ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: AP Physics C – Mechanics, Level I
GRADE LEVEL:
CREATION DATE: July 2002
AP Physics C – Mechanics, Level I
Page 1 of 52
July 2002
MISSION STATEMENT
1.
First and foremost, this IS a college level course and is taught at THAT level. The course is designed to prepare students for the AP Physics
C Exam in Mechanics. Students who have already attended college have returned to critique this course for its appropriateness and level of
difficulty. Five universities, in particular, help determine the level of difficulty, because these are some of the most challenging that OUR
students have attended: MIT, CAL Tech, RPI, Stanford, and Carnegie Mellon.
2.
Lab work is all self-designed and original ideas must be applied to set problems. The AP Physics C Exam has designated about 17% of the
scoring will test students’ knowledge of data-gathering, graphical, statistical analysis, and qualitative/quantitative assessments of what this
data means.
3.
Much of the strategy in the instruction revolves around “spiraling concepts.” An idea or technique such as derivatives, integrals, vectors,
definitions, formulas, etc are introduced in one unit, then they are reintroduced again and again in later chapters. Students are specifically
shown that this is a familiar topic, used again in a new application. Hopefully, it will help them build upon what they have already learned
and reinforce how important it is to thoroughly understand the concept the FIRST TIME around.
4.
Much emphasis is put on using calculus with their other math skills. Although some class time is used to show how these equations are
derived, the emphasis on how they are used to solve problems. Most students take calculus concurrently with physics and will see this
derivation process there. Students, who do not take calculus concurrently, will always have access to an appendix that lists these formulas for
their use.
5.
AP Physics students form the core leadership role for Physics Olympics and the building events for Science Olympiad. They select the team
captains, even leaders, times after school, alternates, and competition groups. They are responsible for running elimination contests to decide
which building projects will represent our school at the tournaments. They rate these devices and grade them. They take attendance at all
practices and tournaments and are generally responsible for running ALL aspects of the competition teams, including tracking costs. This
kind of responsibility is important in developing leadership skills.
AP Physics C – Mechanics, Level I
Page 2 of 52
July 2002
Essential Question, Concept or Theme: A. Calculus Introduction
PA Standards: 3.1.12 A,B,C,D,E
Benchmark/Skills
A.
Benchmark # 1 Demonstrate proficiency
in basic math skills needed to do all
algebraic problem solving and graphing
throughout the year.
Approx. Time Allotment: 1 week
Aligned Materials/
Resources/Technology
Assessment
A.
1. Two quizzes, testing these two basic
skills.
2. One homework assignment of 20
problems is given to check students’
knowledge of these two skills.
A.
1. Textbook (Math Appendices)
2. Teacher generated worksheets
3. Graphing calculator
Benchmark #2 Appropriately use
derivatives to differentiate an equation in
order to graph this function, or solve for a
specific answer.
Benchmark # 3 Appropriately use
integrals to integrate an equation, in order
to graph this function, or solve for a
specific answer.
AP Physics C – Mechanics, Level I
Page 3 of 52
Instructional Strategies
A.
1. Remedial help sessions are offered
mornings and afternoons the week before
school begins.
2. Remedial help is offered after school
until 5:00 p.m., after 5:00 p.m. by
appointment, during ”C” lunch, and after
8:00 p.m. by telephone.
3. Classroom help sessions are structured:
students may work individually or in
groups, at desks and lab tables in the back
of the room … one-on-one or specific
problems are handled by the teacher at the
front of the room, and announced so that
individuals can come “forward” when
needed.
July 2002
Essential Question, Concept or Theme: A. Calculus Introduction
PA Standards: 3.1.12 A,B,C,D,E
Adaptations/Inclusion
Enrichment Strategies
Techniques
All Units A – J can be adapted to any
individual IEP.
. Students with physical handicaps have
full access to academic classroom
exercises, as well as laboratory exercise.
We have handicapped accessible desks.
We also rotate student lab groups, which
will also change their contribution to the
group during each lab exercise.
. Students with mental handicaps can have
individual IEP’s developed so that they
can compete to the best of their ability
with all comparably capable students.
AP Physics C – Mechanics, Level I
Approx. Time Allotment: 1 week
Remediation Strategies
All units A – J.
What opportunities can be offered students
OUTSIDE the regular classroom, to
enhance and enlarge their experience.
How can we give them applicable credit
for this effort?
1. Extra Credit. Each student may receive
no more than 50 EXTRA CREDIT
POINTS each marking period, They may
receive points for:
a. Correctly answering designated
questions in class.
b. Catching the teacher making mistakes
(especially spelling and problem
solutions).
c. Each student is required to do four
building projects (one each marking
period). Exceptionally well-done devices,
or students or who help evaluate other
students’ devices, can receive such points.
d. Making insightful comments, or
demonstrating “extended thinking.”
e. Participating in Physics Olympics or
Science Olympiad competitions.
f. Students who, after school, help, find,
pickup, or help distribute materials for
other students’ use.
2. Students who demonstrate real
capability in lab exercises can become lab
assistants, who help set up and run labs for
their classmates.
3. While students are generally permitted
to select their own seating placement in
class – teachers may assign seats as
needed . . . do well and you may freely
select your seat.
4. Teachers select lab group
All units A – J require a high level of
mathematical competency. This is
addressed before the course begins.
1. A week before school begins, tutoring
and review sessions are offered each day
to assess and help their capabilities.
2. Once school begins, teachers are
available for extra help during the day,
when free; immediately after school; by
mutual appointment; when the afterschool activity period ends, i.e. 5:20 p.m.;
in the evening and weekends with
telephone support.
3. Students, who fail ANY assignment,
lab report or test/quiz, may correct ALL
mistakes and resubmit it. If properly
done, it is recorded as a 60%, a passing
grade.
4. Homework assignments are optional
for students.
5. Each chapter unit is usually three to
four weeks in length. Tests are on the last
Friday of each unit. If class periods
present themselves for a chapter review
before the test, they are used as such. Our
present lab/classrooms provide an
excellent opportunity to divide classes for
this activity. Students who wish to work
in groups, may work together at the lab
tables; students who wish to work alone,
may pull individual desks to the back of
the room; students who wish one-on-one
or small group interaction directly with the
Page 4 of 52
Multicultural/Interdisciplinary
Connection
All units A-J.
WORD PROBLEMS . . . they are part of
every math course . . . they are singular to
Physics.
An interdisciplinary connection with the
Math Department is crucial. This is a
mutually reinforcing combination. IF
YOU CAN LEARN MATH . . . CAN
YOU USE IT!?!?
The laboratory exercise and report are
basic to ALL SCIENCE. They require the
qualitative and quantitative analysis of
what students discover in experimentation.
CAN THEY DESCRIBE AND
COMMUNICATE WHAT THEY
EXPERIMENTALLY FIND?!?! The
expository form of writing is a needed
discipline which the Language Arts and
Science Departments should mutually
support.
The Art and Science Departments have
cooperated to research, design, draw,
document, and build balsa wood bridges.
They then BREAK them to see how
successful they were. Successful students
can compete in the Illinois Institute of
Technology's annual International Bridge
Building Tournament.
The Physical Education teachers and
athletic coaches at Penncrest have the
Science Department's motion detectors
evaluate athlete's motion from rest. Mass,
force, acceleration, momentum and
impulse can all be measured.
July 2002
Essential Question, Concept or Theme: A. Calculus Introduction
PA Standards: 3.1.12 A,B,C,D,E
Adaptations/Inclusion
Enrichment Strategies
Techniques
Approx. Time Allotment: 1 week
Remediation Strategies
combinations. Individual talents can be
distributed through the class, so that
overlapping or conflicts can be avoided . .
. Even more, students with leadership,
organization, data gathering,
mathematical, computer or hands-on
building skills can, and should, be grouped
with other students, who appreciate and
can augment their skills. This is an
important consideration . . . because later
we do not choose the people in life we
work with . . . we just learn how to work
with them!
5. Students who excel in and out of class
may request a letter of recommendation
for their college applications. These
letters are carefully written and document
these contributions and personal
developments.
Multicultural/Interdisciplinary
Connection
teacher, come forward to the front desk.
6. Starting in April, teachers are available
for evening sessions to prepare for the AP
Physics C – Mechanics Exam, college
placement, and military entrance exams.
7. Teachers make a very determined
effort to help students who need it.
Students, who make an active choice to
miss class for another commitment, bear
the responsibility to make up the work
themselves.
An interdisciplinary connection needs to
exist between the Administration and
Science Departments to facilitate
laboratory exercises. ALL double lab
periods occur on Tuesdays and
Wednesdays, for ALL upperclassmen, for
ALL WEEK. If these sessions can be
avoided for class assemblies; workshop
days; mentoring sessions; and unique
scheduling, like IEP's. This is a significant
development.
Also, the first remediation session runs the
week before school begins, it overlaps
with beginning school activities. Physics
teachers will run remediation sessions that
DO NOT conflict with "opening school
activities." Physics teachers, who have
this opening schedule, when they mail
students in beginning August, can exempt
these times for students and parents.
The most significant interdisciplinary
connect that that does exist with Physics,
is the Technology Department. Physics
students' building projects are planned,
drawn, reproduced, diagrammed and built
with their help. This department has
constantly worked with us to develop and
build student projects, using software,
hardware, and draftsmanship quality
drawings. They are one reason for our
overall success in building competitions.
AP Physics C – Mechanics, Level I
Page 5 of 52
July 2002
Essential Question, Concept or Theme: B. One Dimensional Motion
PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
B.
