Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 1
ROTATIONAL MOTION UNIT PACKET
INCLUDES HW AND CW
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 2
Unit 7 Agenda
________ Day 1: Introduction to Rotational Motion
 Lecture
 HW: Read Sections 7.3, 7.4, 8.1, 8.2 and modify notes as is necessary; Manipulating Graphs pg. 43;
________ Day 2: Torque and Static Equilibrium
 Do Now, p. 41
 Torque and Static Equilibrium (p. 4-5)
 HW: Finish Torque and Static Equilibrium (p. 5-6); Lab Report due Thursday
________ Day 3: Static Equilibrium
 Do Now, p. 39
 Static Torque Lab, Part I (p. 6-7)
 HW: Complete Beginning Ideas and Tests (p. 1) of Torque Lab, Part II (Separate); Lab report due
tomorrow
________ Day 4: Static Equilibrium
 Do Now, Homework Check
 Static Torque Lab, Part II (Not in Packet)
 HW: P. 22: #1-2 on a sheet of notebook paper with explanations; quiz tomorrow
________ Day 5: Static Equilibrium
 Static Equilibrium Quiz
 HW: Reread sections 7.1 – 7.2, 7.5 – 7.7 and check notes
________ Day 6: Rotational Kinematics
 Do Now, Quizzes back
 LadyBug Revolution (p.8-9)
 Rotational Kinematics Practice Problems (p.10)
 HW: Finish Rotational Kinematics Practice Problems (p.10)
________ Day 7: Rotational Dynamics
 Do Now, p. 37
 Torque and Angular Acceleration, Parts I and II (p.12-13)
 HW: p. 21: #3, p. 22: #4-6 on a sheet of notebook paper with explanations
________ Day 8: Rotational Dynamics
 Do Now, p. 35
 A Pulley Problem (p.11) and p. 24 #10
 HW: Finish CW and Read and take notes on Angular Momentum (Ch. 9); see note guide
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 3
________ Day 9: Rotational Dynamics and Angular Momentum
 Rotational Dynamics Quiz
 Lecture
 Angular Momentum Problems (p.14)
 HW: p. 22-23; #7-9 on a sheet of notebook paper with explanations.
________ Day 10: Angular Momentum
 Do Now: HW Check
 Conservation of Angular Momentum (p.15-16)
 HW: Finish Classwork; p. 26-27; #12
________ Day 11: AP Angular Momentum
 Do Now: HW Check
 AP Free Response Problem (p.25-26 #11)
 HW: Finish CW
________ Day 12: Angular Momentum
 Do Now, p. 33
 AP Free Response Problem (p.28)
 HW: Choose one of the free response AP problems and redo it on notebook paper.
________ Day 13: The Rotating Lab, Day 1
 Do Now: HW Check
 The Rotating Lab (p.17)
 HW: Begin Lab Report
________ Day 14: The Rotating Lab, Day 2
 Do Now: Grab materials
 The Rotating Lab (p.17)
 HW: The Toilet Paper Challenge (p. 21)
________ Day 15: The Toilet Paper Challenge
 Do Now: HW Check
 The Toilet Paper Challenge (p.20)
 HW: Study for the exam; Write the lab report
________ Day 16: Review
 Do Now, p. 21, 1-3
 Review
 HW: Study for your unit exam and write your lab report.
________ Day 17: Rotational Motion Unit Test
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 4
TORQUE AND STATIC EQUILIBRIUM
1. A teeter-totter (or see-saw) is balanced, as shown below. What
is the length of the see-saw?
2. A meter stick is hanging from a thread at the 50 cm point. M1 has a mass of 3 kg and is hanging from the 0
cm point. If M2 is hanging at the 80 cm mark, and the stick remains horizontal, what does M2 have to be?
m1
3. A 3.0 m board weighing 100 N sits across two sawhorses, as
shown below. What are the magnitudes of the normal forces
of the sawhorses acting on the board?
M2
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 5
4. A 5-meter plank of uniform mass 100 kilograms rests on the top of a building with two meters extended
over the edge, as shown below. How far can a 50 kg person venture past the edge of the building on the
plank before the plank begins to tip?
