Rotational Motion Test v2
AP 1PSI Physics
Name____________________________________
Multiple Choice– Choose the correct answer for each question. No partial credit will be given.
Questions 1-3:
A solid cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s
moment of inertia (I) about the axis is 5.0 kg-m2. At time t = 0 s, the cylinder is at rest. At time,
t = 2.0 s, its angular velocity is 1.0 rad/s.
1. What is the angular acceleration of the cylinder between t = 0 s and t = 2 s?
A)
B)
C)
D)
0.5 rad/s2
1.0 rad/s2
2.0 rad/s2
4.0 rad/s2
2. What is the angular momentum of the cylinder at t = 2 s?
A)
B)
C)
D)
3.0 kg-m2/s
4.0 kg-m2/s
5.0 kg-m2/s
It cannot be determined without knowing the radius of the cylinder.
3. What is the rotational kinetic energy of the cylinder at t = 2 s?
A)
B)
C)
D)
2.0 J
2.5 J
5.0 J
It cannot be determined without knowing the radius of the cylinder.
4. A force of magnitude, F is applied to a doorknob and a second force of magnitude, 2F is
applied to the same door at the middle of the door. Both forces are perpendicular to the door
plane. Which of the following is the correct ratio between the torque of the first force and the
torque of the second force?
A)
B)
C)
D)
1:2
1:1
2:1
4:1
5. The Earth moves around the Sun in an elliptical orbit. The Earth’s linear velocity increases
as it approaches its closest point to the sun. Which of the following does not change in the
Earth – Sun system during the orbit?
A)
B)
C)
D)
Orbital radius.
Kinetic energy.
Potential energy.
Angular momentum.
Questions 6-7:
6. A solid disc with a radius, R, rotates at a constant rate, ω. Which of the points on the above
diagram have the greatest angular displacement?
A)
B)
C)
D)
A
B
C
Points A, B and C have the same angular displacement.
7. A solid disc with a radius, R, rotates at a constant rate, ω. Which of the following equals the
period of the rotation?
A)
B)
C)
D)
2πω
ω/2π
2π/ω
2ω
1
8. A solid cylinder of mass, M and radius, R, whose moment of inertia about its center is 2 𝑀𝑅 2 ,
rolls without slipping along a level surface at a speed, v. It then encounters an incline and
rolls up the incline. What is the maximum vertical height it will reach on the incline?
A)
B)
C)
D)
𝑣2
4𝑔
𝑣2
2𝑔
3𝑣 2
4𝑔
3𝑣 2
2𝑔
9. A physics class performs an experiment to determine the winner of a race. An empty can, a
solid cylindrical battery and a marble roll, all with the same radius) without slipping down an
inclined plane of vertical height H (they are all released at the same height). A box slides
without friction on another inclined plane of the same height, H. Which object reaches the
bottom of the incline first?
A)
B)
C)
D)
Empty can.
Marble.
Box.
Battery.
10. An object accelerates, from rest, at a constant rate, α in a circular path with radius, R. The
radius sweeps through an angle, θ after time, t. Which of the following represents the
angular velocity as a function of θ?
A) 2𝜃𝛼
B) 2⁄𝜃𝛼
C) 2𝜃⁄𝛼
D) √2𝜃𝛼
Multi-Correct: For each of the questions or incomplete statements below, two of the suggested
answers will be correct. For each of these questions, you must select both correct choices to
earn credit. No partial credit will be earned if only one correct choice is selected. Select the two
that are best in each case and then enter both of the appropriate letters in the corresponding
space on the answer sheet.
11. When a spinning skater extends his arms from his side, to pointing straight out, his angular
rotation decreases (he spins slower). Why?
A) The ice exerts a greater torque on his skates.
B) His moment of inertia increases.
C) His moment of inertia decreases.
D) There are no external torques on the skater.
12. A solid sphere rolling without slipping down an incline has:
A)
B)
C)
D)
rotational kinetic energy.
constant angular momentum.
zero external torques.
translational kinetic energy.
Free Response - Solve this problem, showing all work.
Partial credit may be given.
A uniform solid cylinder of mass M and radius R is
mounted on frictionless bearings about a fixed axis
through the center of the cylinder. The moment of
inertia of the cylinder about the axis is ½MR2. A
block of mass m, suspended by a cord wrapped
around the cylinder as shown to the right, is
released. State all answers (aside from part b) in
terms of M, m, R, and g.
a. On the diagrams below, draw and label all the forces acting on the block and the pulley.
b. Use the free body diagrams to write each of the following:
i. The equation of translational motion for the block.
ii. The analogous equation for the rotational motion of the pulley.
c. Solve the equations in part b for the acceleration of the block.
d. Determine the tension force in the segment of the cord attached to the block.
e. Determine the angular momentum of the cylinder as a function of time.
Rotational Motion Test v2
AP 1PSI Physics
ANSWER KEY
Weight 50% Multiple Choice, 50% Free Response
Multiple Choice 1 point each, 12 points total
1. A
2. C
3. B
4. B
5. D
6. D
Free Response – 15 points total
a. 4 points
b.
i.
2 points
𝛴𝐹 = 𝑚𝑎
𝒎𝒈 − 𝑭𝑻 = 𝒎𝒂
ii. 2 points
𝛴𝜏 = 𝐼𝛼
𝑀𝑅 2
)𝛼
2
𝑴𝒂
𝑭𝑻 =
𝟐
𝑅𝐹𝑇 = (
c. 2 points
𝑀𝑎
𝑚𝑔 −
= 𝑚𝑎
2
7. C
8. C
9. C
10. D
11. B,
D
12. A,
D
13.14.15.16.17
𝒂=
𝟐𝒎𝒈
𝑴 + 𝟐𝒎
d. 2 points
𝑀𝑎 𝑀 2𝑚𝑔
𝑴𝒎𝒈
𝐹𝑇 =
= (
)=
2
2 𝑀 + 2𝑚
𝑴 + 𝟐𝒎
e. 3 points
𝑀𝑅 2 𝑎
𝑀𝑅𝑎
𝑀𝑅 2𝑚𝑔
𝑴𝒎𝑹𝒈
𝐿 = 𝐼𝜔 = 𝐼𝛼𝑡 = (
)( )𝑡 =
𝑡=
(
)𝑡 =
𝒕
2
𝑅
2
2 𝑀 + 2𝑚
𝑴 + 𝟐𝒎