Benchmark # 1 Describe and evaluate the
motion of an object undergoing ANY kind
of motion in a straight line.
a. Define displacement, velocity,
acceleration, surge, and alpha, beta (etc.,
terms of motion.
b. Drive the universal equation for
displacement in one dimension.
c. Graph these quantities vs. time, and
find these values at any position or time.
d. Differentiate and integrate known
graphs in order to produce related graphs
of the same motion.
e. Plot graphs of any straight line motion
with given data, and differentiate and
integrate these graphs using Vernier
Graphical Analysis III software.
f. Identify and define vector and scalor
quantities related to motion.
g. Derive algebraically the five kinematic
equations for an object undergoing
constant acceleration.
h. Use these kinematic equations to solve
single object motion, multiple motions by
one object or related motions of two
objects (man trying to catch a bus).
i. Derive, using calculus, all related
equations of motion, for an object
undergoing inconstant acceleration.
j. Use calculus to solve for specific values
of motion, deriving from the universal
displacement equation for one dimension.
B.
1. Two graphing quizzes.
2. One multiple-choice quiz on chapter
concepts.
3. One chapter test with a multiple-choice
section. To be done in class. The test also
has seven problems, and students must
select two of the seven to be done and
turned in as homework.
4. One major homework assignment of
selected problems from the end of the
chapter, to be turned in with the takehome test.
5. One laboratory exercise: The object
undergoing inconstant acceleration.
6. An optional building project or
leadership role in either Physics Olympics
or Science Olympiad.
B.
1. Graphing calculator
2. IBM PC computer
3. PASCO 750 Interface Box
4. PASCO Photogates
5. PASCO Smart Pulleys
6. PASCO Accelerometers
7. PASCO Software
8. Vernier Graphical Analysis III
Software
9. Microsoft Excel
10. Microsoft Word
Benchmark # 2 Evaluate the motion of an
object undergoing inconstant acceleration,
in an original laboratory exercise of their
design.
a. Predict the motion of this object
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Page 6 of 52
Instructional Strategies
B.
1. Students will construct in the lab a
device, which undergoes inconstant
acceleration. They will predict what this
motion will look like graphically, by
producing qualitative graphs of
displacement, velocity, acceleration, and
surge vs. time. This will form the basis of
their hypothesis, and define what they are
measuring. Finally, tin their conclusion,
they will compare their predictions to the
actual graphs they obtained by doing the
lab. They will also address major sources
of error.
2. Students will have three weeks to write
and do the lab:
1st lab session – decide what you will do
and write a formal procedure for teacher
approval.
2nd lab session – After approval, run the
lab.
3rd lab session – adjustments or re-run any
trials with questionable data. Upon
completion, one week and a formal lab
write-up (word-processed only!) is handed
in.
3. The major concepts being “spiraled” in
this unit are:
a. Graphing techniques
b. Using derivatives and anti-derivatives
to produce other related graphs
c. Addressing and deriving formulas as
concept statements (what is the formula
telling you, as to its motion).
d. Using calculus to manipulate formulas
e. Problem-solving techniques.
f. Using a graphing calculator for problem
solving.
4. Students will begin the selection of
July 2002
Essential Question, Concept or Theme: B. One Dimensional Motion
PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E
Benchmark/Skills
Aligned Materials/
Resources/Technology
Assessment
graphically … before experimenting.
b. Qualitatively and quantitatively
describe the motion and relate it to the
actual graphs obtained during the
experiment.
c. Describe all sources of error, which
affect the overall results.
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Instructional Strategies
Physics Olympics team captains and event
leaders for the fall tournament. These
individuals will begin choosing an overall
team and dividing them into events. They
will define their responsibilities for each
event, such as attendance, how much
credit per person, a calendar of activities,
deadlines, selection processes, and how to
divide these responsibilities among
themselves. Also, they will choose an
overall team administrator and a web-site
manager.
5. Students will begin recruiting and
assigning building events to students
wishing to participate in Science
Olympiad, whose competition events
begin in mid-March. Dividing these
responsibilities and awarding credit will
be their decision, based on how much
effort is made by students each marking
period.
Page 7 of 52
July 2002
Essential Question, Concept or Theme: B. One Dimension Motion
PA Standards: 3.1.12 A,C,D,E; 3.2.12 A,B,C,D; 3.4.12 C; 3.6.12 B; 3.7.12 A,B,C,D,E
Adaptations/Inclusion
Enrichment Strategies
Techniques
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
Approx. Time Allotment:
Remediation Strategies
See Unit A
Page 8 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: C. Vectors
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,D; 3.4.12 C; 3.7.12 A,B,D
Benchmark/Skills
C.
Benchmark # 1 Diagram vectors in two
dimensions using mathematical or
directional axes.
a. Define vectors and contrast them to
scalar values.
Benchmark # 2 Diagram vectors in three
dimensions.
a. Draw and evaluate vectors in an I-j-k
component format.
b. Draw and evaluate vectors in a
resultant format.
c. Convert one format to the other,
depending upon which one is given at the
start.
Approx. Time Allotment: 2 weeks
Aligned Materials/
Resources/Technology
Assessment
C.
1. Quiz – multiple choice on chapter
concepts.
2. Quiz – three problems.
3. Test – same format as the chapter test
in part B.
4. Homework – selected problems from
the end of the chapter.
5. Laboratory Exercise – Equilibrium in
Three Dimensions.
6. Participation in Physics Olympics or
Science Olympiad.
7. Class participation for points.
C.
1. Graphing calculator
2. IBM PC
3. PASCO 750 Interface Box
4. PASCO smart pulleys
5. Vernier Graphical Analysis III
6. Microsoft Excel software
7. Microsoft Word software
8. Spring scales
9. Standard single pulleys
10. Tabletop hardware
Benchmark # 3 Add and subtract vector
quantities in two and three dimenisons.
a. Draw vectors graphically, and add and
subtract them using the head-tail method
to find the resultant.
b. Draw vectors mathematically from a
common origin, and resolve each into
components.
c. Add and subtract components, and
resolve their total into a single resultant
value.
Benchmark # 4 Multiply and divide vector
quantities in two and three dimensions.
a. Define a vector dot product, and relate
it to scalar values.
b. Derive the dot product formula in
component or resultant format.
c. Use the dot product formula to solve
problems in the resultant or component
format.
AP Physics C – Mechanics, Level I
Page 9 of 52
Instructional Strategies
C.
1. Vectors is one of the most important
topics to “spiral” through the year – it will
be used in every unit from here on.
a. Use the lab to introduce equilibrium in
three dimensions. First have them
measure displacement vectors and
calculate their components. Use these
values to find the forces and their
components, by using proportions.
Reinforce – “it is the same system for any
vector value (displacements, forces,
velocities, etc.).”
b. The velocity concept mentioned above
will be used to introduce the next chapter,
“Velocities in Two and Three
Dimensions.”
c. Briefly introduce dot and cross
products defined as Work and Torque.
They had these last year and will be able
to relate the system (vector products) to
the scalar value (work), and the vector
value (torque). L These will be addressed
in later chapters as major topics.
2. Relate three dimensional vector
calculations to matrices. Use the graphical
calculators to calculate components in two
and three dimensions. Demonstrate why
uniform methods of drawing vectors is
essential to calculations, since the
formulas are derived from these standard
formats.
3. Show them the three methods for
calculating cross products in the I-j-k
format: a) formula, b) diagram, c)
relational. Each method will “do the job,”
so let students utilize the method which
works best for them and makes the most
July 2002
Essential Question, Concept or Theme: C. Vectors
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,D; 3.4.12 C; 3.7.12 A,B,D
Benchmark/Skills
Approx. Time Allotment: 2 weeks
Aligned Materials/
Resources/Technology
Assessment
d. Define a vector cross product formula
in component or resultant format.
f. Use the cross product formula to solve
problems in the resultant or component
format.
sense to them.
4. Start them early preparing for Physics
Olympics and Science Olympiad. This is
their first time in an independent
leadership role, and they need much
guidance in how to do it successfully.
Also, they need to understand the support
role that the teacher plays in this
relationship for materials, information,
rules and finances.
5. The instructor also needs to do a strong
critique of their first lab. Hopefully it can
be read and evaluated by more than one
person and hopefully by someone at the
college level. MUCH emphasis is put on
the laboratory exercises this year, because
the College Board has dictated that onethird of the free-form problem solving
portion of the AP Physics C Exam, be
dedicated to “laboratory situations and
applications.”
Benchmark # 5 Qualitatively relate dot
and cross products to known values.
a. Define Work as a dot product.
b. Define torque as a cross product.
AP Physics C – Mechanics, Level I
Instructional Strategies
Page 10 of 52
July 2002
Essential Question, Concept or Theme: C. Vectors
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,D; 3.4.12 C; 3.7.12 A,B,D
Adaptations/Inclusion
Enrichment Strategies
Techniques
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
Approx. Time Allotment: 2 weeks
Remediation Strategies
See Unit A
Page 11 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: D. Motion in Two and Three Dimensions
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,C,D; 3.4.12 C; 3.6.12 C; 3.7.12 A,B,C,D,E
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
D.
Benchmark # 1 Evaluate an object’s
motion in two or three dimensions.
a. Define and calculate total displacement
of an object in two or three dimensions, in
the component or resultant format.
b. Define and calculate the total velocity
of an object in two or three dimensions, in
the component or resultant format.
c. Define and calculate the total
acceleration of an object in two or three
dimensions, in the component or resultant
format.
d. Use differential calculus to derive
velocity, acceleration, surge, etc., from the
universal displacement equation, written
in the I-j-k format. This equation is
displacement, with respect to time.
e. Use vector addition to combine I-j-k
components to find resultant
displacements, velocities, accelerations,
etc., at any position or time.
f. Sketch, identify and analyze graphs of
motion for displacement, velocity,
acceleration, surge, etc., for motion in the
i, j, or k direction.
D.
1. Quiz – multiple choice on chapter
concepts.
2. Two quizzes – each three problems on
“multiple motion.”
3. Test – same format as the chapter test
in part B.
4. Homework – selected problems from
the end of the chapter.
5. Laboratory Exercise –
I. Find the algorithm for a PASCO
Launcher to predict actual ranges.