5. A 50 m bridge is held up by two suspension cables, each of which is 5 meters from either end of the bridge.
If the bridge itself is made of concrete and has a mass of 400 kg, what is the tension in each of the cables?
Assume the bridge’s center of gravity is at its center.
6. A beam is supported as shown. The beam is uniform and weighs 300.0 N and is 5.50
m long. A 635 N person stands 1.50 m from the building. What is the tension in the
cable?
55.0
5.50 m
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 6
STATIC TORQUE LAB (Part I)
Set-Up:
A piece of 50 cm string was tied to a spring-scale handle. A Simple Form Truss was set-up using a half-meter
stick two binding clips, a 500 gram mass, and a support stand, as shown in Figures 5 and 6. A 15-cm string was
tied around the binder clip to form a loop that was just large enough to allow the string to slide along the meter
stick, according to Figure 7. The binder clip was clipped from the bottom edge of the meter stick. The hooked
mass was hung from the string.
With your group, use the set-up above to determine if the following claims are valid or invalid. Provide direct
evidence from your lab and reasoning from your textbook.
1. Claim: With the 500 g mass and the string attachment points fixed at given distances (see Figure 5), the
force needed to maintain equilibrium increases when the string angle is increased. (Measure all angles with
respect to the horizontal.)
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 7
2. Claim: When the distance from the pivot point is increased for the 500 g mass in question #1 and the string
is held at a fixed angle, the force needed to maintain equilibrium increases.
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
3. Claim: In the arrangement in question #1, if the string attachment point is moved closer to the pivot point
and the string angle is fixed, the force needed to maintain equilibrium increases.
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 8
LADYBUG REVOLUTION
Google the following: Phet Ladybug Revolution. Click on the first link, and click “Run Now.” For each of the
following statements, use the simulation to determine if the given claim is valid or invalid. Support your
answer with specific evidence from the simulation (this can include measured values, sketches of graphs, or
sketches of the turn-table, for example) and reasoning from the textbook (this can be direct quotes or
summaries, but it should include page numbers).
1. Claim: Objects at different locations from the central axis of a rotating object have different angular
velocities.
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 9
2. Claim: Objects at different locations from the center of a rotating object have different circular velocities.
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
3. Claim: An object rotating with a constant angular acceleration will have a constant angular velocity.
a. Valid or Invalid? _____________________
b. Evidence:
c. Reasoning:
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 10
ROTATIONAL KINEMATICS PRACTICE PROBLEMS
1. Compute the angular velocity in rad/s of the crankshaft of an automobile engine that is rotating at 4800
rev/min.
2. A circular saw blade 0.6 m in diameter starts from rest and accelerates with a constant angular acceleration
to an angular velocity of 100 rad/s in 20 s. Find the angular acceleration and the angle through which the
blade has turned.
3. A flywheel requires 3 s to rotate through 234 rad. Its angular velocity at the end of this time is 108 rad/s.
Find:
a. the angular velocity at the beginning of the 3 s interval.
b. the constant angular acceleration.
4. A flywheel whose angular acceleration is constant and equal to 2 rad/s2 rotates through an angle of 100 rad
in 5 s. How long had it been in motion at the beginning of the 5 s interval if it started from rest?
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 11
A PULLEY PROBLEM
A hanging weight of 30 g is attached to a string which is wrapped around a frictionless pulley of radius 5 cm.
The weight is released from rest and falls a distance of 1.5 meters in 2.1 seconds as the string unwinds from the
pulley, causing it to rotate. Using this information, calculate:
1. The initial potential energy of the weight.
2. The final kinetic energy of the pulley and the weight.
3. The linear acceleration of the falling weight as it falls.
4. The linear speed of the weight just before it hits the floor.
5. The angular speed of the pulley just before the weight hits the floor.
6. The moment of inertia of the pulley.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 12
TORQUE AND ANGULAR ACCELERATION – PART I
Consider the system at right. There is no friction anywhere in the system except to keep the rope from slipping
around the pulley. The pulley is a solid disk that has mass M and radius R. Find:
