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AP Physics
Rotational Motion Practice test
1) When a rigid object rotates about a fixed axis, what is true about all the points in the object?
(There could be more than one correct choice.)
A) They all have the same angular speed.
B) They all have the same tangential speed.
C) They all have the same angular acceleration.
D) They all have the same tangential acceleration.
E) They all have the same radial acceleration.
Answer: A, C
Var: 1
2) A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane.
They are all uniform and roll without slipping. In what order do they reach the bottom?
A) disk, hoop, sphere
B) hoop, sphere, disk
C) sphere, disk, hoop
D) sphere, hoop, disk
E) hoop, disk, sphere
Answer: C
Var: 1
3) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After
reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When
the ball reaches its maximum height on the frictionless surface, it is
A) higher than when it was released.
B) lower than when it was released.
C) at the same height from which it was released.
D) It is impossible to tell without knowing the mass of the ball.
E) It is impossible to tell without knowing the radius of the ball.
Answer: B
Var: 1
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4) If the answer to your calculation has units of kg ∙ m2/s, what type of quantity could it be?
(There could be more than one correct choice).
A) force
B) work
C) angular momentum
D) linear momentum
E) power
F) rotational kinetic energy
G) moment of inertia
H) torque
Answer: C
Var: 1
5) When is the angular momentum of a system constant?
A) Only when its total kinetic energy is constant.
B) Only when no net external force acts on the system.
C) Only when the linear momentum and the energy are constant.
D) Only when no net external torque acts on the system.
E) Only when the moment of inertia is constant.
Answer: D
Var: 1
6) At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?
A) 11 rad/s
B) 22 rad/s
C) 45 rad/s
D) 69 rad/s
E) 660 rad/s
Answer: B
Var: 1
7) An electrical motor spins at a constant
linear acceleration of the edge of the rotor?
A) 5707 m/s2
B) 281.6 m/s2
C) 572,400 m/s2
D) 28.20 m/s2
Answer: A
Var: 50+
If the rotor radius is
2
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what is the
8) A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a
distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping?
A) 1.8 rad/s2
B) 0.90 rad/s2
C) 5.7 rad/s2
D) 11 rad/s2
Answer: B
Var: 1
9) A machinist turns on the power to a grinding wheel at time t = 0 s. The wheel accelerates
uniformly from rest for 10 s and reaches the operating angular speed of
The wheel is run
at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at
until the wheel stops. In this situation, what is the angular acceleration of the wheel
between
and
A) 3.8 rad/
B) 4.6 rad/
C) 5.3 rad/
D) 6.1 rad/
E) 6.8 rad/
Answer: A
Var: 50+
10) A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates
uniformly from rest for 10 s and reaches the operating angular speed of
The wheel is run
at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at
until the wheel stops. For how long a time after the power is shut off does it take the
wheel to stop?
A) 64 s
B) 62 s
C) 66 s
D) 68 s
E) 70 s
Answer: A
Var: 50+
11) A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41
rad/s2. Through what angle does the pulley turn in 5.26 s?
A) 113 rad
B) 22.6 rad
C) 42.6 rad
D) 19.3 rad
E) 160 rad
Answer: A
Var: 1
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12) A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its
center with an angular speed of 33.4 rpm. What is its kinetic energy?
A) 0.18 J
B) 0.092 J
C) 0.96 J
D) 1.1 J
E) 17 J
Answer: B
Var: 1
13) A futuristic design for a car is to have a large flywheel within the car to store kinetic energy.
The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m, and it can rotate up
to
Assuming all of this stored kinetic energy could be transferred to the linear speed of
the
car, find the maximum attainable speed of the car.
Answer: 221 m/s
Var: 50+
14) While spinning down from 500 rpm to rest, a flywheel does
of work. This flywheel is
in the shape of a solid uniform disk of radius 1.2 m. What is the mass of this flywheel?
A) 4.0 kg
B) 3.4 kg
C) 4.6 kg
D) 5.2 kg
Answer: A
Var: 50+
15) As shown in the figure, two blocks are connected by a light string that passes over a
frictionless pulley having a moment of inertia of 0.0040 kg ∙ m2 and diameter 10 cm. The
coefficient of kinetic friction between the table top and the upper block is 0.30. The blocks are
released from rest, and the string does not slip on the pulley. How fast is the upper block moving
when the lower one has fallen 0.60 m?
A) 1.2 m/s
B) 5.4 m/s
C) 3.2 m/s
D) 2.0 m/s
E) 1.4 m/s
Answer: E
Var: 1
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16) An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0
kg over a frictionless pulley with a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm.
If the system is released from rest, what is the speed of the masses after they have moved
through 1.25 m if the string does not slip on the pulley?
A) 2.0 m/s
B) 2.3 m/s
C) 4.0 m/s
D) 5.0 m/s
E) 6.0 m/s
Answer: B
Var: 1
17) A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of
5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the
speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp?
A) 4.0 m/s
B) 8.0 m/s
C) 1.9 m/s
D) 2.2 m/s
E) 3.5 m/s
Answer: E
Var: 1
18) The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle.