II. Hit the target, with a ball rolling down
a ramp.
6. Participation in Physics Olympics or
Science Olympiad
7. Class participation for points.
Benchmark # 2 Evaluate an object’s
motion as a projectile on earth (or under
other gravitational constants).
a. Define a projectile’s constant
horizontal motion due to inertia, and
derive equations of motion with respect to
time.
b. Define a projectile’s accelerated
vertical motion due to gravity, and derive
equations of motion with respect to time.
c. Combine components of horizontal and
AP Physics C – Mechanics, Level I
Approx. Time Allotment: 4 weeks
Page 12 of 52
Instructional Strategies
D.
1. If spiraling topics works – use the ideas
of kinematics and vectors to have students
define and explain and derive multiple
motion and its equations. Have them
differentiate how this is done in a
component format, (first), then how it is
combined into a resultant format. This
methodology should be utilized with the
reading of the chapter units, so that
students can develop these ideas
intuitively, or with the aid of the reading
material. Either way, make them work for
it in the classroom, then put it in their
notes, in their own words.
2. Note taking has been emphasized
throughout the year to date, but now it
takes on a new significance – students are
combining multiple concepts, and levels
of thought. Come chapter test time, or
more importantly, final exam and AP
exam time ... which is easier to review? ...
the entire textbook, or your concise notes,
written in your own words? Stress note
taking.
3. The laboratory exercises are very
different. The first is to find an algorithm
to add or multiply with the predicted range
of a launcher, so that the combination will
identify the actual range the PASCO
launcher throws a marble. This is done for
every 5o of elevation of the launcher.
Students must utilize the Microsoft Excel
and Vernier Graphical Analysis III
software to really do this lab. It really
stretches their ability to utilize these
packages to do the bulk of the
calculations, come up with a list of %
July 2002
Essential Question, Concept or Theme: D. Motion in Two and Three Dimensions
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,C,D; 3.4.12 C; 3.6.12 C; 3.7.12 A,B,C,D,E
Benchmark/Skills
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
errors for each 5o of elevation, find how
they differ every 5o, and then find an
overall algorithm to reduce all the errors
simultaneously. There is no one way to
do this, and we have seen five or six
different approaches to the problem over
the years. The second lab is one session
… walk into the room … be given the
problem: to hit a target with an adjustable
ramp (elevation) with an adjustable length,
that a ball must roll along. The target is
scored like an archery ring target, and they
may use any method to predict the effects
of two simultaneous variables: elevation
and length. They are then given five trial
positions by the teacher, and must place
the target on the floor to hit center,
without a test roll. It is fast-paced, open
thinking, with some luck and too many
ideas to try in one period. You just love
this one.
vertical motion with vector addition to
find the resultant displacement, velocity,
acceleration of the projectile at any
position or time.
Benchmark # 3 Evaluate an object’s
motion, as it moves uniformly, in a
circular path.
a. Define the object’s constant speed and
changing velocity, then derive equations
for each one.
b. Derive the equation for centripetal
acceleration using components of the
change in velocity with vector addition.
Then do the same thing using the resultant
values of velocity in a circle.
c. Calculate an object’s speed, velocity,
displacement, and centripetal acceleration
for any position or time.
Benchmark # 4 Evaluate two objects’
motion, relative to one another, in one and
two dimensions.
a. Define relative motion for two objects,
in terms of “frames of reference.”
b. Drive equations for this motion, in one
and two dimensions, as seen from either
“frame of reference.”
c. Solve problems for any kinematic
value, including time for either object, as
it moves relative to the other.
AP Physics C – Mechanics, Level I
Approx. Time Allotment: 4 weeks
Page 13 of 52
July 2002
Essential Question, Concept or Theme: D. Motion in Two and Three Dimensions
PA Standards: 3.1.12 A,B,C,D,E; 3.2.12 B,C,D; 3.4.12 C; 3.6.12 C; 3.7.12 A,B,C,D,E
Adaptations/Inclusion
Enrichment Strategies
Techniques
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
Approx. Time Allotment: 4 weeks
Remediation Strategies
See Unit A
Page 14 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: E. Forces and Motion
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A, C; 3.6.12 C; 3.7.12 A-E
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
E.
Benchmark # 1 Define and evaluate force
as the “push” or “pull” on an object.
a. Relate mass to the size of the object.
b. Define mass as gravitational or inertial,
and derive its’ units.
c. Qualitatively, and then quantitatively,
relate force and mass to acceleration.
d. Derive units of force from mass and
acceleration.
e. Discriminate between mass and weight.
f. Draw Free-Body-Diagrams (F-B-D) for
any object, at rest or undergoing any kind
of motion.
g. Define “net force” and derive its’
equation.
h. Calculate the net force on any
individual object or system using vector
resolution.
1. Quizzes-two will be given on multiple
choice on chapter concepts.
2. Quiz with three problems.
3. Test-same format as the chapter test in
part B
4. Homework-selected problems from the
end of the chapter.
5. Laboratory exercise-coefficient of
friction to Net Force Lab.
6. Participation in Physics Olympics or
Science Olympiad.
7. Class participation for points.
1. Graphing calculator
2. IBM PC
3. PASCO 750 Interface Box
4. PASCO Smart Pulleys & Photogates
5. PASCO Picket Fences
6. PASCO Force Meters and
Accelerometers
7. Vernier Graphical Analysis III Software
8. Microsoft Excel & Word Software
9. Spring scales
10. Slotted weights and weight hangers
11. Scales
12. Tabletop hardware
Benchmark # 2 Define and evaluate
Newton’s First Law of Motion.
a. Differentiate, both qualitatively and
quantitatively, what is unique about his
first law, compared to the other two, in
terms of motion.
b. Relate all three laws to one another in
terms of force.
c. Use F-B-D’s to define equilibrium.
d. Use F-B-D’s to derive equations of
equilibrium in resultant and component
formats.
e. Define inertia, and derive its’ unit of
measurement.
f. Differentiate inertia from a force, and
relate it to F-B-D’s for any object in
motion.
g. Solve problems for unknown forces and
AP Physics C – Mechanics, Level I
Page 15 of 52
Instructional Strategies
1. The greatest single problem that a
physics teacher faces, when he or she tries
to explain some phenomenon is
MISCONCEPTIONS! You, as the
teacher, believe the student understands
your explanation . . . but if they do not . . .
this misconception is carried over into the
next unit, . . . and the next . . . It is
“spiraling” in reverse. You perpetuate the
problem. This unit is especially difficult
for students, because it encompasses a
great many concepts, definitions,
relationships, and derived thoughts. The
teacher must CONSTANTLY question,
and requestion students; give them
examples that they must explain;
encourage them to ask their own
questions; and emphasize the multiple
choice quiz and test preparation AND
follow-up, to find and eliminate these
misconceptions.
2. This unit is two chapters in the
textbook. It is easier to combine, than
separate them. The first chapter is Force
and Motion-I (Without Friction); the
second chapter is Force and Motion-II
(With Friction). Teach them everything . .
.with friction . . . and be able to solve any
kind of problem. The discriminator is
them . . . “sometimes friction is so small it
may be neglected from the overall
solution, but it is always there in real life.”
3. The number one misconception is that
static friction: FFSTATIC = (MS) (FN)
This is not always the case. This is how
large static friction can be. Static friction
is a reaction force, and if the action force
July 2002
Essential Question, Concept or Theme: E. Forces and Motion
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A, C; 3.6.12 C; 3.7.12 A-E
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
kinematic values, (including time), using
equilibrium and Newton’s First Law of
Motion
is less than this value, the static friction
will equal the action force. However,
FFKINETIC = (MK) (FN) will always be true
as the object slides along.
4. The topics needed to be “spiraled” in
this unit, (for use in the next two units),
will be
a. Force and the calculation of its’
components.
b. Using acceleration to relate and unite
forces with motion. This is because
acceleration is the ONLY variable found
in both the kinematic AND force
equations.
c. There is no such thing as “centrifugal
force,” this is actually inertia; and inertia
is not a force. There is, however,
centripetal force. This is a net force, and
creates a unique system called “dynamic
equilibrium.” This concept is absolutely
essential when you start the double
chapter unit on Rotational Motion and
Rolling.
d. Units, Units, Units
5. It is usually about this time the Physics
Olympics has its’ first tournament in the
autumn. If need be, use lab periods to
permit the AP Physics kids to organize
their events, make announcements, draw
up schedules, and mostly communicate
with each other, since it is the only time
that they can be together to get this done.
These are usually the students who are
MOST involved in after school activities.
It is usually easier for them to come in
after school to do labs in groups of four or
five, than to get together as the single
Physics Olympics Leadership.
Benchmark # 3 Define and evaluate
Newton’s Second Law of Motion.
a. Relate the “unbalanced force” in his
first law to net force, outside force, and
resultant force, and show they are all the
same.
b. Differentiate “outside” forces from
“internal” forces, using the concept of
“system of forces.”
c. Relate net force to acceleration.
d. Derive the equation for the second law
in component, and then resultant formats.
e. Relate ALL kinematic motion to
resultant force.
f. Solve problems for any unresolved force
or kinematic motion designated.
Benchmark # 4 Define and evaluate
Newton’s Third Law of Motion.
a. Define and identify Action-Reaction
(A-R) pairs from examples given to
students.
b. Define “forces at a distance,” and
identify their A-R pairs, especially gravity.
c. Explain friction as a reaction force.
d. Solve problems for systems of internal
and external forces.
Benchmark # 5 Evaluate friction as a
force.
a. Define and derive the two properties
that create and affect the size of friction.
b. Qualitatively and quantitatively
describe and derive the equation for
“normal force.”