1. The moment of inertia of the pulley.
2. The net torque on the pulley.
3. The net force on each of the blocks.
4. The acceleration of the two blocks.
5. The angular acceleration of the pulley.
6. The tension in the rope.
7. Assume m1 = 0.05 kg, m2 = 1.3 kg, M = 0.178 kg, and R = 6.0 cm. Find the time for the mass m1 to fall 90
cm.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 13
TORQUE AND ANGULAR ACCELERATION – PART II
Two weights, each of mass m, are attached to the ends of a rigid, weightless rod of length L. The rod is held in
the horizontal position and then released.
1. Calculate the moment of inertia of the system about the axis at
point P, a distance L/4 from the left end.
2. Calculate the torque due to gravity about the axis P.
3. Calculate the initial angular acceleration of the weights and rod just after they are released.
4. As the rod rotates, does the angular acceleration increase, decrease, or remain the same? Explain.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 14
ANGULAR MOMENTUM PROBLEMS
1. Joey, whose mass is 36 kg, stands at the center of a 200 kg merry-go-round that is rotating once every 2.5s.
While it is rotating, Joey walks out to the edge of the merry-go-round, 2.0 m from its center. What is the
rotational period of the merry-go-round when Joey gets to the edge?
2. An ice skater spins around on the tips of his blades while holding a 5.0 kg weight in each hand. He begins
with his arms straight out from his body and his hands 140 cm apart. While spinning at 2.0 rev/s, he pulls
the weights in and holds them 50 cm apart against his shoulders. If we neglect the mass of the skater, how
fast is he spinning after pulling the weights in?
3. A little girl is going on the merry-go-round for the first time, and she wants her 47 kg mother to stand next
to her on the ride, 2.6 m from the merry-go-round’s center. If her mother’s speed is 4.2 m/s when the ride is
in motion, what is the mother’s angular momentum around the center of the merry-go-round?
4. Divers change their body position in midair while rotating about their center of mass. In one dive, the diver
leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of
inertia of the diver in a straight position is 14 kg m2 and in a tucked position is 4.0 kg m2, by what factor is
her angular velocity when tucked greater than when straight?
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 15
CONSERVATION OF ANGULAR MOMENTUM
1. A uniform disk such as a record turntable turns at 7 rev/s around a frictionless spindle. A non-rotating rod,
of the same mass as the disk and length equal to the disk’s diameter is dropped onto the freely spinning disk.
They then both turn around the spindle with their centers superposed. What is the angular velocity in rev/s
of the combination?
2. An asteroid of mass 100,000 kg traveling at a speed of 30 km/s relative to the Earth, hits the Earth at the
equator. It hits the Earth tangentially and in the direction of the Earth’s rotation and stops moving. Use
angular momentum to estimate the fractional change in the angular speed of the Earth as result of the
collision.
3. Suppose our sun eventually collapses into a white dwarf, in the process losing about half its mass and
winding up with a radius 1.0 percent of its existing radius.
a. What would its new rotation rate be? Take the sun’s current period to be about 30 days.
b. What would its final KE be in terms of its initial KE of today?
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 16
4. A non-rotating cylindrical disk of moment of inertia I is dropped onto an identical disk rotating at an angular
speed ω0. Assuming no external torques, what fraction of the original disk’s rotational energy is lost to
friction in the collision?
5. A bullet of mass 5.0 grams and velocity 330 m/s is shot into a wheel that is initially at rest. The wheel is
solid disk of mass 2.0 kg and radius 18 cm. The bullet strikes the edge tangentially and sticks to the edge.
What are the disks final angular velocity, angular momentum, and rotational kinetic energy?
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 17

Due Date:
Student Name:
, 2015 at
11:59 pm1
Course Name: AP Physics
Student did not
submit the assignment.
Period: 3
Teacher Name: Mr. Khalilian
Assignment Title:
The Rotating Lab Write-Up
Assignment
Summary:
Your job is to calculate the moment of inertia, I, of the pulley system provided using
what you have learned this unit.
