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AP PHYSICS 1
(SECONDARY)
ESSENTIAL UNIT (E07)
(Rotational Motion & Torque)
(Giancoli Chapter 8)
(July 2015)
Unit Statement: Until now, only translational motion has been discussed, namely; kinematics,
dynamics and the role that force and energy have on this type of motion. This unit will focus on
rotational motion including torque and the affect energy, angular momentum and force have on
rotational motion. This unit will significantly help in the understanding of the world around us
from rotating bicycle wheels, how DVD’s play, to amusement park rides, planet rotation and
centrifuges. All of the information mastered in the last units will be reiterated and used for
further investigations. (Estimated class time three weeks)
Essential Outcomes: (must be assessed for mastery)
1. The Student Will describe the force component as being perpendicular to the line
connecting the axis of rotation and the point of application of the force resulting in a
torque about that axis. Including:
a. The lever arm is the perpendicular distance from the axis of rotation or revolution
to the line of application of the force.
b. The magnitude of the torque is the product of the magnitude of the lever arm and
the magnitude of the force.
c. The net torque on a balanced system is zero. (EK 3.F.1)
2. TSW predict the behavior of rotational collision situations, by the same processes that are
used to analyze linear collision situations, using an analogy between impulse and
change of linear momentum and angular impulse, and change of angular
momentum. (LO 3.F.3.1)
3. TSW justifies that a torque exerted on an object can change the angular momentum of an
object. (EK 3.F.3)
4. TSW will recognize the presence of a net torque along any axis causes a rigid system to
change its rotational motion or an object to change its rotational motion about that
axis. Including:
a. Rotational motion can be described in terms of angular displacement, angular
velocity, and angular acceleration about a fixed axis.
b. Rotational motion of a point can be related to linear motion of the point using the
distance of the point from the axis of rotation.
c. The angular acceleration of an object or rigid system can be calculated from the
net torque and the rotational inertia of the object or rigid system. (EK3.F.2)
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5. TSW characterize torque, angular velocity, angular acceleration, and angular momentum
as vectors and classify as positive or negative depending upon whether they give
rise to or correspond to counterclockwise or clockwise rotation with respect to an
axis. (EK 4.D.1)
6. TSW calculate the change in angular momentum given by the product of the average
torque and the time interval during which the torque is exerted. (EK 4.D.3)
7. TSW justify that if the net external torque exerted on the system is zero, the angular
momentum of the system does not change. (EK 5.E.1)
8. TSW describe or calculate the angular momentum and rotational inertia of a system in
terms of the locations and velocities of objects that make up the system. (LO
5.E.2.1)
Guided or Essential Questions:
1. What are the conditions necessary for two people with significant differences in mass to
balance on a seesaw?
2. What are the conditions necessary for static equilibrium?
3. In what ways are rotational motion and linear motion related?
4. What are the relationships among angular momentum, angular velocity, angular
acceleration, rotational inertia, and torque?
Key Concepts:
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Rigid Object
Axis of rotation
Instantaneous angular velocity
Frequency
Constant angular acceleration
Lever arm (moment arm)
Rotational Kinetic Energy
Law of conservation of angular
momentum
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Radian
Average angular velocity
Instantaneous angular acceleration
Period
Torque
Moment of inertia
Angular momentum
Right-hand rule
Some Common Equations for this Unit:

t


t
vT  r
aT  r
Angular Velocity

Angular Acceleration
Tangential velocity
Tangential acceleration
Centripetal acceleration
vT2
 r 2
r
1
  it   (t ) 2
2
f  i  t
f 2  i 2  2
1
KEr  I 2
2
ac 
v
Uniformly accelerated rotational motion
Rotational kinetic energy
2r
T
Velocity of a satellite in circular orbit, with period
T
Centripetal force on an orbiting satellite
mv 2
Fc 
r
v
T
Velocity of a satellite in circular orbit
GmE
r
2r
Period of a satellite in circular orbit
3
2
GmE
  FL sin 
Torque
I  mL2
Moment of inertia
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Schedule of suggested laboratory experiments (guided inquiry format is suggested for labs
shaded in gray)
TSW #
Lab #
1
33
Name of Laboratory
Balancing Act
Description of Lab
In this activity, students work in groups to discover the
relationship between force and torque. Students are
given hooked masses and a meterstick with predrilled
holes, and they must create as many different
configurations as they can that balance the stick
horizontally. Then students calculate the torques
produced (clockwise and counterclockwise) in each
configuration. Follow-up questions include
the following:
1. Does the angle at which a force is applied
affect the total torque?