AP Physics C – Mechanics, Level I
Instructional Strategies
Page 16 of 52
July 2002
Essential Question, Concept or Theme: E. Forces and Motion
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A, C; 3.6.12 C; 3.7.12 A-E
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
c. Qualitatively and quantitatively describe
and derive the equation for the coefficient
of static and kinetic friction.
d. Derive the equation for the force of
friction.
e. Define and derive the equations for
“drag force” and “terminal velocity.”
f. Describe circular motion in terms of net
force.
g. Derive the equation for centripetal
force, using the equation for net force.
h. Solve problems for unknown values of
friction, normal force, coefficients of
friction, drag forces, and centripetal
forces.
AP Physics C – Mechanics, Level I
Page 17 of 52
July 2002
Essential Question, Concept or Theme: E. Forces and Motion
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A, C; 3.6.12 C; 3.7.12 A-E
Adaptations/Inclusion Techniques
See Unit A
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Enrichment Strategies
See Unit A
Remediation Strategies
See Unit A
Page 18 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: F. Work/Energy/Power
PA Standards: 3.1.12 A-E; 3.2.12 A-D; 3.4.12 A-D; 3.6.12 C; 3.7.12 A-E
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
F.
Benchmark # 1 Define and evaluate
kinetic energy.
a. Derive equation for kinetic energy and
its’ units of measurement.
b. Use dot products to derive its value as a
scalar.
c. Solve equations for kinetic energy, mass
or velocity
1. Quizzes (2)- multiple choice on
concepts in the chapter.
2. Quizzes (2)-three problems each.
3. Test-same format as the chapter test in
part B.
4. Homework-selected problems from the
end of the chapter.
5. Laboratory exercise-efficiency of an
electric motor.
6. Participation in Physics Olympics or
Science Olympiad.
7. Class participation for points.
Benchmark # 2 Define and evaluate work.
a. Derive equation for work and its’ units
of measurement.
b. Use dot products to derive its value as a
scalar.
c. Relate work to kinetic energy, and
derive the equation for work as the change
in kinetic energy.
d. Solve equations for unknown values for
force, displacement, work, kinetic energy,
mass, velocity, or time.
1. Graphing calculator
2. IBM PC
3. PASCO 750 Interface Box
4. PASCO smart pulleys
5. PASCO force meters
6. Vernier Graphical Analysis III Software
7. Microsoft Excel & Word Software
8. Electric power sources
9. Electric motors
10. Ammeters & voltmeters
11. Wire connectors
12. Ramps
13. Pulleys
14. Stopwatches
15. Tabletop hardware
Benchmark # 3 Evaluate work done by a
variable force.
a. Graph force vs. displacement for a
varying force as it accelerates or slows
down an object.
b. Integrate this graph to find work, by
calculating the “area under the curve.”
c. Derive an equation for the curve of such
a graph, and use calculus to integrate this
equation for work done.
d. Use this method to define and derive the
work done by a spring or elastic force.
e. Use integration to derive the equation
for work done by a spring.
f. Solve problems for unknown values,
when a variable force is applied to an
object.
AP Physics C – Mechanics, Level I
Page 19 of 52
Instructional Strategies
1. This is a critical unit in students’
development, because many of their
previous problems can be solved using net
force and kinematics OR conservation of
energy. It is important to reinforce that
either system may be used, and that they
may use one system to check another.
2. Topics that need to be spiraled are:
a. Vector dot products, to find work and
energy; vector cross products for the next
unit to find angular momentum.
b. Derivatives, and especially integrals, to
find impulse caused by a variable force in
the next unit.
c. All units of measurement defined in
terms of mass, length and time, in order to
relate them to one another. These units
are: force, work, energy, power, (and in
the next unit), momentum, impulse and
torque).
d. Work and energy are scalars, even
though you can get a value of negative
work. In the next unit, momentum and
impulse are vectors, and direction is one
of the main differences between
work/energy and momentum/impulse.
Both systems may be used to solve certain
problems.
e. Eventually, this means certain problems
may be solved with one of three systems:
1) net force/kinematics, 2) work/energy, 3)
momentum/impulse
f. Conservation is a concept unto itself.
We use conservation of energy to solve
closed systems. We introduce the
conservation of matter and energy to
explain nuclear fission and fusion. We
will also use conservation of momentum
in the next unit to explain how to solve
July 2002
Essential Question, Concept or Theme: F. Work/Energy/Power
PA Standards: 3.1.12 A-E; 3.2.12 A-D; 3.4.12 A-D; 3.6.12 C; 3.7.12 A-E
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
problems with momentum. Then add the
fact that when we include the conservation
of kinetic energy, it differentiates between
elastic and inelastic collisions.
3. By now, students will have run at least
one Physics Olympics tournament.
Discuss the successes and failures, what
worked well, what didn’t, strategies and
tactics (like never lose any single event by
a big score . . . you may not win an event,
but never lose big).
4. This is about the “little past halfway
point in the year.” This is a good time to
assess students’ overall progress to date.
They are seniors, and most will have their
first semester sent to colleges they have
applied to for admission. If you do not get
on them right now, the second semester
will see a real drop off in effort. Remind
them that everything they learn this year,
is something that you don’t have to relearn
for next year. Their freshman year at
college will be busy enough learning
NEW material. Also, if you establish a
brisk pace, you can ease up slightly, since
the last two units on gravitation and
equilibrium are quite straight- forward if
you have been successfully spiraling
topics all year. IT’S SECOND WIND
TIME-GET ‘EM!
Benchmark # 4 Define and evaluate
power.
a. Derive both equations for power, and
its’ units of measurement.
b. Use dot products to derive its’ value as
a scalar.
c. Solve equations for unknown values of
work, force, displacement, time, velocity,
mass or kinetic energy.
Benchmark # 5 Define and relate “frames
of reference” to motion and displacement.
a. Derive equations to differentiate kinetic
energy, work and power done in one
frame of reference, compared to the other.
b. Solve equations for all unknown values
above as seen in one frame compared to
the other.
Benchmark # 6 Define and evaluate
potential energy
a. Derive an equation for potential energy
and its’ units of measurement.
b. Use dot products to derive its’ value as
a scalar.
c. Solve equations for potential energy,
force or displacement.
Benchmark # 7 Define and relate
conservative and non-conservative forces
to potential energy.
a. Derive equation for potential energy by
conservative forces.
b. Relate this equation to “path
independence,” when solving for potential
energy, (using conservative forces).
c. Graph potential energy curve for any
system of conservative forces.
AP Physics C – Mechanics, Level I
Instructional Strategies
Page 20 of 52
July 2002
Essential Question, Concept or Theme: F. Work/Energy/Power
PA Standards: 3.1.12 A-E; 3.2.12 A-D; 3.4.12 A-D; 3.6.12 C; 3.7.12 A-E
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
d. Use this graph to find potential and
kinetic energy values.
e. Use calculus or measured derivatives to
find force on these graphs.
f. Calculate the work done by nonconservative forces, especially friction.
g. Solve problems for unknown values of
potential or kinetic energy, force, mass,
velocity, or displacement by any kind of
force.
Benchmark # 8 Define and evaluate the
conservation of Energy Principle.
a. Derive a series of equations for any
situation involving a closed system of an
object (s) acted upon by a force.
b. Solve problems for any closed system
involving energy transfers.
Benchmark # 9 Define and relate matter
and energy, in terms of conservation.
a. Derive an equation for the energy found
in matter.
b. Define quantized energy, and relate it to
phenomena in nature such as emission
spectra, photo-electric effect, or photons
measured in electron-volt units.
AP Physics C – Mechanics, Level I
Page 21 of 52
July 2002
Essential Question, Concept or Theme: F. Work/Energy/Power
PA Standards: 3.1.12 A-E; 3.2.12 A-D; 3.4.12 A-D; 3.6.12 C; 3.7.12 A-E
Adaptations/Inclusion Techniques
See Unit A
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Enrichment Strategies
See Unit A
Remediation Strategies
See Unit A
Page 22 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: G. Momentum and Impulse
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A-C; 3.7.12 A-D
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
G.
Benchmark # 1 Define center of mass, and
relate it to a system of particles in three
dimensions.
a. Calculate the location of a center of
mass in a system of particles, by finding
its’ displacement, from a given reference,
in one, two, or three dimensions. Use
vector resolution.
b. Calculate the velocity of a center of
mass in a system of particles, in one, two,
or three dimensions, using vector
resolution.
c. Calculate the acceleration of a center of
mass in a system of particles, in one, two,
or three dimensions, using vector
resolution.
d. Calculate the same acceleration of a
center of mass, using the vector resolution
of all the forces on all the particles in the
system, (i.e.: the total net force of the
SYSTEM).
e. Equate this same system of particles to a
single object, rotated or moved about its’
center of mass.
1. Two quizzes, both multiple choice will
be given on concepts in the chapter.
2. Two quizzes, with three problems.
3. A test will be given with the same
format as in the chapter test in part B.
4. Homework will be selected problems
from the end of the chapter.
5. Laboratory exercise will be
“Momentum in Two Dimensions.”
6. Participation in Physics Olympics and
Science Olympiad.
7. Class participation for points.
1. Graphing calculator
2. IBM PC
3. PASCO 750 Interface Box
4. PASCO Smart Pulleys and Photogates
5. PASCO Force meters and
Accelerometers
6. Air tracks, gliders, springs, magnets
7. Vernier Graphical Analysis III Software
8. Microsoft Excel and Word Software
9. Two-dimensional Collision Devices
10. Carbon Paper
11. Meter sticks
12. Stop watches
13. Strobe lights and camera
1. This is one of the last “double chapter
units” of the year. Watch your year-end
scheduling. It students pick up on the
concepts well, reduce the quizzing and
MOVE ON! They have had much of this
last year in Level I, so this is one area you
can pick up time if you have suffered from
class assemblies on lab days, pep rallies,
early dismissals and senior cut days.
