β United States Physics C: Mechanics
United States Β· College BoardSyllabus
Physics C: Mechanics syllabus, dot point by dot point
Every dot point in the United States Physics C: Mechanicssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Unit 1: Kinematics
Module overview β- How are velocity and acceleration defined as derivatives of position, and how do we recover motion by integration when the acceleration is known?Topic 1.2 Displacement, Velocity, and Acceleration: define velocity and acceleration as the time derivatives of position and velocity, integrate to recover velocity and position, and apply the constant-acceleration kinematic equations.11 min answer β
- How do position, velocity and acceleration depend on the reference frame, and how do we transform motion between frames that move at constant velocity relative to one another?Topic 1.4 Reference Frames and Relative Motion: define inertial reference frames, transform velocities between frames using vector addition, and recognize that acceleration is the same in all inertial frames.10 min answer β
- How do position, velocity and acceleration graphs relate to one another through slopes and areas, and how do we read calculus information directly off a motion graph?Topic 1.3 Representing Motion: relate position, velocity and acceleration graphs through slopes (derivatives) and areas (integrals), and translate between graphical, equation and verbal descriptions of motion.10 min answer β
- How do we distinguish scalar from vector quantities, and how do we add, resolve and manipulate vectors in the calculus-based mechanics of AP Physics C?Topic 1.1 Scalars and Vectors: describe scalar and vector quantities by magnitude and direction, resolve a vector into perpendicular components, and add vectors by components and graphically.10 min answer β
- How do we treat motion in two dimensions as two independent one-dimensional problems, and how does calculus describe projectile motion and general planar motion?Topic 1.5 Vectors and Motion in Two Dimensions: analyze two-dimensional motion by resolving into independent perpendicular components, apply this to projectile motion, and use vector calculus for general planar motion.11 min answer β
Unit 2: Force and Translational Dynamics
Module overview β- Why does uniform circular motion require a net inward force, and how do we find the centripetal acceleration and the force that supplies it?Topic 2.10 Circular Motion: relate centripetal acceleration to speed and radius, identify the real force that supplies the centripetal force, and apply Newton's second law to circular motion including vertical circles.11 min answer β
- How do we represent the forces acting on an object with a free-body diagram, and how do we resolve those forces to set up the equations of motion?Topic 2.2 Forces and Free-Body Diagrams: identify the forces acting on a chosen object, represent them on a free-body diagram, and resolve them into components on chosen axes to find the net force.10 min answer β
- How does Newton's law of universal gravitation describe the attraction between masses, and how does it give the gravitational field and weight near a planet?Topic 2.6 Gravitational Force: apply Newton's law of universal gravitation, define the gravitational field strength, relate it to weight, and treat gravity inside and outside a spherical mass.11 min answer β
- How do static and kinetic friction differ, and how do we use the friction models to decide whether motion starts and to find the acceleration once it does?Topic 2.7 Kinetic and Static Friction: model kinetic friction as proportional to the normal force, treat static friction as adjustable up to a maximum, and apply both to decide whether and how an object slides.10 min answer β
- What does it mean for an object to be in translational equilibrium, and how do we use the condition of zero net force to solve for unknown forces?Topic 2.4 Newton's First Law: state the law of inertia, define translational equilibrium as zero net force, and apply the equilibrium conditions to find unknown forces.10 min answer β
- How does the net force on an object determine its acceleration, and how do we apply Newton's second law axis by axis and to connected systems?Topic 2.5 Newton's Second Law: relate net force, mass and acceleration through the vector equation, apply it component by component, and extend it to connected systems and the general form with momentum.11 min answer β
- Why do forces always come in equal and opposite pairs acting on different objects, and how does this constrain interactions and underpin momentum conservation?Topic 2.3 Newton's Third Law: state that forces arise in equal-and-opposite pairs on different objects, identify the members of a third-law pair, and use this to analyze interacting systems.10 min answer β
- How do velocity-dependent resistive forces such as air resistance change motion, and how do we use calculus to find terminal velocity and the approach to it?Topic 2.9 Resistive Forces: model a velocity-dependent resistive force, set up and solve the equation of motion for fall with drag, and determine the terminal velocity and the exponential approach to it.11 min answer β