2. You are stranded in a situation where you
need to loosen a rusty bolt.
You have a wrench, but using it you are still
unable to apply enough torque to loosen the
bolt. You also have some pieces of steel pipe.
How can you loosen the bolt without much
effort?
Associated Science
Practices
1.1, 1.2, 1.4, 1.5,
2.1, 2.2, 3.1, 4.1,
4.2, 4.3, 5.1, 5.3,
6.1, 6.4, 7.2
Teacher Produced
Or PhET Balancing Act could be used instead (see link
below)
2
3, 4, 5
34
35
“Lady Bug: Angular
Kinematics”
and “Ladybug Revolution”
Merry Go Round
“Lady Bug: Angular Kinematics,” a guided-inquiry activity
that involves the “Ladybug Revolution” simulation, is
used to help students discover the basics of rotational
kinematics. Angular velocity, angular acceleration, and
the relationships of the angular kinematic equations to
their linear counterparts are investigated. Answers to
questions embedded within the activity are submitted for
grading, and student–teacher discussions are held as
needed to address student misconceptions.
PhET- see link below
Working in small groups, students use a playground
merry-go-round to investigate how the application of an
external torque affects the angular velocity and angular
momentum of an object. Once students believe they
have a qualitative idea of the relationship, they must
collect and analyze data to support their conclusions
quantitatively. A lab report is required from each group
at the conclusion of the activity.
Teacher Option
1.http://hendrix2.uoregon.edu/~dlivelyb/phys101/lab4_s
07.pdf
2.http://dev.physicslab.org/Document.aspx?doctype=3&f
ilename=RotaryMotion_CentripetalAccRotation.xml
3.http://www.dartmouth.edu/~physics/labs/writeups/ro
tational.motion.pdf
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1.1, 1.2, 1.4, 1.5,
2.1, 2.2, 3.1, 4.1,
4.2, 4.3, 5.1, 5.3,
6.1, 6.4, 7.2
1.1, 1.2, 1.4, 1.5,
2.1, 2.2, 3.1, 4.1,
4.2, 4.3, 5.1, 5.3,
6.1, 6.4, 7.2
1,4
1-5
36
37
Popper toy, circular rotating
Platforms
Conservation of Angular
Momentum and Energy
Working in groups, students analyze and predict the
motion of two adjacent merry-go-round analogs when a
popper toy is used to exert a force from one onto the
other in two situations:
1. From the bottom of the left-hand merry-goround to the bottom of the right-hand merrygo-round (viewed from above)Along a line
tangent to the circles, from one onto the other,
where the adjacent merry-go-rounds touch
2. Students should easily determine the expected
direction of rotation for both merry-go-rounds
after the forces are applied, but they should
find an apparent discrepant event in terms of
conservation of angular momentum. Group
members conduct research and collaborate to
determine why the law of conservation of
angular momentum is not broken. Each group
provides a written explanation.
WebQuest
In pairs or small groups, students investigate how the
angular momentum of a rotating system responds to
changes in the rotational inertia. The experiment involves
the collection of data of angle versus time and angular
velocity versus time. Students use a rotary motion sensor
with an aluminum plate that is spun to a certain angular
speed, and then a second plate is dropped onto the first
one, resulting in a change of the moment of inertia and
the angular speed. The students analyze the graphs
before and after the changes in the rotational inertia and
determine the effect of changes in the rotational inertia
on the angular momentum of the system.