2. Topics for spiraling in this unit are
critical for the next unit (two chapters), in
rotation and rolling. These topics are:
a. Kinematics
b. Vectors
c. Net Force
d. Kinetic and Potential Energy
e. Work and Power
f. Momentum and Impulse
It is even worth a period or class session
to do a quick overview or make a “key
formula” list on the board . . . then when
you are doing the next double chapter,
show them that EVERY linear formula
you have covered so far, has an
EQUIVALENT rotational formula. Some
have different units, some have the same
units. There is also a key set of formulas
that translate linear motion into rotational
motion . . . highlight these.
3. A warning should now be put up to
begin three things:
a. Preparing for the AP exam. As you
spiral the main topics for a look at
rotation, this is a good time to have
students taking the AP exam do some
extra problems . . . while you are stressing
the CONCEPTS to the class.
b. Become more demanding . . . “Up the
Benchmark # 2 Define and evaluate linear
momentum.
a. Derive an equation for momentum and
its’ units of measurement.
b. Identify and use this equation to produce
a vector quantity.
c. Calculate the linear momentum of a
system of particles, using vector resolution
of the total of all their momentum.
Benchmark # 3 Define conservation, and
relate it to the concept of momentum
before, during, and after a collision.
AP Physics C – Mechanics, Level I
Instructional Strategies
Page 23 of 52
July 2002
Essential Question, Concept or Theme: G. Momentum and Impulse
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A-C; 3.7.12 A-D
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
ante.” Spend time critiquing lab reports.
Go back and review the rubric; there
aren’t many more labs left, and you want
them to improve their
report/analysis/writing/presentation skills.
Also, take some of the best conclusions
and copy them for everyone, “a good
example.”
c. Strategies and tactics: Every unit until
now has been an extension of something
learned last year. ‘Rotation’ and
‘Rolling,’ (two chapters), are the
exceptions. An approach that can be
taken at this point in the year is the
“lecture format.” What is it like to go to
college and have lectures? Can you really
concentrate for an hour straight through?
Take notes while someone is going that
fast? What if you have a question, but
you’re not allowed to raise your hand and
ask? What is it like? How do you do it?
I. Have them read the chapter on Rotation.
II. Give them a full period lecture (no
stopping, no questions from students
permitted).
III. Give them a quiz the next day
(multiple choice, concepts)
IV. Review the quiz the next day
following, and discuss tactics on how to
succeed under this kind of system: reading
ahead, taking key notes ahead of time
from the reading, listening more than
writing, writing down main ideas only,
etc.
When this chapter is done, repeat I-IV for
the chapter on ‘Rolling,’ to see if they can
do it!
a. Derive an equation, based on
momentum, for systems of particles, and
identify their units of measurement.
b. Solve problems for any system or type
of collision, using momentum before and
after an event, (i.e.: collision, explosion,
applied force, joining together, etc.)
Benchmark # 4 Identify systems with a
varying mass, and relate this to the
“Conservation of Momentum Principle.”
a. Derive an equation for a system of
particles, SEPARATING from one another
so that the mass of each unit changes, but
the total system does not. (An example is a
rocket ejecting its’ fuel out the back at
tremendous speed, making the rocket’s
mass lighter).
b. Use integral calculus to derive an
equation for the change in velocity of the
unit or part of the system that you wish to
measure. (Example: the rocket’s change in
velocity).
c. Evaluate the external forces and internal
energy changes in a system of particles,
and use the equations already derived, to
find these values.
d. Solve any problem, in a system of
particles, for mass, displacement, time,
velocity, acceleration, force or energy
change, (gained or lost), using
conservation of momentum.
Benchmark # 5 Define and evaluate
Impulse.
a. Define impulse as a collision and
describe the interaction of systems of
particles, center of mass, and forces
involved.
AP Physics C – Mechanics, Level I
Instructional Strategies
Page 24 of 52
July 2002
Essential Question, Concept or Theme: G. Momentum and Impulse
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A-C; 3.7.12 A-D
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
b. Derive both equations for impulse,
involving force and time, and the change in
momentum.
c. Derive their units of measurement and
mathematically compare them.
d. Graph examples of a varying force on an
object versus time, and find impulse, by
finding the area under the curve,
(integration).
e. Use calculus, and with the formula for
the curve, integrate this equation to find the
impulse at any time.
f. Solve problems and graphs for unknown
values of impulse, momentum, force, time,
mass, and velocity.
Benchmark # 6 Define and evaluate elastic
and inelastic collisions, in one and two
dimensions.
a. Differentiate between elastic and
inelastic collisions using the action of the
objects after colliding, heat loss, and
kinetic energy, before and after.
b. Compare both elastic and inelastic
collisions using the Conservation of
Momentum Principle, and show they both
conform to this law.
c. Derive a series of equations for
examples demonstrating collisions that are
elastic, inelastic, and partially both.
d. Solve these equations using vector
resolution for conservation of momentum
values, (i.e.: mass, velocity, direction).
e. Solve these equations using kinetic
energy conservation or loss to measure the
percent elasticity during the collision.
f. Solve problems involving “explosions”
or decay, such as in radioactive atoms,
with these same principles and energy loss.
AP Physics C – Mechanics, Level I
Page 25 of 52
July 2002
Essential Question, Concept or Theme: G. Momentum and Impulse
PA Standards: 3.1.12 A-E; 3.2.12 B-D; 3.4.12 A-C; 3.7.12 A-D
Adaptations/Inclusion Techniques
See Unit A
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Enrichment Strategies
See Unit A
Remediation Strategies
See Unit A
Page 26 of 52
Multicultural/Interdisciplinary
Connection
See Unit A
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1 Define and differentiate
1. Quizzes – 2 - multiple
1. Graphing calculator
between translation and rotation.
choice on concepts in chapter. 2. IBM PC
a.) Define and derive units of measurement 2. Quizzes - 2 -three problems. 3. PASCO 750 Interface Box
for rotation.
3. Test - same format as the
4. PASCO smart pulleys,
b.) Identify and define variables of rotation chapter test in part B.
photogates, laser switches
c.) Match and compare these variables of
4. Homework - selected
5. PASCO picket fences
rotation to their counterparts in linear
problems from the end of the
6. PASCO force meters
translation.
chapter.
7. Vernier Graphical Analysis
d.) Match and compare both their units of
5. Laboratory exercise –
III Software
Conservation of angular
measurement
8. Microsoft Excel & Word
momentum, OR, finding the
e.) Identify which rotational variables are
Software
vectors, and which are scalars, using the Rotational Inertia of an
9. Wood Ramps
unknown object. (Student lab 10. Discs, hoops, spheres,
right-hand rule.
groups may choose either one). spools, etc, (made of wood,
Benchmark # 2 Define and evaluate rotation 6. Participation in Physics
plastic, metal, etc.)
Olympics or Science Olympiad 11. Slotted weights and weight
with constant acceleration.
7. Class participation for
a.) Derive equations for rotational or
hangers
points.
angular motion, and compare them to
12. Tabletop hardware
the kinematic equations for linear
13. Hinges, pivots, and
motion.
connectors
b.) Identify units of measurement for all
14. Meter sticks and rulers
variables
15. Stopwatches
c.) Solve problems involving rotational or
16. Electronic balance, (triple
angular velocity, displacement,
beam balance for larger
acceleration and time.
objects).
17. Sand and clay
Benchmark # 3 Relate linear and angular
variables
a.) Identify and differentiate between linear
and angular variables for velocity,
displacement, acceleration and time.
AP Physics C – Mechanics, Level I
Page 27 of 52
Approx. Time Allotment:
Instructional Strategies
1. If the strategies from the last
unit, regarding lecture formats,
were used and discussed by
students . . . survey them now.
Many like the approach, because
the whole chapter is presented as a
single unit. They see it front to
back in one period. After that
overview, it gives individual topics
a “place” in the sequence.
Extremely large sets of topics, like
this unit, can be addressed to great
advantage. The next three units, by
contrast, are very short, and either
approach is effective.
2. TIME CHECK . . . how long
until the AP Exam? This last unit,
(all two chapters), is not covered at
all in Level I Physics last year.
Therefore, it deserves a thorough
coverage. Of the next three units,
EQUILIBRIUM is the easiest and
most thoroughly covered to date.
Do not do elasticity in the chapter,
because it is not covered on the AP
Exam. So do EQUILIBRIUM last,
in case you need to hurry. The
next chapter in the textbook is
GRAVITATION. It is longer then
EQUILIBRIUM, but fairly straight
forward, and was covered last year.
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
b.) Derive equations translating angular
motion into linear motion, (and vice
versa), emphasizing proper units.
c.) Solve problems involving velocity,
displacement, acceleration and time, in
both angular and linear measurement,
for objects which are rotating.
Emphasize proper units, to reinforce
which are linear and angular values.
Benchmark # 4 Define and evaluate
rotational inertia.
a.) Define and derive units of measurement
for rotational inertia.
b.) Use calculus, (integral), to derive an
equation for rotational inertia.
c.) Use this equation to find the rotational
inertia for several common objects, (i.e.
hoop, disc, hollow and solid sphere,
etc.), that rotate about their centers of
mass.
d.) Use calculus to derive an equation to
find the rotational inertia of these
objects, when rotated around a point that
is not at their center of mass.
e.) Use these equations to predict which
objects will roll down a ramp faster or
slower than other objects by
proportionally comparing their rotational
inertias. (Demonstrate this in class and
lab).
f.) Solve problems for unknown values
AP Physics C – Mechanics, Level I
Approx. Time Allotment:
Instructional Strategies
Do it second to last. The next
chapter is FLUIDS, ignore it; it is
not on the AP Exam. Finally,
OSCILLATIONS is the unit to do
next after rotation/rolling. It is the
least covered from last year, is
longer, and students will be able to
use their knowledge of angular
velocity and its radian measure to
calculate periodicity. Also, their
calculators will still be in “radian
mode,” along with their brains!