Format: 5 – 10
deductions
possible for any
infraction
Procedure and
Helpful Hints:
This will require an incorporation of everything you have learned so far. You will be
expected to collect data from multiple trials (3-5) and average those trials before
performing calculations. You will also be expected to run trials with different masses
(at least 3).
 MLA Format heading
 Section headers for each section from the
rubric.
 Title: The Rotating Lab WriteUp
 You do NOT need to submit a paper copy.
 Submitted to Turnitin.com.
(Without this, the lab report is a
0.)
Before writing your paper, you should:
1. List out everything you have learned this unit that may be helpful in solving this
problem. From that information, determine what can be measured and what must be
calculated.
2. Make measurements and record these in a data table.
3. Calculate the necessary pieces, and record these in a separate table. Graphs are nice
here, too.
4. Read the rubric to write your lab report.
Rubric
1
Computer errors reported the day the lab report is due or the day before will not be excused. Start early.
Student:
Mr. Khalilian
AP Physics
Due Date:
Beginning
Ideas
Tests
Observations
and Data
Claims
Evidence
Unit 8 – Rotational Motion
Practice Packet, page. 18
I
Student is able to articulate the purpose of the lab (what he or she should attain) as either a
statement or an overarching question. This articulation may be vaguely on the topic or more
specific.
II
Student is able to do two of the following: 1) include a prior knowledge on the topic at hand, 2)
craft a simple hypothesis for what he or she expects to see/do, 3) break the testable question
down into smaller, more concrete questions that will lead to the answering of the testable
question.
III
In addition to everything in level II, student can relate the prior knowledge to the testable
questions and use their hypothesis to connect what they already know to their testable question.
I
Student does one of the following: (1) Student states/describes what was manipulated (only if
applicable), what was measured, and what was controlled; (2) Student describes the set-up of the
lab, including any techniques. Student includes the tools used to measure.
II
Student does both things at the level I.
III
Student is quantitative (when necessary) and describes calculations (when necessary), and clearly
connects the test section back to their purpose question/statement.
I
Student is inclusive in what he has seen. (All necessary data are present.) Data tables are clearly
organized (though they may not be in the proper order), with units where appropriate. All
language used is accurate.
II
Data tables are translated into graphs, which include axis labels with units and a title. Data are
correctly graphed. No inferences or generalizations are present. Data tables and graphs are
clearly and neatly organized and labeled. All appropriate visuals are used.
III
In addition to II, calculations are separated from measurements and are accounted for. Data
analysis is separated and references R2 values and standard deviation with a discussion about the
accuracy and precision of the data. Verbal description of data table without interpretation is
included.
I
Student creates a claim that is based on the data though it is not necessarily answering the
original question.
II
Student answers the question(s) at the beginning, and claim is clearly related to the data.
Example: Carbon dioxide impacts plant growth.
III
Student is directional and specific in answering the question(s) at the beginning. When
necessary, null-hypothesis or A/B testing is addressed.
Example: Plants growth increases when carbon dioxide is higher.
I
Evidence from the student’s data section is specifically cited in support of the claim. When
applicable, numerical evidence must be used. Erroneous evidence may be present as long as
correct evidence is also cited.
II
Includes only the evidence that pertains to the claim (numbers, math calculations, findings from
outside articles). Explains variations in the evidence/data.
III
In addition to II, organizes data into subsections, is concise, and includes numbers, math
calculations, and findings in outside articles. Also explains variations and level of confidence in
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 19
evidence (with a scientifically sound rationale). % error is referenced when appropriate and used
correctly to discuss variance in evidence.
Reasoning
Reflection
Writing
Conventions
I
Student is able to cite similar labs and parts of textbooks that pertain to the lab.
II
Student is able to pull relevant parts of other labs and/or textbooks to address the concepts in the
lab. Sources are properly cited.
III
In addition to II, student builds off of texts, using the results of his or her lab. The concepts are
elaborated on. Several sources (more than two) are compared to the student’s experiment.
I
Student is able to identify what he has learned from the lab but does not necessarily compare this
to what he knew before. (NOTE: Specifically what did you do in this lab that you had not done
before?)
