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AP Physics C Mechanics – Syllabus
Course Description: AP Physics C is a college level course designed to prepare
students for the AP Physics C Mechanics exam given in May. A prior physics course is
not required but desired for enrollment, and students must have strong background
in math, since a basic understanding of calculus (differentiation and integration) is
used to derive formulas in the course. This course uses labs, lecture, guided inquiry,
student centered learning, and teacher support to foster the development of critical
thinking skills.
Topics are typically introduced with discussions and demonstration. From there,
relations are derived from the basic definitions, students work on problems to apply
the concepts learned, and solutions are presented so students and the teacher can
discuss the solutions. Each class session allows time for students to discuss the
previous night’s assignment (typically five problems) to ensure they understand the
information. The goal is to have a deep understanding of the concepts and why
things happen instead of simply memorizing the formulas. In addition to the
availability of the teacher in and outside of class, students are encouraged to
participate in study groups for additional support.
Co-prerequisite: Calculus (BC): Calculus (8th edition 2006) by Larson, Hostetler,
Edwards: Houston, Miffing Corp
Text Book:
Physics for Scientists and Engineers, by Serway and Beichner, 5th Edition
Homework: 10%. The students will have a set of problems each day and that will be
completed for the teacher the following day. Problems from each chapter are
assigned. Additional problems are used in the class to develop solution strategies.
Quizzes: 25%. After each five class meetings, the students will receive a one page
quiz assessing their understanding of concepts and their ability to solve problems.
Tests: 30%. At the completion of each unit, the students will take a computer test
with multiple choice questions and a paper set of free response questions similar to
those found on the AP exam.
Labs: 20%. At least one class session each week will have a hands-on lab activity
with maximum usage of digital monitoring and measuring devices. A formal lab
report will be required for each activity which will be formatted in Excel to maximize
its calculation and graphic functionality.
Research Project: 15%. A project will be assigned each quarter that incorporates
both literature search and laboratory investigation of a principle under current study.
Organization, reasoning, method and decision making process will be emphasized to
be used in decision making and problem solving. Students must be able to solve the
multi-concept physics problems by using Newton’s laws of motion and the
conservation laws by using differential and integral calculus. They must learn how to
translate word problems into calculus problems and solve it by using proper limits.
The class meets 3 days each week for 95 minutes or 1 session. (285 minutes/week)
Mechanics
Kinematics: Vectors And Scalars: 11 sessions:
Introduction to measurement, powers of ten, metric prefixes, density and formula
computations. SI units are defined and physical units derived. Basic equation
solutions are reviewed, and rules are defined for homework problem formats.
Introduce strategies for problem solving.
Homework: p 17-22 Ch. 1:
2, 5, 6, 9, 12, 14, 18, 20, 26, 30, 33, 36, 38, 51, 52, 55
To ask questions in the class about home work is strongly encouraged.
Falling behind will make the subject more difficult.
Kinematics: distance, displacement, speed, velocity, acceleration: constant, average
and instantaneous: Motion in one dimension, Graphical representation of d, v and a
vs. time - Displacement, Velocity, and Speed, Instantaneous Velocity and Speed,
Acceleration
Slope and area under the graph and inter-relation between d, v and a. Free fall.
Introduction to derivative, integration and application to varying d, v and a.
Motion in two dimensions: Projectile motion- leveled and unleveled ground,
horizontal range, maximum height, total time of flight and the important conditions.
Homework: Ch.2: p. 50-57: Problems: 1, 2, 3, 4, 7, 11, 13, 15, 23, 28, 29, 31, 40, 46, 51
Coordinate Systems, Vectors and Scalars, Vector Addition and Subtraction, Vector
Components, Unit and i-j-k Vectors Kinematics Graphics—days Difference between
scalar and a vector, unit vector and notation of a vector, addition of vectors:
Parallelogram, Head –Tail and the decomposition method, Multiplication of vectors:
Dot or scalar product and cross or vector product, RHR for the direction of the vector
product, mention how and where these will be used in physics, introduction to i, j, k
components in rectangular coordinates.