3. Topics to be spiraled:
a. Units, units, units. First, these
are ESSENTIAL in distinguishing
between rotational values and
linear values. Some must be
emphasized, because they are the
same, (units of work, energy,
power, time, etc). You also
encounter overlaps, such as BOTH
torque and work have units of Nm,
(Newtons x meters). So to
distinguish them, we label energy
units as joules. Finally units of
radians are NOT units at all. They
are a ratio of meters divided by
meters, which equals one. So, if in
a calculation, you obtain no units
divided by time; that is actually
angular velocity, measured in
radians per second.
Page 28 of 52
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
using formulas for rotational inertia in
class, and in a laboratory exercise.
Benchmark # 5 Use Newton’s Second Law
for rotation, to define and evaluate torque.
a.) Define torque as an applied force
causing rotation, and identify the three
factors which affect the size of its value.
These are force; moment arm, (radius);
and angle of applied force.
b.) Use these three values to derive an
equation for torque, and derive its units
of measurement.
c.) Differentiate these units of measurement
from those of work and energy, using
vector dot and cross products.
d.) Resolve these values vectorially, using
cross products, to show that torque is a
vector resultant; find its resultant
direction using the right hand rule.
e.) Relate torque to Newton’s Second Law
of Motion, and derive an equation for
this law involving rotation of an object
with mass.
f.) Derive units of measurement for this
equation.
g.) Solve problems related to torque and the
accelerated rotation of an object with
mass, using Newton’s Second Law of
Motion.
Benchmark # 6 Define and evaluate the
AP Physics C – Mechanics, Level I
Page 29 of 52
Approx. Time Allotment:
Instructional Strategies
b. Derivatives and Integrals,
especially as they relate to sine
waves and sinusoidal functions.
We will need this badly in the next
unit. Also, we will need angular
velocity again, to derive the
equation for displacement of an
oscillator. So emphasize the
concept, and its units.
c. The only oscillators they have
not seen before, are a physical
pendulum, and a torsional
pendulum. Both rely upon finding
the rotational inertia, I, of each
object, and calculating the
rotational Hooke’s Law constant,
K. So, make sure you also
emphasize rotational inertia;
especially for a system of objects . .
. AND UNITS of rotational inertia.
d. Start making a formula page for
the final exam-list; all formulas for
linear and rotational equivalents
NEXT TO EACH OTHER.
4. By now, the Physics Olympics
season is coming to an end, and the
Science Olympiad season is
beginning . . . make sure they end
Olympics CLEANLY, (i.e., file all
sample problems, event rules,
maps, everything; put away all
unused materials and label them;
make lists of any information that
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
work, energy, and power of an object with
mass, undergoing rotational motion.
a.) Relate work, kinetic energy, and power
of an object in linear motion, to an
object undergoing rotational motion.
b.) Derive an equation for work, kinetic
energy, and power for a rotating object,
and emphasize the units of measurement
for each one.
c.) Relate the formula for kinetic energy of
rotation, to rotational inertia, and
compare the units of measurement for
ALL values involved.
d.) Solve problems involving work, kinetic
energy, power, and all related variables
for an object or system undergoing
rotation.
Benchmark # 7 Relate the major systems for
rotation and their equations, so as to solve
major problems using variables alone, or
numerical values, when given. (This will
involve algebra, trigonometry, calculus, and
graphing, used in conjunction with one
another).
Approx. Time Allotment:
Instructional Strategies
came up and can be used again;
display all awards in the library;
notify the administration as to the
year’s accomplishments, and
update the banner in the library;
put everything away and shut the
machine down for the year!)
5. Begin afternoon/evening extra
help sessions: with practice
multiple choice and free-form
problems tests. Get them familiar
with the test format; time
restrictions; when to guess and
when not to; problems with
variables and no numbers; using
written explanations for a problem,
if you can’t do the math,
(especially calculus); appropriate
use of calculators; the
experiment/graphing problem,
etc… Basically, “Practice!
Practice! Practice!”
Benchmark # 8 Define and evaluate rolling.
a.) Differentiate rolling from rotation, and
define rolling as a specialized type of
rotation.
b.) Vectorially describe the motion and
velocity of ALL points on a rolling
AP Physics C – Mechanics, Level I
Page 30 of 52
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
object, as measured from a single
reference point, (i.e. where the object
touches the ground).
c.) Calculate the velocity and direction of
ALL points, by vectorially adding the
rotational and translational motions
simultaneously.
d.) Derive the equations related to rolling,
especially that for kinetic energy, and
their units of measurement.
e.) Relate the translational velocity to the
angular velocity, and derive their
common value, (the radius of the object
or wheel).
f.) Solve problems for any unknown value,
related to an object rolling along, up, or
down any inclined surface.
Approx. Time Allotment:
Instructional Strategies
Benchmark # 9 Resolve rolling systems, or
objects using systems of torque.
a.) Use Free Body Diagrams, (F-B-D), to
draw and label all forces on an object;
translate them into torque vectors.
b.) Use the concept of “moment arm,” to
create systems of torques about ANY
arbitrary or actual point of rotation.
c.) Calculate the net torque on the system,
including those created by friction or other
contact forces.
d.) Calculate the direction of rotation, and
the rate at which it accelerates, for both
rotation and translation.
AP Physics C – Mechanics, Level I
Page 31 of 52
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
e.) Solve problems for systems of torque,
for any object or system of objects, rolling
along a flat or inclined surface.
Approx. Time Allotment:
Instructional Strategies
Benchmark # 10 Define and evaluate
angular momentum for an object, or system
of objects
a.) Define angular momentum and
differentiate it from linear momentum.
b.) Derive the equation for angular
momentum, and its units of
measurement.
c.) Using vector cross products, derive an
equation for the angular momentum,
created when an object with linear
momentum strikes or collides with a
system, which can rotate
d.) Define and derive the concept of
Conservation of Angular Momentum,
and the unique equation that is created
for each example or system studied.
e.) Differentiate between systems which
exhibit angular conservation of
momentum and those that do not, based
upon axes of rotation, slipping and
friction, changes in rotational inertia,
and systems of rotating objects.
f.) Find unique solution strategies and
equations for systems which do NOT
exhibit conservation of angular
momentum.
g.) Solve problems, for selected variables,
AP Physics C – Mechanics, Level I
Page 32 of 52
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
involving single or systems of objects,
which touch or connect, and transfer
rotation to other objects or systems.
Solutions may or may not be
conservative, and if not, identify the
losses of energy and/or momentum.
AP Physics C – Mechanics, Level I
Page 33 of 52
Approx. Time Allotment:
Instructional Strategies
July 2002
Essential Question, Concept or Theme: H. Rotation and Rolling
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.7.12.A, B, C, D, E; 3.8.12.A
Adaptations/Inclusion
Enrichment Strategies
Remediation Strategies
Techniques
Approx. Time Allotment: 4 weeks
See Unit A
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
See Unit A
Page 34 of 52
Multicultural/Interdisciplinary
Connection
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1 Define oscillation
1. Quiz - 1- multiple choice on
1. Graphing calculator
and periodic motion.
concepts in chapter.
2. IBM PC
2. Quiz - 1 - three problems
3. PASCO 750 Interface Box
Benchmark # 2 Define and evaluate 3. Test - same format as chapter
4. PASCO Smart pulleys,
Simple-Harmonic-Motion (S-H-M)
test in part B
photogates, and laser switches
a.) Relate oscillation and periodicity 4. Homework - selected
5. PASCO picket fences
problems from the end of the
to S-H-M.
6. PASCO force meters
chapter.
b.) Relate displacement, velocity,
7. Vernier Graphical Analysis III
and acceleration (vectors) to S5. Laboratory Exercise - Confirm Software
the factors which affect a physical 8. Microsoft Excel and Word
H-M.
or torsional pendulum.
c.) Graph displacement, velocity
Software
and acceleration versus time for
6. Participation in Science
9. Physical springs and elastics of
an oscillating object, (a
Olympiad (Physics Olympics
varying sizes
sinusoidal curve).
season has ended by now)
10. Discs, hoops or spools, (made
d.) From these graphs, define and
7. Class participation for points.
of plastic, wood or metal)
derive amplitude, period,
11. Slotted weights and weight
frequency and wavelength for
hangers
each one.
12. Tabletop hardware
e.) Relate S-H-M to uniform
13. Hinges, pivots, connectors
circular motion in one
14. Meter sticks and rulers
dimension.
15. Stop watches
f.) Define this periodic motion in
16. Electronic balance/triple beam
terms of angular velocity, ω, and
balance
derive its units of measurement.
17. Sand and clay
g.) Derive the equation for
displacement in terms of
amplitude, angular velocity,
time, and the sine of the angle
they create, at any given moment
in time.
h.) Compare this equation to the
AP Physics C – Mechanics, Level I
Page 35 of 52
Approx. Time Allotment:
Instructional Strategies
1. A reminder to leverage students’
knowledge of angular velocity,
motion, acceleration, and
displacement to develop the
relationship between these
variables and simple harmonic
motion.
2. This is the second major
application of angular motion. Its
resolution in formulas uses radian
measure and its units of
measurement. Practice a lot with
units; make students use their
calculators in radian, (not degrees)
mode…over and over…again, until
it is second nature. They see
angular motion, they put their
calculator into radian mode.
3. This unit is the last major unit to
utilize differential and integral
calculus; to go back and forth
between displacement equations
and graphs, AND acceleration
equations and graphs. Spending
some extra time and emphasis here
can help them review derivatives
and anti-derivatives in general.