1.1, 1.2, 1.4, 1.5,
2.1, 2.2, 3.1, 4.1,
4.2, 4.3, 5.3, 6.1,
6.4, 7.2
1.1, 1.2, 1.4, 1.5,
2.1, 2.2, 3.1, 4.1,
4.2, 4.3, 5.1, 5.3,
6.1, 6.4, 7.2
Vernier
Suggested Materials:
1. Giancoli, D.C. Physics: Principles with Applications. Englewood Cliffs, NJ: Pearson
Education.
2. Appel, K, Ballen, C, Gastineau, J, Vernier, D. Physics with Vernier. Beaverton, OR;
Vernier Software and Technology, 2010.
3. Puri, O; Zober, P. Physics. A laboratory manual; Boston, Mass. N.Y: Pearson Custom
Pub., 2002. 8th edition
4. Optional- Van Hook, Stephen J. “Battle of the Merry-Go-Rounds: An Angular
Momentum Demonstration.” The Physics Teacher 44, no. 5 (2006): 304-307.
http://scitation.aip.org/content/aapt/journal/tpt/44/5/10.1119/1.2195403
Suggested Technology Resources:
Labs, in class activities, quizzes, videos and demos:
1. Quick Podcast explaining equilibrium by drawings so everyone can understand the topic.
This is the first in a series. Hewitt-Drew-it! PHYSICS 1. Equilibrium Rule Hewitt-Drew-it!https://www.youtube.com/watch?v=t0akAKlJ3nc&safe=active
2. A figure skater, and Dartmouth student, demonstrates the conservation of angular
momentum. https://www.youtube.com/watch?v=VmeM0BNnGR0
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3. More on figure skating and physics- http://www.bsharp.org/physics/spins
4. Notes on Kepler’s Laws- http://www.nuffieldfoundation.org/node/1785
5. Calculating Torques Online Activity- In this activity we learn to calculate the torque caused
by a force.
http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/Calcul
atingTorques/Main.html
6. Ball hits Bat- Angular Momentum Online Activityhttp://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/BallH
itsBat/Main.html
7. Armed Levers- In this activity, we use the principles of statics to analyze the biceps and the
triceps muscle systems of the arm.
http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/RotMotionStatics/ArmL
evers/Main.html
8. Interactive Circular Motion Tutorialhttp://www.mhhe.com/physsci/physical/giambattista/circular/circular.html
9. Circus Physics: Conservation of Angular Momentum.
http://video.pbs.org/video/1607951704/
10. Rotational Kinematics Online Lab Activityhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_RotationalKi
nematics.xml
11. Online Notes about Forces and Torques in Muscles and Jointshttp://cnx.org/contents/[email protected]:66/College_Physics
12. PhET- Balancing Act- Seesaw Interactive labhttp://phet.colorado.edu/en/simulation/balancing-act
13. PhET- Lady Bug Angular Kinematics- http://phet.colorado.edu/en/contributions/view/3020
14. PhET- Lady Bug Revolution- http://phet.colorado.edu/en/simulation/rotation
Note- All links to online resources were verified before publication. In cases where links are no longer
working, we suggest that you try to find the resource by a keyword internet search.
RUBRIC FOUND ON FOLLOWING PAGE………………………………………
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SUGGESTED RUBRIC AP PHYSICS 1 E07
Student Name: __________________________
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Date: _______________________
To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSW’s).
The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work and class
discussions will determine ‘A’ level mastery.
If grading for AP test preparation, please refer to Course Outcome Rubric.
The Student Will
1. TSW describe the force component as being
perpendicular to the line connecting the axis of
rotation and the point of application of the force
results in a torque about that axis. Including:
a. The lever arm is the perpendicular
distance from the axis of rotation or
revolution to the line of application of
the force.
b. The magnitude of the torque is the
product of the magnitude of the lever
arm and the magnitude of the force.
c. c. The net torque on a balanced system
is zero. (EK 3.F.1)
2. TSW predict the behavior of rotational
collision situations by the same processes that are
used to analyze linear collision situations using an
analogy between impulse and change of linear
momentum and angular impulse and change of
angular momentum. (LO 3.F.3.1)
‘A’* LEVEL
Calculates torques on a two-dimensional system in
static equilibrium, by examining a representation or
model (such as a diagram or physical construction).
