Download AP PHYSICS C: MECHANICS

AP PHYSICS C: MECHANICS
COURSE OVERVIEW
AP Physics-C is equivalent to a college-level calculus-based Physics course and is
designed for students with strong interest and ability in Physics and mathematics. It is
rigorous, with emphasis on problem-solving and applying concepts, both in class work
and laboratory exercises.
Topics include:
 Vector Mathematics
 Calculus – derivatives and integrals are used throughout the course.
 Kinematics: Linear, 2- and 3-Dimensional Motion
 Newton’s Laws of Motion, Forces
 Work, Energy, Power and Energy Conservation
 Systems of Particles, Linear Momentum, Momentum and its Conservation
 Circular and Rotational Motion: Kinematics, Dynamics, Energy,
Momentum, Torque, and Equilibrium
 Oscillations
 Gravitation and Planetary Motion.
Students will be prepared take the AP Physics C exam in Mechanics. Students can apply
for college credit based on the AP exam results and course laboratory work.
Prerequisite: Honors or CP Physics
Co-requisite: Calculus
UNIT
1
TOPIC
Mathematical Foundations
Calculus—Derivatives
Understand what a derivative is, finding the derivative of a given function, and the
physical meaning of a derivative.
Calculus—Integrals
Understand what an integral is, finding the integral of a given function, and the physical
meaning of an integral.
2
Kinematics – 1-D Motion
Describe and calculate the motion of objects undergoing zero- or constant acceleration,
including free-fall, utilizing kinematics equations.
Write expressions for position and velocity as a function of time.
Use calculus to determine the instantaneous velocity or acceleration of an object, and/or
the maximum/minimum value.
Analyze graphs and equations of motion for displacement, velocity, or acceleration by
applying calculus—taking the derivative or integral of the function.
3
Vectors
Review the proper drawing of vectors; calculate vector components, perform vector
addition and subtraction.
Describe a vector in Unit-Vector Notation, as well as Magnitude-Angle notation.
Multiply vectors using the dot product or cross product.
4
Motion in 2- and 3-Dimensions
Describe position, velocity, and acceleration in 2- and 3-dimensions using unit-vector
notation and magnitude-angle notation.
Given functions for 2-D motion, determine the components of displacement, velocity,
or acceleration in each component direction.
Use calculus to determine the instantaneous velocity or acceleration of an object.
Describe, calculate, and analyze the x- and y- components of projectile motion.
Describe and calculate velocity and acceleration of an object undergoing uniform
circular motion.
Relate radius, speed, and acceleration for uniform circular motion.
Make a vector equation for the relative motion of objects in 1- or 2-dimensions.
5
Forces
Describe the motion of an object that is in static equilibrium (first law).
Define “inertia” and its relation to mass.
Understand and apply the relationship between force and acceleration, and mass and
acceleration. Perform related calculations.
Draw a vector diagram, and determine the net force on a given object, considering all
forces in all directions that may act on the object: gravity, friction, tension, etc.
Understand the coefficient of friction (static and kinetic), relating the normal and
frictional forces on various surfaces (horizontal, inclined).
Calculate static friction; understand the conditions under which an object will slip.
Understand drag forces, and determine terminal velocity of an object that has a
velocity-dependent drag force. Describe the factors that affect terminal velocity.
Use graphs or differential equation to describe the velocity or acceleration of an object
moving with a drag force.
Apply Newton’s third law to identify action-reaction pairs of forces.
Apply Newton’s second and third laws to solve various problems involving tension,
friction, gravity, etc., for various situations (pulleys, inclines, various horizontal or
vertical accelerated motions).
Solve systems of linear equations for unknown forces or accelerations.
Define and calculate “centripetal force”.
Calculate and relate quantities (mass, radius, acceleration, velocity, force) for uniform
circular motion, including horizontal motion and banked curves.
Calculate and relate quantities (mass, radius, acceleration, velocity, force) for nonuniform circular motion (vertical circular motion).
6
Work and Energy
Define and calculate the Work done by a constant force, using area under a force-time
graph or calculation as a dot product.
Relate Work and change in Kinetic Energy through the Work-Kinetic Energy Theorem.
Describe the characteristics of conservative and non-conservative forces.
Determine the work done by conservative forces, including gravity and spring forces.
Calculate the work done by a varying force, using integration of a force function (area
under the curve).
Determine power as the time rate of work done, or from force and velocity.
State the general relation between force and potential energy, and explain why
potential energy is associated with conservative forces.
Determine potential energy of an object from a given force function F(x).
Determine force on an object from a given potential energy function U(x).
Calculate the potential energy of an object in a uniform gravitational field.
Calculate potential energy associated with springs.