4. Topics which need to be spiraled
for the last two units:
a.) Vector resolution is used here
for displacement, velocity, and
acceleration. It will be used for
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
graph of displacement versus
time, and demonstrate that they
both represent the exact same
motion…the displacement of the
object at any moment in time.
i.) Using calculus, derive the
equation for velocity with
respect to time, from the
displacement equation.
j.) Compare this equation to the
graph of velocity versus time,
and demonstrate that they both
represent the exact same motion
k.) Using calculus, derive the
equation for acceleration with
respect to time, from the velocity
equation.
l.) Compare this equation to the
graph of acceleration versus
time, and demonstrate that they
both represent the exact same
motion.
m.) Demonstrate from actual
demonstrations and examples,
that these graphs and equations
may be used for ANY oscillating
object in nature.
n.) Solve problems for any variable
requested, using graphs or
equations, for any oscillating
object given.
AP Physics C – Mechanics, Level I
Page 36 of 52
Approx. Time Allotment:
Instructional Strategies
b.)
c.)
d.)
e.)
FORCES in both of the last two
units.
Rotational inertia…by doing
this unit right after rotational
motion, it helps give more
continuity in the lab, using the
same basic ideas again,
(especially rotational inertia
and torque).
Laboratory exerciseconclusions, and the rubrics
used to grade them. By now,
the level of their conclusions
and how they are written
should be quite high. Keep
raising the bar!
Review units for ALL variables
by concentrating on the ones
involved with your present
unit…and differentiating them
from others…make them
identify these “other” units, and
the variables they represent.
Remember to STRESS linear
variables and their units, AND
rotational variables and their
units.
Continue building a single
major formula page, for each
student, to use as a year-end
review for the final exam in
this course; and to help
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 3 Define and relate SH-M to the varying force on an
oscillating object.
a.) Use Newton’s Second Law of
Motion to directly relate force
and acceleration.
b.) Use the graph and equation of
acceleration versus time to relate
the net force on the object to the
time.
c.) Use the graph and equation of
displacement versus time to
relate the net force on the object
to its displacement.
d.) Use vector resolution to find the
net force on an oscillating object,
and its corresponding
displacement, velocity, and
acceleration at any moment in
time.
Approx. Time Allotment:
Instructional Strategies
organize all the formulas and
their units into working
relationships.
5. After school reviews, and
evening help sessions; lunch clubs;
and whenever you can give them
practice problems and
questions…go over them with the
students!
Practice, practice, practice…
Benchmark # 4 Relate specific
oscillators to the general formulas
and graphs derived for all objects in
S-H-M.
a.) Use Hooke’s Law to directly
relate force and displacement,
when applied to a mass being
acted upon by a spring or elastic.
b.) Through experimentation or
demonstration, identify which
factors affect an oscillator’s
AP Physics C – Mechanics, Level I
Page 37 of 52
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
period, (such as mass and spring
constant affect the periodicity of
an object being acted upon by a
spring).
c.) Derive an equation, (using these
unique factors), for each of the
four specific kinds of oscillators:
I. Simple Pendulum
II. Mass acted upon by a spring
(elastic)
III. Torsional Pendulum
IV. Physical Pendulum
d.) Solve problems for unknown
variables using different kinds of
physical oscillators.
e.) Confirm the factors and period
equation, for one physical
oscillator, in a laboratory
exercise.
Approx. Time Allotment:
Instructional Strategies
Benchmark # 5 Relate the overall
Conservation of Energy Theorem, to
an oscillator, by treating it as a
closed system.
a.) Define Potential Energy, (PE),
and Kinetic Energy, (KE), in an
oscillator.
b.) Derive an equation for both PE
and KE in an oscillator.
c.) Demonstrate and confirm that
the total energy, E, in such a
system is ALWAYS the sum of
AP Physics C – Mechanics, Level I
Page 38 of 52
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
KE plus PE.
d.) Graph PE vs displacement for
any oscillator.
e.) Use derivatives to find the force
at any point; the displacement to
find the KE and PE at any point;
and the constant total energy, E,
at any point.
f.) Define and relate the work done
by friction to, (heat), and the loss
of kinetic energy in a non-closed
system.
g.) Define and describe this loss as
damping, and how it affects such
variables as frequency, period,
amplitude, energy, velocity, and
acceleration.
h.) Derive an equation for damping.
i.) Solve problems for unknown
variables involving energy,
force, mass, displacement,
velocity, acceleration, frequency,
period, and amplitude at any
position or time.
AP Physics C – Mechanics, Level I
Page 39 of 52
Approx. Time Allotment:
Instructional Strategies
July 2002
Essential Question, Concept or Theme: I. Oscillations
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.B, C; 3.6.12.C; 3.7.A, B, C, D, E; 3.8.12.C
Adaptations/Inclusion
Enrichment Strategies
Remediation Strategies
Techniques
Approx. Time Allotment:
See Unit A
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
See Unit A
Page 40 of 52
Multicultural/Interdisciplinary
Connection
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
Benchmark # 1 Demonstrate a
1. Quiz – 1 - multiple choice on
1. Graphing calculator
1. A key point in this unit, and the
working knowledge of the
cause of a major misconception is
concepts in chapter.
2. IBM PC
historical development of the
the DIFFERENCE between
2. Quiz – 1 - three problems
3. PASCO 750 Interface Box or
theories of the universe, and solar
gravitational Potential Energy,
3. Test - same format as chapter
remote 500 Interface Box
(PE), when it is near the Earth’s
system.
test in part B.
4. PASCO force meters or
surface, or when it is far away.
4. Homework - selected problems accelerometers
Near the surface, it is:
Benchmark # 2 Relate how these
from the end of the chapter.
5. Vernier Graphical Analysis III
theories and developments affected 5. Laboratory exercise - “Circular
Software
the political/theological status of
Motion,” - derive and confirm the
PE= mgh
6. Microsoft Excel and Word
the past, (Renaissance), through to centripetal force with force meter
Software
today.
or accelerometer.
7. Brass weights (hanging and
where ‘h’ is the height above the
6. Participation in Science
slotted)
surface. Far out in space the
Benchmark # 3 Define gravity as a Olympiad.
8. Tabletop Hardware
formula is:
force, with its units of
7. Class participation for points.
9. Revolving stool or bicycle wheel ____________________________
measurement.
____________________________
10. String
______________________
11. Pulleys
Benchmark # 4 Define gravitation
12. Stopwatches
PE= Gm1m2
as a field, and diagram this field
__________
about a mass located in space.
R
Benchmark # 5 Define and
evaluate Newton’s Law of
Gravitation
a.) Derive Newton’s proportion for
gravitation.
b.) Derive Newton’s equation for
gravitation, and define G, the
universal constant for
gravitation.
c.) Define the role of G in this
equation, and derive its units of
measurement.
AP Physics C – Mechanics, Level I
where R is the distance between
the CENTER of m1, and the
CENTER of m2. The surface
distance is ignored. The real
difference between the two is in
problem solving. The first formula
basically ignores the change in g,
the acceleration due to gravity,
because it remains so close to the
surface. It is concerned with
problems done on our planet’s
surface, (usually by people).
Page 41 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
Therefore, as a rule of thumb, tell
d.) Relate how Cavendish’s
students that when doing problems,
experiment measured the value
which remain in the Earth’s
of G.
atmosphere, use the first formula.
e.) Solve problems for unknown
When doing problems, which
values using Newton’s
involve Earth satellites or problems
gravitation equation.
in “outer space,” use the second
formula. This difference MUST be
Benchmark # 6 Define and
addressed, however.
evaluate the Principle of
Superposition.
2. Topics that are finished being
a.) Use vector resolution to find
spiraled here are:
gravitational forces in space;
a.) Conservation of energy-this
near the earth’s surface; and
topic is necessary when
inside the Earth.
deriving the formula for escape
b.) Use vector resolution to find
velocity and satellite orbits.
gravitational forces and field
MAKE SURE, you address the
lines, between multiple (major)
rotational and linear velocity of
masses in space.
the Earth launch site, and the
c.) Solve problems for unknown
kinetic energy a rocket has
values using Newton’s
EVEN WHEN SITTING ON
gravitation equation and vector
THE LAUNCH PAD. It is
resolution.
why Cape Kennedy is located
as far SOUTH as possible in
Benchmark # 7 Define and
the United States. Also, why
evaluate gravitational potential
rockets are directed eastward
energy.
after launch, to utilize this
a.) Derive an equation for the
kinetic energy that it already
gravitational potential energy
has, and increase it.
of an object in space, (above
b.) To do most gravitation
the earth’s surfacing); use the
problems, six formulas are
concept of the work done, to
necessary, and it is critical to
place it there from the earth’s
AP Physics C – Mechanics, Level I
Page 42 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
show how they relate to one
surface.
another. They are the formulas
b.) Derive the units of
for:
measurement for this
gravitational Potential Energy,
I. Newton’s Law of
(PE).
Gravitation
c.) Differentiate between
II. Kepler’s Third Law of
gravitational PE near the
Planetary Motion
earth’s surface, and much
III. Velocity of an object in
further out in space.
circular motion
d.) Differentiate between the
IV. Centripetal Force
equations used to find these
V. Escape Velocity
two values, and explain the
VI. Conservation of
discrepancy between the
mechanical energy, (PE and
distances from the Earth’s
KE)
center, (when calculating these
values).
c.) One common “trick question”
e.) Relate gravitational PE to
that is used by many teachers to
Kinetic Energy, (KE), of
see if students truly understand
objects moving in relation to
these relationships, is that of a
Earth.
“twin star” situation. The key
f.) Use this relationship to derive
is that the radius of their orbits,
the equation for Escape
R1, is used in the centripetal
Velocity from the Earth’s
force equation; the distance
gravitational field.
between their centers, R2, is
g.) Use the formula for escape
used in the gravitation formula.
velocity, to relate how orbits
Therefore, R2 is twice as big as
combine gravitational PE and
R1. This is one of the very few
KE in the conservation of
exceptions that occurs -where
energy principle.
R1 does NOT equal R2.
h.) Solve problems for unknown
variables using the principles of
3. Finally, this unit has been
gravitational PE and the overall
dogged with student complaints in
AP Physics C – Mechanics, Level I
Page 43 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
the past, which basically asked,
conservation of energy.
