z
= 160 N
E. F
Y
= 160 N, F
Z
=80N
ans: D
180 Chapter 12: EQUILIBRIUM AND ELASTICITY