Apply the Conservation of Energy in various systems, and understand the conditions
under which Energy is / is not conserved.
Determine the energy of a system when work is done by an external force.
7
Linear Momentum
Determine the center of mass of a system of particles.
Determine the center of mass of a continuous uniform mass by integration.
Define linear momentum, and calculate the momentum of an object or a system of
particles.
Describe velocity, momentum, and acceleration in terms of motion of the center of
mass.
Relate force and momentum, where force it the time rate of change of momentum.
Define impulse, and relate it to momentum through the impulse-momentum theorem.
Explain how momentum conservation is a consequence of Newton’s Third Law.
Identify conditions under which linear momentum is, or is not conserved.
Apply the law of conservation of linear momentum to “explosions” (ex: spring forces)
and collisions (both inelastic and elastic).
Analyze momentum conservation for collisions in 2-dimensions.
Analyze collisions in terms of energy and momentum conservation.
Analyze motion from a frame of reference moving at constant speed or constant
acceleration.
8
Rotational Motion
Define and calculate rotational quantities, including: angular position, angular speed,
angular acceleration, and relate each to its linear counterpart.
Describe the vector nature of angular quantities, and use the right-hand rule to
determine the direction of angular velocity.
Perform rotational kinematics calculations; relate the quantities to those of linear
motion.
Determine the rotational inertia for a system of particles and for particular shapes of
objects.
Compare the rotational inertia of various shaped objects, and how it is affected by
changes in the object’s dimensions.
State and apply the parallel-axis theorem.
Determine the magnitude and direction of torque on a rigid object.
Apply Newton’s Second Law to rotational motion, relating torque, moment of inertia,
and angular acceleration; and relate the rotational quantities to their linear counterparts.
Determine angular acceleration of an object, and the radial and tangential accelerations
of a given point on an object.
Determine the work done on a rotating object, and its kinetic energy.
Apply the conservation of energy to a rotating system.
Describe/explain the nature of rolling (without slipping) motion as translational and
rotational.
Determine forces involved in rolling motion, including rotational and translational
motion.
Calculate torque as a cross product.
Define and calculate angular momentum
Use the right-hand rule in torque and angular momentum determinations.
Analyze and perform calculations for the conservation of angular momentum,
understanding situations in which angular momentum is conserved.
Analyze motion between a moving object which collides with a rigid object that can
rotate.
Describe gyroscopic motion and its real-world applications.
9
Equilibrium
Determine the magnitude and direction of the torque associated with a given force on
an object
State and apply the conditions of translational and rotational equilibrium to analyze an
object with various coplanar forces applied.
10
Gravitation
State and apply Newton’s law of Universal Gravitation to determine the gravitational
force exerted.
Describe the effect of mass and distance on gravitational force.
Determine the gravitational field strength at a given point outside of a spherical mass.
Describe the gravitational force inside and outside of a spherical mass, and how the
field at the surface depends on the radius and density of the sphere.
For a circular orbit, relate velocity, period, and acceleration to the radius of orbit, and
derive mathematical expressions for velocity of an object in orbit.
Determine and relate the kinetic, potential, and total energy for an object in orbit.
State and apply Kepler’s three laws of planetary motion for an elliptical orbit.
Apply angular momentum conservation and energy conservation to relate the speed of
an object at the two extremes of an elliptical orbit.
Apply energy conservation in analyzing the motion of an object that is projected
straight up from a planet’s surface, or that is projected directly toward the planet from
far above the surface.
11
Oscillations
Determine the amplitude, period, and frequency of an object in simple harmonic
motion (SHM).
Relate period and frequency
Write an expression in the form of Asinωt or Acosωt for displacement in SHM, and for
velocity and acceleration.
Relate the acceleration, velocity, and displacement functions, and identify positions in
which the quantities are zero, maximum positive, or maximum negative, for SHM.
Recognize the form of the differential equation that shows SHM, and determine the
frequency and period of that motion.
From a graph of energy vs. time for SHM, identify points where the energy is kinetic or
potential; and understand that the total energy depends on the amplitude of the
oscillation.
Determine the kinetic, potential, and total energy of an oscillating system.
Calculate the maximum displacement or velocity of a particle that moves in SHM with
an initial position and velocity.
Describe the conditions under which a system will resonate in response to an external
force.
Analyze the oscillation of a mass on a spring, oscillating horizontally or vertically.
Determine the period of oscillation of a system of springs in series or parallel, or of
different lengths.
11
Oscillations
(continued)
Determine the period of a simple pendulum, the variables that affect it, and the
approximation used in the determination.
Analyze the motion of a torsional pendulum or physical pendulum to determine the
period of small oscillations.