“How does this relate to
everyday…?” Tell them: In today’s
Benchmark # 8 Define and
marketplace, (full of satellite TVs,
evaluate Kepler’s Laws of
cell phones, pagers, etc.), there is a
Planetary Motion
tremendous growing need for more
a.) Define and draw an ellipse.
communications satellites, that go
b.) Identify its major
beyond spy satellites and weather
characteristics, (major/minor
satellites put up by NASA. Several
axes, foci, center, etc.)
companies in the U.S. and abroad,
c.) Define and derive the equation
now regularly launch their own
for eccentricity in ellipses.
satellites for private industry.
d.) Relate this definition to
These companies need, for
Kepler’s First Law, and how all
technical people, will only increase
orbiting objects in space follow
in the future. NASA is no longer
this principle.
the only way into space.
e.) Identify the position of masses
orbiting and being orbited;
4. One last “Gee, wow!” look, at
maximums and minimums; the
the universe. It is relevant here,
acceleration and velocity of the
and is a small look at gravity waves
orbiting satellite; and how this
and why they exist. Also, how
affects the center of mass while
they relate to the “Big Bang”
orbits occur.
theory of the birth of our universe,
f.) Relate the area swept out
and how we would use them to
during orbit, to the equal
discover the age of our
intervals of time that create
universe…all care of gravitation!
these areas, in Kepler’s Second
Law of Planetary Motion.
g.) Define and derive the equation
for Kepler’s constant, in his
Third Law of Planetary Motion.
h.) Relate which bodies use the
same constant, and differentiate
AP Physics C – Mechanics, Level I
Page 44 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
which bodies use different
constants, for all objects in
space.
i.) Solve problems for unknown
variables using Kepler’s Laws
of Planetary Motion.
Benchmark # 9 Solve for unknown
variables, by relating Newton’s
Law of gravitation, with equations
for: acceleration, centripetal force,
kinetic and potential energy, mass,
circular motion, and Kepler’s Third
Law.
Benchmark # 10 Define and relate
Einstein’s theory of gravitation
with three-dimensional space.
a.) Define the relationship
(according to Einstein) between
mass and gravity.
b.) Relate this to the “distortion” of
space around a large mass, then
a smaller mass.
c.) Use this “model” of “bent
space” to explain all the
possible motions of moving
objects, coming near a large
mass in space.
d.) Use this model to explain how
a black hole can be created in
“bent space.”
AP Physics C – Mechanics, Level I
Page 45 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment:
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
e.) Explain how black holes can be
detected and mapped in the
universe.
AP Physics C – Mechanics, Level I
Page 46 of 52
July 2002
Essential Question, Concept or Theme: J. Gravitation
Approx. Time Allotment: 4 weeks
PA Standards: 3.1.12.A, B, C, D, E; 3.2.12.A, B, C, D; 3.4.12.A, B, C, D; 3.6.12.C; 3.7.12.A, B, C, D; 3.8.12.A, B, C
Adaptations/Inclusion
Multicultural/Interdisciplinary
Enrichment Strategies
Remediation Strategies
Techniques
Connection
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
See Unit A
Page 47 of 52
See Unit A
July 2002
Essential Question, Concept or Theme: K. Equilibrium
PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1 Define and
1. Quiz – 1 - multiple choice on
1. Graphing calculator
evaluate equilibrium, at a single
concepts in chapter
2. IBM PC
point.
2. Quiz - 1 - three problems
3. PASCO 750 Interface Box
a.) Derive an equation for
3. Test - same format as chapter
4. PASCO Smart pulleys,
equilibrium as the sum of all
test in part B
photogates, and laser switches
force vectors equals zero.
4. Homework - selected problems
5. PASCO force meters,
b.) Relate these forces as all
from the end of the chapter
accelerometers, picket fences
coming from a single point.
5. Laboratory exercise - student
6. Vernier Graphical Analysis III
c.) Resolve all force vectors into
originated and designed, from any
Software
components.
topic throughout the year.
8. Microsoft Excel and Word
d.) Redefine equilibrium as force
6. Participation in Science
Software
components:
Olympiad
9. Tabletop hardware
I. The sum of all force
7. Class participation for points
10. Any other resources previously
components on the x-axis
mentioned, or materials necessary
equal zero.
for students to build their own
II. The sum of all force
devices and test platforms.
components on the y-axis
equal zero.
III. The sum of all force
components on the z-axis
equal zero.
e.) Define the center of gravity as
representing: all gravity, on all
parts of an object.
f.) Solve problems for unknown
variables involving the vector
resolution of all forces on an
object.
Benchmark # 2 Define and
evaluate equilibrium, when forces
are applied to different points on an
AP Physics C – Mechanics, Level I
Page 48 of 52
Approx. Time Allotment: 4 weeks
Instructional Strategies
1. All the separate concepts for
this unit have been seen before.
They merely must be brought
together, in a formal presentation,
with the EMPHASIS ON
EXAMPLES. Also, concentrate on
systems where BOTH force vectors
AND torque are needed to solve
these problems. Be sure to include
friction, as a means to review;
constantly require both components
and resultant forces at a single
point. This is strong review
material. Remember, both the AP
Exam and the course final exam
are coming VERY SHORTLY.
2. The course final exam is a
former AP Exam, given some years
back. A new group of multiple
choice questions AND free form
problems, are selected each year
from the collection of past AP
Exams, (sent to the teacher, after
their formal training by the College
Board instructors). The course
final exam is traditionally given a
few days after the AP Exam: 35
multiple choice questions during
one class period; 3 free-form
problems, (selected by students
from 5 possible), during another
period. These may be over two
days or a double lab period…THE
July 2002
Essential Question, Concept or Theme: K. Equilibrium
PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
object.
a.) Redefine torque as a force;
applied to a moment arm; at
some distance from a pivot
point; at an angle to that
moment arm.
b.) Select any arbitrary pivot point, and identify all the
torques applied to the object
using one or more moment
arms.
c.) Vectorially resolve all torques
involved in equilibrium, by
labeling them clockwise or
counter -clockwise around this
pivot point.
d.) Derive torque equations for
equilibrium as the sum of all
clockwise torques plus the sum
of all counter –clockwise
torques equal zero.
e.) Calculate the sum of all force
components is also equal to
zero, when no rotation is
involved.
f.) Solve problems for unknown
variables involving the vector
resolution of both force
components, and torques
applied to an object.
Benchmark # 3
Relate the
AP Physics C – Mechanics, Level I
Page 49 of 52
Approx. Time Allotment: 4 weeks
Instructional Strategies
INCENTIVE is, study ONCE, and
take the AP Exam AND the course
final exam within a few days of
each other. This will hopefully
encourage students to sign up for
the AP Exam.
3. Needless to say…PRACTICE,
practice, practice!!!
4. The final exam and AP Exam
now out of the way, their year now
has about two weeks until classes
are over, and regular final exams
begin. This is when AP Physics
does their final formal lab project:
a lab of their own choice, and their
own design - any topic you have
covered. They may choose their
own lab partners, (up to six,
maximum), and it can be a new
topic, or an extension of something
they have done before. It can even
be related to Science Olympiad or
Physics Olympics. BUT it is a
formal laboratory exercise, turned
in by the start of regular final
exams, and graded as a major
chapter test. When done properly,
this is a fun time to really see some
creative thinking, building, and
evaluating! For the most part, the
pressure is off, and this is
CREATIVE TIME, for MOST are
seniors.
July 2002
Essential Question, Concept or Theme: K. Equilibrium
PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
motion of an object to equilibrium.
a.) Demonstrate that objects at
rest, or constant velocity in a
straight line, are in equilibrium.
b.) Demonstrate that objects not
rotating, or rotating at constant
angular velocity, are also in
equilibrium; their net torque
equals zero.
c.) Demonstrate that systems of
objects, exhibiting these
characteristics are also in
equilibrium.
d.) Solve problems for unknown
variables, involving single
objects or systems of objects,
moving as described above.
AP Physics C – Mechanics, Level I
Page 50 of 52
Approx. Time Allotment: 4 weeks
Instructional Strategies
5. One last very important
step…stay in touch with these
students after they graduate. Have
them bring back syllabi and lab
manuals from the colleges and
universities they are attending.
Have them critique this course for
strong and weak points; level of
difficulty; appropriate topics; time
dedicated to each topic; lecture and
class time usage; laboratory
exercises and lab write-ups; and all
the ideas they bring up to make this
course stronger EVERY year. This
particular course has evolved for
22 years, and has NEVER been
taught the same twice in a row.
USE all the research tools available
to you: Physics Teacher Magazine
and other publications; the
American Association of Physics
Teachers, (the AAPT), and
National Science Teachers
Association, (the NSTA), and other
organizations; competitions like
Physics Olympics and Science
Olympiad, and their coaches and
activities; the numerous web sites
for teachers and students to use;
new textbook offerings, which will
be sent to you on request from
publishers, (also ask for the
teacher’s edition and other
July 2002
Essential Question, Concept or Theme: K. Equilibrium
PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment: 4 weeks
Instructional Strategies
accompanying manuals); and
visitations to other schools,
especially events like Middle
States Evaluations;
ETC…Remember - in a topic area
like physics, if you are not
constantly trying to improve and
update…you are not standing still you are losing ground!!
AP Physics C – Mechanics, Level I
Page 51 of 52
July 2002
Essential Question, Concept or Theme: K. Equilibrium
PA Standards: 3.1.12.A, B, C, D; 3.2.12.A, B, D; 3.4.12.C; 3.6.12.C; 3.7.12.A, B, C, D, E
Adaptations/Inclusion
Enrichment Strategies
Remediation Strategies
Techniques
Approx. Time Allotment:
See Unit A
See Unit A
AP Physics C – Mechanics, Level I
See Unit A
See Unit A
Page 52 of 52
Multicultural/Interdisciplinary
Connection
July 2002