Homework:
31, 33, 35
Ch.3: p. 71-75: Problems: 1, 3, 5, 6, 8, 9, 11, 14, 15, 17, 19, 20, 21, 25, 27,
Two Dimensional Motion with Constant Acceleration, Motion in a Plane and
Projectiles, Uniform Circular Motion, Relative Motion
Homework: Ch.4: p. 101—108: Problems: 3, 4, 5, 6, 9, 10, 13, 14, 15, 19, 20, 21, 22, 23,
24, 27, 29, 30,31, 32, 33, 34, 35, 39, 41, 47, 48, 53, 57, 59, 69, 82, 84
Dynamics-Newton’s Laws of Motion: 9 sessions:
Law of inertia, linear equilibrium Net F = 0, rest or constant velocity
Law of acceleration, Net F = ma =m dv / dt.
Law of action and reaction.
Forces: Pull or push, gravity, normal and frictional, Tension, electric and magnetic
Labeled free body diagrams, Technique of isolating the bodies and applying Newton’s
laws.
Homework: Ch.5: p. 140-149: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 19, 21,
23, 24, 25, 26, 27,29, 30, 31, 33, 34, 35, 37, 39, 41, 45, 49, 51,55, 57, 63, 67, 69, 77, 78,
82, 85, 87, 88
Circular motion, curved and banked roads, motion in horizontal and vertical circles
and park rides, centripetal force and acceleration. Newton’s 2 nd law for circular
motion. Direction of F, a and v in linear and circular motion. Nonuniform Circular
Motion, Motion in a Resistive Medium
Homework: Ch.6: p. 173-181: Problems: 1, 2, 3, 4, 5, 7, 8, 11, 12, 14, 15, 16, 17, 21, 26,
28, 29, 30, 31, 32, 33, 34, 35, 36, 39, 41, 43, 45, 48, 49, 50, 52
Work, Energy, Power, KE and PE: 8 sessions:
Units defined, Work as a line integral and force as a space derivative of work,
Power as time rate of change of work, graphical representation,
Work-Energy principle derived from Newton’s 2nd law as space dependent by using
chain rule and definition of KE. Work Done by a Constant Force, Scalar Product, Work
Done by a Variable Force, Work Done by a Spring, Kinetic Energy and the WorkEnergy Theorem, Power and Efficiency, Conservative and non-conservative forces,
Gravitational and elastic potential energy.
Homework: Ch.7: p. 207-213: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19 20,21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35 36, 37, 38, 39, 40
41, 42, 43, 44, 45,46, 47, 48, 49, 50, 52, 53, 55, 56, 57, 59, 70, 71, 73, 75 77, 79, 81, 86
Potential Energy, Conservative and Nonconservative Forces, Conservative Forces and
Potential Energy, Conservation of Mechanical Energy, Potential Energy Function
Potential energy curves, KE + PE = mechanical energy, Law of conservation of
energy when external force is zero. Use of calculus in solving problems.
Gravitational PE, U equal to negative of the line integral of the force of gravity,
Force expressed as the negative of the space derivative of the potential energy
function, F = - dU(r) / dr.
Homework: Ch.8: p. 239-249: Problems: 1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41
43, 46, 47, 49,52, 53, 55, 57, 58, 60, 61, 63, 67, 68, 69
Momentum: 6 sessions:
Linear Momentum and its Conservation, Impulse and Momentum, Collisions in One
Dimension, Two Dimensional Collisions, Center of Mass, Rocket Propulsion Property
of motion and a vector quantity defined by using Newton’s 2nd law as time
dependent. Net F = dp/dt, where p = mv, Impulse theorem and definition of
impulse. Graph of t vs. F and its relation to change in momentum, graph of p vs. t
and its relation to force. Law of conservation of momentum from impulse theorem
when an external force is zero.
