9) A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to
the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the
road is
A) 2v.
B) v.
C) 1.5v.
D) zero.
E) The velocity depends on the radius of the tire.
Answer: A
11) A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of
uniform density. If the three are released simultaneously at the top of an inclined plane and roll
without slipping, which one will reach the bottom first?
A) solid sphere
B) hollow pipe
C) solid cylinder
D) They all reach the bottom at the same time.
Answer: A
12) A uniform disk, a uniform hoop, and a uniform solid sphere are released at the same time at
the top of an inclined ramp. They all roll without slipping. In what order do they reach the
bottom of the ramp?
A) disk, hoop, sphere
B) hoop, sphere, disk
C) sphere, disk, hoop
D) sphere, hoop, disk
E) hoop, disk, sphere
Answer: C
14) The angular momentum of a system remains constant
A) when the total kinetic energy is constant.
B) when no net external force acts on the system.
C) when the linear momentum and the energy are constant.
D) when no torque acts on the system.
E) all the time since it is a conserved quantity.
Answer: D
15) A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is
moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this
collision
A) the angular momentum of the system (ball and bar) is conserved about the hook because only
gravity is acting on the system.
B) the angular momentum of the system (ball and bar) is not conserved because the hook exerts a
force on the bar.
C) the angular momentum of the system (ball and bar) is conserved about the hook because
neither the hook nor gravity exerts any torque on this system about the hook.
D) both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.
E) both the linear momentum and the angular momentum of the system (ball and bar) are
conserved.
Answer: C
Var: 1
16) If the torque on an object adds up to zero
A) the forces on it also add up to zero.
B) the object is at rest.
C) the object cannot be turning.
D) the object could be accelerating linearly but it could not be turning.
E) the object could be both turning and accelerating linearly.
Answer: E
14) A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is
the moment of inertia of this sphere about an axis through its center?
A) 1/7 I
B) 2/7 I
C) 2/5 I
D) 3/5 I
E) 7/5 I
Answer: B
23) A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of
What is the angle (assumed to be less than 90°) between the wrench handle and the
direction of the applied force?
A) 18°
B) 14°
C) 22°
D) 25°
Answer: A
27) A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the
surface of the door. The doorknob is located 0.800 m from axis of the frictionless hinges of the
door. The door begins to rotate with an angular acceleration of 2.00 rad/s2. What is the moment
of inertia of the door about the hinges?
A) 4.28 kg∙m2
B) 7.52 kg∙m2
C) 1.88 kg∙m2
D) 0.684 kg∙m2
E) 2.74 kg∙m2
Answer: C
42) A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up
a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is
2.63 m/s. While the ball is moving up the ramp, find
(a) the acceleration (magnitude and direction) of its center of mass and
(b) the friction force (magnitude and direction) acting on it due to the surface of the ramp.
Answer: (a) 2.94 m/s2 down the ramp (b) 3.43 N up the ramp
43) A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls
without slipping down a 35° incline that is 7.0 m long.
(a) Calculate the linear speed of the center of the sphere when it reaches the bottom of the
incline.
(b) Determine the angular speed of the sphere about its center at the bottom of the incline.
(c) Through what angle (in radians) does this sphere turn as it rolls down the incline?
(d) Does the linear speed in (a) depend on the radius or mass of the sphere? Does the angular
speed in (b) depend on the radius or mass of the sphere?
Answer:
(a) 7.5 m/s (b) 50 rad/s (c) 47 rad
(d) The linear speed depends on neither the radius nor the mass of the sphere. The angular speed
depends on the radius of the sphere.
53) A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25
kg∙m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg∙m2, what is the
final angular speed?
A) 2.25 rad/s
B) 4.60 rad/s
C) 6.25 rad/s
D) 1.76 rad/s
E) 0.810 rad/s
Answer: C
54) A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg∙m2 is
rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are
standing right outside the edge of the merry-go-round and step on it with negligible speed. What
is the angular speed of the merry-go-round right after the two people have stepped on?
A) 0.20 rad/s
B) 0.40 rad/s
C) 0.60 rad/s
D) 0.80 rad/s
E) 0.67 rad/s
Answer: B
56) A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is
rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless
bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a
velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on
the rim of the turntable (see figure). What is the angular velocity of the turntable just after the
ball is caught?
A) 2.1 rad/s
B) 1.3 rad/s
C) 0.94 rad/s
D) 0.75 rad/s
E) 0.30 rad/s
Answer: B
57) A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is
rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless
bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a
velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on
the rim of the turntable (see figure). The percent of the initial kinetic energy of the system that is
lost during the capture of the ball is closest to
A) 45%.
B) 51%.
C) 55%.
D) 60%.
E) 65%.
Answer: B
60) An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by
two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the
force exerted on the diving board
(a) by pillar A.
(b) by pillar B.
Answer: (a) 1.71 kN downwards
(b) 2.51 kN upwards
74) A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and
reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough
horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of
concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the
figure. What is the magnitude of the friction force that the floor exerts on the ladder?
A) 538 N
B) 706 N
C) 1290 N
D) 833 N
E) 601 N
Answer: A