(LO 3.F.5)
3. TSW justifies that a torque exerted on an
object can change the angular momentum of an
object. (EK 3.F.3)
Plans data collection and analysis strategies designed
to test the relationship between torques exerted on an
object and the change in angular momentum of that
object. (LO 3.F.3.3)
4. TSW will recognize the presence of a net
torque along any axis will cause a rigid system to
change its rotational motion or an object to
change its rotational motion about that axis.
Including:
Plans data collection and analysis strategies designed
to test the relationship between a torque exerted on an
object and the change in angular velocity of that
object about an axis. (EK3.F.2.2)
Or
Designs an experiment and analyzes data testing a
question about torques in a balanced rigid system.
(LO 3.F.4)
Appropriate concepts that are fully understood
(right hand rule, perpendicular distance angular
inertia, etc.) clearly stated and employed correctly.
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‘B’ LEVEL
Uses representations to compare and estimate the
torques on an object caused by various forces.
(LO 3.F.1 and LO 3.F.1.2)
In an unfamiliar context or using representations
beyond equations, the student is able to justify the
selection of a mathematical routine to solve for
the change in angular momentum of an object
caused by torques exerted on the object. (LO
3.F.3.2)
Makes predictions about the change in the angular
velocity about an axis for an object when forces
exerted on the object cause a torque about that
axis. (EK3.F.2.1)
Comments
a.
Rotational motion can be described in
terms of angular displacement, angular
velocity, and angular acceleration about
a fixed axis.
b. Rotational motion of a point can be
related to linear motion of the point
using the distance of the point from the
axis of rotation.
c. The angular acceleration of an object or
rigid system can be calculated from the
net torque and the rotational inertia of
the object or rigid system. (EK3.F.2)
5. TSW characterize torque, angular velocity,
angular acceleration, and angular momentum as
vectors and as positive or negative depending
upon whether they give rise to or correspond to
counterclockwise or clockwise rotation with
respect to an axis. (EK 4.D.1)
6. TSW calculate the change in angular
momentum given by the product of the average
torque and the time interval during which the
torque is exerted. (EK 4.D.3)
7. TSW justify that if the net external torque
exerted on the system is zero, the angular
momentum of the system does not change. (EK
5.E.1)
Plans data collection strategies designed to establish
that torque, angular velocity, angular acceleration, and
angular momentum can be predicted accurately when
the variables are treated as being clockwise or
counterclockwise with respect to a well-defined axis
of rotation, and refine the research question based on
the examination of data. (LO 4.D.1.2 )
Plans a data collection strategy designed to test the
relationship between the change in angular
momentum of a system and the product of the average
torque applied to the system and the time interval
during which the torque is exerted. (LO 4.D.3.2)
Describes a representation and use it to analyze a
situation in which several forces exerted on a
rotating system of rigidly connected objects
change the angular velocity and angular
momentum of the system.
(LO 4.D.1.1 )
Makes calculations of quantities related to the angular
momentum of a system when the net external torque
on the system is zero. (LO 5.E.1.2)
Makes qualitative predictions and justifications
about the angular momentum of a system for a
situation in which there is no net external torque.
(LO 5.E.1.1)
8. TSW describe or calculate the angular
momentum and rotational inertia of a system in
terms of the locations and velocities of objects
that make up the system. (LO 5.E.2.1)
Approach and starting equations chosen are
clearly shown, clearly written & all elements are
valid.
Students are expected to do qualitative reasoning
with compound objects. Students are expected to
do calculations with a fixed set of extended
objects and point masses.
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Uses appropriate mathematical routines to
calculate values for initial or final angular
momentum, or change in angular momentum of a
system, and/or average torque or time during
which the torque is exerted in analyzing a
situation involving torque and angular
momentum.
(LO 4.D.3.1)