To emphasize special conditions for conservation laws. Interactions and elastic and
inelastic collisions in 1D and 2D and conservation laws.
Perfectly elastic collisions: KE and Momentum both are conserved when external
force is zero and the relative velocity before collision is equal to the negative of the
relative velocity after collision.
In inelastic collision KE is lost and only Momentum is conserved.
Center of mass, center of gravity and center of mass motion.
Homework: Ch.9: p. 282-291: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
17, 18, 19, 20 22,23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 43, 45
51, 52, 53, 54, 57,58, 59, 60, 63, 65, 69, 71, 72, 73, 75, 80, 81, 82, 84, 85
Rotation Dynamics: 7 sessions:
Rotational Dynamics: Define torque = r x F and derive N’s 2nd law for rotation
Net Torque = M of I times angular acceleration. Units of torque and work and the
difference, Rotational KE, Linear KE for rolling objects.
Angular Displacement, Velocity, and Acceleration, Rotational Kinematics, Angular and
Linear Quantities, Rotational Energy. Calculations of Moments of Inertia, Use calculus
to find the M of I of a uniform rod, a ring, a disc, etc. Torque and Angular
Acceleration, Work, Power, and Energy in Rotational Motion, Parallel axis and
perpendicular axis theorem.
Homework: Ch.10; p. 317-327: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19 20,21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 37, 40, 42, 43, 44, 47, 48
50, 51, 52, 54
Law of conservation of energy. Angular momentum L = r x p and L = M of I x
angular velocity and Net Torque = dL/dt as Net F = dp/dt in linear dynamic.
Law of conservation of angular momentum when Net torque is zero.
Comparison with Liner momentum will help. Motion of spinning top and gyroscope,
precession motion, center of percussion. Rolling Motion of a Rigid Body, The Kinetic
Energy of a Rolling Body, The Angular Momentum of a Particle, The Angular
Momentum of a Rolling Rigid Body, The Conservation of Angular Momentum
Homework: Ch.11; p. 350-359: Problems: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 14, 15, 16, 17, 21,
24, 25, 27, 28,29, 31, 32, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 49, 50, 54, 55, 56
Equilibrium: 5 sessions:
The Conditions for Equilibrium, The First Condition of Equilibrium. The Second
Condition of Equilibrium, Cranes, Ladders, and Other Systems, Thermal Expansion,
Elasticity, Free body diagrams, Linear and rotational equilibrium, Net F = 0 and net
Torque about axis = zero are to necessary and sufficient conditions for equilibrium.
Direction of rotation, torque and angular momentum by RHR. All the forms of Newton’s
laws will be presented. Labeling the axis of rotation is a must.
Homework: Ch.12; p. 377- 387: Problems: 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 19,
20, 21, 23, 24,25, 26, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 41, 42, 46, 47, 49, 50, 53, 54
55, 57
Simple Harmonic Motion: 6 sessions:
Hooke’s law, F = -kx, Elastic PE. For spring mass system KE + PE constant, velocity
and acceleration of the mass as a function of displacement. Energy curve, simple
pendulum and compound pendulum. Motion in small oscillations. Linear and
rotational SHM. Displacement, velocity and acceleration as function of time.
Acceleration a = -kx /m and a = -ω2x . Solution of the second order differential
equation of the form d2x/dt2= -ω2x. x = C sinωt + D cosωt .
Homework: Ch.13: p.414-421 Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 18, 19, 20 21,23, 25, 26, 27, 28, 29, 31, 35, 36, 37, 39, 41, 43, 44, 45, 46, 47, 48, 54,
56, 57, 59, 60, 61,62, 65
Gravitation: 7 sessions:
Newton’s law of universal gravitation-an inverse square law. Gravity PE U = mgh, for
constant force on the earth and U =0 on the surface. For variable force Gravity U = GmM/ r, and U at infinity is zero as a reference. Satellite motion in circular orbits.