II
Student is able to clearly and concisely indicate how his ideas have changed by the lab. (NOTE:
How is the level I thing different than what you had done up until this lab?)
III
Student is able to self-assess prior misconceptions and explain how his results render the
misconceptions incorrect. (NOTE: What did you overcome to be successful in this lab? What
had you struggled with previously that this lab made clear?)
I
Student is able to provide at least one real-world application of either the concepts or the lab
techniques used in the experiment.
II
Student is able to clearly and concisely explain the importance of the lab work outside of the
classroom.
III
In addition to II, student builds off of his explanation to include further research in this area.
I
Appropriate sections are written in paragraph form. Few major grammar errors are present.
II
No major grammar errors are present. Sentence structure is varied and not awkward.
III
Few to no minor grammar errors are present. Sentence structure is varied and not awkward. Lab
report is written in professional voice.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 20
THE TOILET PAPER CHALLENGE (AKA ROLLS IN SYNCH)
The Task: You will be given two rolls of toilet paper and a meter stick. Your task is to determine the ratio of
heights so that both rolls land at the same time when dropped as shown in the sketch below (one is dropped; for
the other, the first square is held such that it unrolls as it falls).
Useful information:
M: Mass of dropped toilet paper
m: Mass of unrolled toilet paper
R: Outer radius (from center to the far side of the roll)
r: Inner radius (from center to the cardboard)
1
Moment of Inertia for a cylinder: 𝐼𝑐 = 2 𝑀(𝑟 2 + 𝑅 2 )
Moment of Inertia for unrolled roll rotating about its outer radius:
1
𝐼𝑢𝑛 = 𝑀(𝑟 2 + 3𝑅 2 )
2
Your Homework: On notebook paper, Draw Force Diagrams for each
toilet paper roll. (Hint: for the roll subject to rotational motion, it does
matter where the forces are drawn and where you define the axis of
rotation.) Figure out an equation for each roll that solves for height for
each roll. (Hint: You will use one of the two moments of inertia, depending on where you define your “axis of
rotation” to be. Either will work.) On this paper, write any questions you have for your group mates.
In Class: Compare your solutions to those of your group mates. When your group has reached a consensus, test
it!
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 21
ROTATIONAL MOTION PRACTICE AND REVIEW
1. A rod of negligible mass is pivoted at a point that is off-center, so that length l 1 is different from length l2.
The figures above show two cases in which masses are suspended from the ends of the rod. In each case
the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is
the value of m in terms of the known masses?
(A) Ml + M2
(B) ½(Ml + M2)
(C) Ml M2
(D) M1 M 2
2. A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common
center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the
wheels, as shown above. The magnitude of the net torque on the system about the axis is
(A) FR
(B) 2FR
(C) 5FR
(D) 14FR
3. A light rigid rod with masses attached to its ends is pivoted about a horizontal axis as shown above. When
released from rest in a horizontal orientation, the rod begins to rotate with an angular acceleration of
magnitude
g
5g
g
g
(A) 7l
(B) 5l
(C) 4l
(D) 7 l
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 22
Questions 4-5
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates
clockwise on a horizontal shaft S with constant angular velocity . As the wheel rotates, the ant revolves
past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its
own weight.
4. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?
(A) I
(B) II
(C) III
(D) IV
5. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point
III?
(A) mg
(B) m2r
(C) m2r - mg
(D) m2r + mg
6. Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and
moment of inertia I about its center. T1 and T2 are the tensions in the string on either side of the pulley and α
is the angular acceleration of the pulley. Which of the following equations best describes the pulley's
rotational motion during the time the blocks accelerate?
(A) m2gR = Iα (B) T2R = Iα (C) (T2 - T1)R = Iα (D) (m2 – m1)gR = Iα
7. A bowling ball of mass M and radius R. whose moment of inertia about its center is (2/5)MR2, rolls without
slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an
incline is
2
(A) v
5g
2
(B) 2v
5g
2
(C) v
2g
2
(D) 7v
10 g
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 23
8. The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars
with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the
diagram. The body rotates about a vertical axis along the support post with constant angular speed . If the
masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the
two upper spheres to that of the two lower spheres?