You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of
33.0 cm. What is the angular acceleration of the wheel?
A) 10.4 rad/s2
B) 20.8 rad/s2
C) 5.20 rad/s2
D) 3.43 rad/s2
E) 1.06 rad/s2
Answer: A
Var: 1
19) A force of
is applied tangentially to a wheel of radius 0.340 m and causes an angular
acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?
A) 4.78 kg ∙ m2
B) 3.59 kg ∙ m2
C) 5.98 kg ∙ m2
D) 7.17 kg ∙ m2
Answer: A
Var: 50+
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20) A particular motor can provide a maximum torque of 110 N ∙ m. Assuming that all of this
torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00
m, how long will it take for the flywheel to accelerate from rest to
A) 3.33 s
B) 2.83 s
C) 4.03 s
D) 4.36 s
Answer: A
Var: 50+
21) A uniform rod is 2.0 m long. It is hinged to a wall at its left end, and held in a horizontal
position at its right end by a vertical very light string, as shown in the figure. What is the angular
acceleration of the rod at the moment after the string is released if there is no friction in the
hinge?
A) 15 rad/s2
B) 3.3 rad/s2
C) 7.4 rad/s2
D) 11 rad/s2
E) It cannot be calculated without knowing the mass of the rod.
Answer: C
Var: 1
22) As shown in the figure, a 35.30-kg box is attached to a light string that is wrapped around a
cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m2. The spool is
suspended from the ceiling, and the box is then released from rest a distance 3.50 m above the
floor. How long does it take for the box to reach the floor?
A) 2.97 s
B) 2.85 s
C) 0.892 s
D) 4.18 s
E) 5.89 s
Answer: A
Var: 50+
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23) A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through
its center with an angular speed of 3.50 rad/s. What is the magnitude of the angular momentum
of the stick?
A) 0.0394 kg ∙ m2/s
B) 0.473 kg ∙ m2/s
C) 0.0739 kg ∙ m2/s
D) 0.158 kg ∙ m2/s
E) 0.0236 kg ∙ m2/s
Answer: A
Var: 1
24) A light-weight potter's wheel, having a moment of inertia of
is spinning freely at
40.0 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a
distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is
32 rpm, what is the mass of the clay?
A) 4.2 kg
B) 2.8 kg
C) 3.7 kg
D) 4.6 kg
Answer: A
Var: 38
Free response
1) A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway,
of each of the following points on one of its tires?
(a) the highest point on the tire
(b) the lowest point on a tire
(c) the center of the tire
Answer: (a) 130 mph (b) 0 mps (c) 65 mph
Var: 1
2) A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll
without slipping at the same forward speed. It is correct to say that the total kinetic energy of the
solid sphere is
A) more than the total kinetic energy of the cylinder.
B) less than the total kinetic energy of the cylinder.
C) equal to the total kinetic energy of the cylinder.
Answer: B
Var: 1
3) The diameter of the Moon is 3.47 × 106 m, and it subtends an angle of 0.00904 rad when
viewed from the surface of Earth. How far is the Moon from Earth?
Answer: 3.84 × 108 m
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4) A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees
does the cylinder turn during this time?
Answer: 140°
Var: 1
5) A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through
of a
revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was
constant during the motion, how long will it take the wheel to make the
revolution?
Answer: 0.67 s
Var: 50+
6) The L-shaped object shown in the figure consists of three small masses connected by
extremely light rods. Assume that the masses shown are accurate to three significant figures.
What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?
Answer: (a) 6.48 kg ∙ m2
Var: 1
(b) 32.7 kg ∙ m2
7) The figure shows two blocks connected by a light cord over a pulley. This apparatus is known
as an Atwood's machine. There is no slipping between the cord and the surface of the pulley. The
pulley itself has negligible friction and it has a radius of 0.12 m and a mass of 10.3 kg. We can
model this pulley as a solid uniform disk. At the instant that the heavier block has descended 1.5
m starting from rest, what is the speed of the lighter block?
Answer: 2.4 m/s
Var: 1
8) A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm.
This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket
has been released, (a) what is the angular acceleration of the pulley, and (b) what is the
acceleration of the bucket?
Answer: (a) 4.5 rad/s2 (b) 3.0 m/s2
Var: 1
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9) A ballerina spins initially at 1.5 rev/s when her arms are extended. She then draws in her arms
to her body and her moment of inertia becomes 0.88 kg ∙ m2, and her angular speed increases to
4.0 rev/s. What was her initial moment of inertia?
Answer: 2.3 kg ∙ m2
Var: 1
10) NASA puts a satellite into space that consists of two small 32-kg balls connected by a 12-m
long light cable, as shown in the figure. The entire system is initially rotating at 4.0 rpm about an
axis perpendicular to the cable at the center of mass. Motors in each mass reel out more cable so
that the masses double their separation to 24 m.
(a) What is the final rotational speed (in rpm) of the balls?
(b) If the initial rotational kinetic energy of the system was K, what is the final rotational kinetic
energy in terms of K?
Answer: (a) 1.0 rpm
Var: 1
(b) K/4
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