Planetary motion in elliptical orbits. Kepler’s 3 laws of planetary motion. Laws of
conservation of total energy and that angular momentum. Orbital or tangential
velocity, escape velocity and terminal velocity. Two body system and reduced mass.
Geocentric satellite. 3 in 1 equation: mgr = GmM/r2 = mv2 /r.
Homework: Ch 14: p. 450-457: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16,
17, 19, 20, 21 22,23, 25, 26, 28, 29, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 4849,
52, 54, 56, 57, 58, 61, 62, 64, 65, 66
References: Physics by Holliday and Resnick
Physics for scientists and engineers by Serway
Physics for scientists and engineers by Tippler
Hands-On Lab Activities:
1. Constant velocity of battery powered cars or wind-up toys. Constant acceleration,
ticker tape timer, Plot t vs. d graph and derive t vs. v and t vs. a graph. Conversely
drive t vs. v graph from the t vs. a graph and t vs. d graph from t vs. v.
2. Design the experiment to predict the landing of a projectile and verify given a ball,
a ramp, a horizontal table, meter stick, a timer.
3. Circular motion in horizontal circle, conical pendulum- a toy battery powered
airplane. Find the tension in the string and verify by taking required different
measurement. Draw the free body diagram and analyze the forces and determine
which measurements you would take. Can you calculate acceleration due to earth’s
gravity by this method? Explain
4. Design the experiment to measure the acceleration due to earth’s gravity in this
lab. Verify by different methods. Write the sources of errors and find the percent
error in your measurement. In simple pendulum what graph will you plot and how
will use to find more accurate value of g?
5. Use of inertial balance to measure the mass of unknown object. Which graph will
plot and how will you use it?
6. Push a car with bathroom scales and measure acceleration to find mass of car.
Find the coefficient of static and kinetic friction.
7. Force table to use to derive the law of parallelogram to add to vectors and from
this to understand head and tail method.
8. Use Atwood’s machine to calculate g. Draw free body diagram, derive the
relationship and figure out what measurements you would have to take.
9 The vibrating spring mass system. To determine spring constant. For various
masses find the period T and tabulate the data. What kind of relationship can you
predict between m and T? Is it a linear, square or square root, inverse or
logarithmic? How will you find out? By trial and error method, derive the formula for
T and see that T2 vs. m is a straight line. Read both intercepts and interpret them.
Can you predict the mass of the spring?
10. Find the velocity of the projectile by two methods. Newton’s 2nd law and
projectile motion and by using ballistic pendulum where, law of conservation of
energy and momentum will be used. Discuss the reasons why the values of speed
are different in two methods?
11. Rotational and translational motion of a cylinder or a sphere on the inclined
plane. When rolled from the top determine the linear speed and acceleration of the
center of mass at the bottom of the plane. Think about various methods.
a. Torque and dynamic method; draw free body diagram and consider normal and
frictional forces, find a and then v.
b. Law of conservation of energy: find the final v and then linear acceleration.
c. Take the torque and the moment of inertia (by using parallel axis theorem) about
the instantaneous axis of rotation, write torque = I x alpha, find angular
acceleration and the linear acceleration and from a find v at the bottom.
Neat, well organized with tabulated data, lab set up, procedure, conclusion, graphs
and error analysis, percent error the labs are due during the next session.
A P Examination Review:
Throughout the course, problems are presented that are at the same level of
difficulty as AP exam. Students are expected to solve this rigorous level of work but
the teacher is there to support them along the way. As the AP exam approaches,
students are expected to independently solve additional practices items at home,
both multiple-choice and free-response, in order to prepare them for the style of the
AP exam.
Review Mechanics
Review Topics: 1 to 2 days for each topic
Kinematics and Projectiles
Newton’s Laws
Work and Energy
Linear Momentum
Circular Motion
Rotational Kinematics
Rotational Dynamics
Angular Momentum
Equilibrium
AP Mechanics Free Response Problems from Previous Exams