(A) 2/1
(B) 1/2
(C) 1/4
(D) 1/8
Top View
9. Multiple Correct. A disk sliding on a horizontal surface that has negligible friction collides with a rod that
is free to move and rotate on the surface, as shown in the top view above. Which of the following quantities
must be the same for the disk-rod system before and after the collision? Select two answers.
I. Linear momentum
II. Angular momentum
III. Kinetic energy
(A) Linear Momentum
(B) Angular Momentum
(C) Kinetic Energy
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 24
10. 1983M2. A uniform solid cylinder of mass m1 and radius R is mounted on frictionless bearings about a
fixed axis through O. The moment of inertia of the cylinder about the axis is I = ½m1R2. A block of mass
m2, suspended by a cord wrapped around the cylinder as shown above, is released at time t = 0.
a. On the diagram below draw and identify all of the forces acting on the cylinder and on the block.
b.
In terms of ml, m2, R. and g, determine each of the following.
i. The acceleration of the block
ii. The tension in the cord
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 25
Disk: mass = 3m, radius = R, moment of inertia about
center ID = 1.5mR2
Rod: mass = m, length = 2R, moment of inertia about
one end IR = 4/3(mR2)
Block: mass = 2m
11. 1999M3 As shown above, a uniform disk is mounted to an
axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk so that it will
rotate with the disk. A block is attached to the end of the rod. Properties of the disk, rod, and block are to
the left of the picture.
The system is held in equilibrium with the rod at an angle 0 to the vertical, as shown above, by a horizontal
string of negligible mass with one end attached to the disk and the other to a wall. Express your answers to
the following in terms of m, R, 0, and g.
a. Determine the tension in the string.
The string is now cut, and the disk-rod-block system is free to rotate.
b.
Determine the following for the instant immediately after the string is cut.
i. The magnitude of the angular acceleration of the disk
ii. The magnitude of the linear acceleration of the mass at the end of the rod
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 26
As the disk rotates, the rod passes the horizontal position shown above.
c. Determine the linear speed of the mass at the end of the rod for the instant the rod is in the horizontal
position.
12. 2004M2. A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as
shown above. A small block of mass m is attached to a string, the other end of which is attached to the
pulley and wrapped around it several times. The block of mass m is released from rest and takes a time t to
fall the distance D to the floor.
a. Calculate the linear acceleration a of the falling block in terms of the given quantities.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 27
b. The time t is measured for various heights D and the data are recorded in the following table.
i. What quantities should be graphed in order to best determine the acceleration of the block? Explain your
reasoning.
ii. On the grid below, plot the quantities determined in b. i., label the axes, and draw the best-fit line to the
data.
iii. Use your graph to calculate the magnitude of the acceleration.
c. Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants.
d. The value of acceleration found in b.iii, along with numerical values for the given quantities and your
answer to c., can be used to determine the rotational inertia of the pulley. The pulley is removed from its
support and its rotational inertia is found to be greater than this value. Give one explanation for this
discrepancy.
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 28
13. 2005M3. A system consists of a ball of mass
M2 and a uniform rod of mass M1 and length d.
The rod is attached to a horizontal frictionless
table by a pivot at point P and initially rotates
at an angular speed ω, as shown above left.
The rotational inertia of the rod about point P
is
1
3
M1d2 . The rod strikes the ball, which is
initially at rest. As a result of this collision, the
rod is stopped and the ball moves in the
direction shown above right. Express all
answers in terms of M1, M2, ω, d, and fundamental constants.
a. Derive an expression for the angular momentum of the rod about point P before the collision.
b. Derive an expression for the speed v of the ball after the collision.
c. Assuming that this collision is elastic, calculate the numerical value of the ratio M1 / M2
d. A new ball with the same mass M1 as the rod is now placed a distance x from the
pivot, as shown above. Again assuming the collision is elastic, for what value of
x will the rod stop moving after hitting the ball?
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 29
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 30
FOUR IN FIVE
Questions 1-2
Questions 3-4
A student obtains data on the magnitude of force
applied to an object as a function of time and
displays the data on the graph above.
1. The slope of the "best fit" straight line is
most nearly
a. 5 N/s
b. 6 N/s
c. 7 N/s
d. 8 N/s
e. 10 N/s
2. The increase in the momentum of the object
between t = 0 s and t = 4 s is most nearly
a. 40 N•s
b. 50 N•s
c. 60 N•s
d. 80 N•s
e. 100 N•s
A horizontal, uniform board of weight 125 N
and length 4 m is supported by vertical chains at
each end. A person weighing 500 N is sitting on
the board. The tension in the right chain is 250
N.
3. What is the tension in the left chain?
a. 250 N
b. 375 N
c. 500 N
d. 625 N
e. 875 N
4. How far from the left end of the board is the
person sitting?
a. 0.4 m
b. 1.5 m
c. 2 m
d. 2.5 m
e. 3 m
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 31
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 32
FOUR IN FIVE
1. An object attached to one end of a string
moves in a circle at constant speed. Which
of the following is correct?
(A) The object is accelerating as it moves.
(B) The object's velocity is the same as its
speed.
(C) The object does not require a force to
keep its state of circular motion.
(D) If the string breaks, the object will keep
its circular motion.
(E) If the string breaks, the object will move
radially away from the center of the circle.
2. Two skaters are initially at rest next to each
other on frictionless ice. Skater A pushes on
skater B. If skater A has greater mass than
skater B, which of the following correctly
relates the magnitudes of their momentums
p and their kinetic energies K after the push?
(A) pA = pB and KA < KB
(B) pA = pB and KA = KB
(C) pA = pB and KA > KB
(D) pA < pB and KA < KB
(E) pA < pB and KA =
3. Which of the following is true of the
conservation of momentum and kinetic
energy?
(A) Momentum is conserved only in elastic
collisions.
(B) Momentum is conserved only in
inelastic collisions.
(C) Kinetic energy is conserved only in
elastic collisions.
(D) Kinetic energy is conserved only in
inelastic collisions.
(E) Both require the same conditions in
order to be conserved.
4. A force of constant magnitude F and fixed
direction acts on an object of mass m that is
initially at rest. If the force acts for a time
interval t over a displacement x, what is
the magnitude of the resultant change in the
linear momentum of the object?
(A) Ft
(B) Fx
(C) Ft / m
(D) Fx / m
(E) mFt
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 33
Student:
Mr. Khalilian
AP Physics
Due Date:
FOUR IN FIVE
1. A ball is thrown with an initial speed of 20
m/s at an angle of 60° to the ground. If air
resistance is negligible, what is the ball's
speed at the instant it reaches its maximum
height from the ground?
(A) Zero
(B) 10 m/s
(C) 14 m/s
(D) 17 m/s
(E) 20 m/s
2. A box is given a sudden push up a ramp.
Friction between the box and the ramp is not
negligible. Which of the following diagrams
best represents the directions of the actual
forces acting on the box as it moves upward
after the push?
Unit 8 – Rotational Motion
Practice Packet, page. 34
3. In a lab, a block weighing 80 N is attached
to a spring scale, and both are pulled to the
right on a horizontal surface, as shown
above. Friction between the block and the
surface is negligible. What is the
acceleration of the block when the scale
reads 32 N?
(A) 2.0 m/s2
(B) 2.5 m/s2
(C) 4.0 m/s2
(D) 6.0 m/s2
(E) 8.0 m/s2
4. The system shown above is released from
rest. If friction is negligible, the acceleration
of the 4.0kg block sliding on the table
shown above is most nearly
(A) 0
(B) 1.7 m/s2
(C) 3.3 m/s2
(D) 5.0 m/s2
(E) 10.0 m/s2
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 35
Student:
Mr. Khalilian
AP Physics
Due Date:
FOUR IN FIVE
1. A small car with mass m and speed 2v and a
large car with mass 2m and speed v both
travel the same circular section of an
unbanked road. If the frictional force
required to keep the small car on the road
without skidding is F, then the frictional
force required to keep the large car on the
road without skidding is
(A) 4F
(B) 2F
(C) F
(D) F/2
(E) F/4
2. For which of the following motions of an
object must the acceleration always be zero?
I. Any motion in a straight line
II. Simple harmonic motion
III. Any motion in a circle
a. I only
b. II only
c. III only
d. Either I or III, but not II
e. None of these motions guarantees zero
acceleration.
3. A rope of negligible mass supports a block
that weighs 30 N, as shown above. The
breaking strength of the rope is 50 N. The
largest acceleration that can be given to the
block by pulling up on it with the rope
without breaking the rope is most nearly
a. 6 m/s2
b. 6.7 m/s2
c. 10 m/s2
2
2
d. 15 m/s
e. 16.7 m/s
Unit 8 – Rotational Motion
Practice Packet, page. 36
4. A block attached to the lower end of a
vertical spring oscillates up and down. If the
spring obeys Hooke's law, the period of
oscillation depends on which of the
following?
I.
Mass of the block
II.
Amplitude of the oscillation
III.
Force constant of the spring
a. I only
d. I and II
b. II only
e. I and III
c. III only
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 37
Student:
Mr. Khalilian
AP Physics
Due Date:
FOUR IN FIVE
1. An empty sled of mass M moves without
friction across a frozen pond at speed vo.
Two objects are dropped vertically into the
sled one at a time: first an object of mass m
and then an object of mass 2m. Afterward
the sled moves with speed vf . What would
be the final speed of the sled if the objects
were dropped into it in reverse order?
a. vf /3
b. vf /2
c. vf
d. 2vf
e. 3vf
2. A new planet is discovered that has twice
the Earth's mass and twice the Earth's radius.
On the surface of this new planet, a person
who weighs 500 N on Earth would
experience a gravitational force of
a. 125 N
b. 250 N
c. 500 N
d. 1000 N
e. 2000 N
Unit 8 – Rotational Motion
Practice Packet, page. 38
3. The graph above represents position x
versus time t for an object being acted on by
a constant force. The average speed during
the interval between 1 s and 2 s is most
nearly
a. 2 m/s
b. 4 m/s
c. 5 m/s
d. 6 m/s
e. 8 m/s
4. Two objects, A and B, initially at rest, are
"exploded" apart by the release of a coiled
spring that was compressed between them.
As they move apart, the velocity of object A
is 5 m/s and the velocity of object B is -2
m/s. The ratio of the mass of object A to the
mass of object B, mA/mB, is
a. 4/25
b. 2/5
c. 1/1
d. 5/2
e. 25/4
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 39
Student:
Mr. Khalilian
AP Physics
Due Date:
Unit 8 – Rotational Motion
Practice Packet, page. 40
MANIPULATING GRAPHS
The following assignment requires your graphing calculator. At any point, you can check your work by typing
the values into your calculator and seeing if they match your correct parent function. The first three examples
have been done for you.
Original
Parent function Substitution
New X
New Y
Slope of line
Function
(including x and
y)
y = 3x;
f(x) = mx
None (straight
x
y
3
graphing y and
line)
x
y = 5kx2 ;
f(x) = mx2
u = x2
u (x2)
y
5k
graphing y and
x
f(x) = mx
None (straight
t
v
𝑥 = 𝑥𝑥 ;
x
line)
graphing x and t
Σ𝑥 = 𝑥𝑥;
graphing ΣF
and a
1
𝑥 = 2 𝑥𝑥2 ;
graphing K and
v
Δ𝑥
𝑥=
;
𝑥
graphing I and
R
𝑥2
𝑥𝑥 = 𝑥 ;
graphing a and r
𝑥2
𝑥𝑥 = 𝑥 ;
graphing a and
v
𝑥 = √2𝑥ℎ ;
graphing v and
h
𝑥
𝑥𝑥 = 2𝑥√𝑥 ;
graphing Ts and
m
𝑥
𝑥𝑥 = 2𝑥√𝑥 ;
graphing Ts and
k