- How does an ideal spring exert a restoring force proportional to its displacement, and how does this linear force law set up oscillation and elastic energy?Topic 2.8 Spring Forces: model the ideal spring with Hooke's law as a linear restoring force, combine springs in series and parallel, and connect the force law to elastic potential energy by integration.10 min answer β
- How do we define a system and locate its center of mass, and why does only the net external force govern the motion of the center of mass?Topic 2.1 Systems and Center of Mass: define a system, locate the center of mass by a mass-weighted average (including by integration for continuous bodies), and apply that only external forces accelerate the center of mass.11 min answer β
Unit 3: Work, Energy, and Power
Module overview β- How does conservation of mechanical energy let us solve problems, and how do we account for energy dissipated by non-conservative forces?Topic 3.4 Conservation of Energy: apply conservation of mechanical energy for conservative systems, and extend the energy balance to include the work done by non-conservative forces.11 min answer β
- How is potential energy defined for conservative forces, and how do we move between a force and its potential energy by integration and differentiation?Topic 3.3 Potential Energy: define potential energy for conservative forces, relate force and potential energy by , and use gravitational and elastic potential energy, including the general gravitational form.11 min answer β
- What is power as the rate of energy transfer, and how do we compute average and instantaneous power from work, force and velocity?Topic 3.5 Power: define power as the rate of energy transfer, distinguish average from instantaneous power, and compute it from and .10 min answer β
- What is the kinetic energy of a moving object, and how does it connect to the work done on the object through the work-energy theorem?Topic 3.1 Translational Kinetic Energy: define translational kinetic energy, recognize it as a scalar that depends on the square of speed, and connect it to net work through the work-energy theorem.10 min answer β
- How is work defined for constant and variable forces, and how do we compute it as a dot product and as an integral of force over displacement?Topic 3.2 Work: define work as the dot product of force and displacement, compute the work done by a variable force as an integral, and interpret work as the area under a force-position graph.11 min answer β
Unit 4: Linear Momentum
Module overview β- How does an impulse change an object's momentum, and how do we compute impulse as the integral of force over time and as the area under a force-time graph?Topic 4.2 Change in Momentum and Impulse: define impulse as the integral of force over time, relate it to the change in momentum, and interpret the force-time graph and the average force.11 min answer β
- How do elastic, inelastic and perfectly inelastic collisions differ, and how do we use momentum and energy conservation to analyze each?Topic 4.4 Collisions: classify collisions as elastic, inelastic or perfectly inelastic, apply momentum conservation to all and kinetic-energy conservation to elastic collisions, in one and two dimensions.11 min answer β
- When is the total momentum of a system conserved, and how do we use conservation of momentum to analyze interactions such as explosions and recoil?Topic 4.3 Conservation of Linear Momentum: state that the total momentum of an isolated system is conserved, and apply it to recoil, explosions and interactions in one and two dimensions.11 min answer β
- What is linear momentum as a vector, and how does it relate to a system's mass and velocity and to Newton's second law?Topic 4.1 Linear Momentum: define linear momentum as the product of mass and velocity, treat it as a vector, and relate the net force to its rate of change.10 min answer β
Unit 5: Torque and Rotational Dynamics
Module overview β- How are linear and angular quantities related for a point on a rotating body, and how do tangential and centripetal accelerations arise?Topic 5.2 Connecting Linear and Rotational Motion: relate arc length, tangential velocity and tangential acceleration to the angular quantities through the radius, and distinguish tangential from centripetal acceleration.10 min answer β
- How does the net torque on a rigid body produce angular acceleration, and how do we apply the rotational form of Newton's second law to combined translational and rotational problems?Topic 5.6 Newton's Second Law in Rotational Form: relate net torque, rotational inertia and angular acceleration through , and apply it to pulleys and combined translational-rotational systems.11 min answer β
- What does it mean for a rigid body to be in rotational equilibrium, and how do we use zero net force and zero net torque to solve statics problems?Topic 5.5 Rotational Equilibrium and Newton's First Law: state the two conditions for static equilibrium (zero net force and zero net torque) and apply them to find unknown forces on rigid bodies.11 min answer β
- What is rotational inertia, and how do we compute it by summation, by integration for continuous bodies, and by the parallel-axis theorem?Topic 5.4 Rotational Inertia: define rotational inertia as the mass-weighted sum of , compute it by integration for continuous bodies, and apply the parallel-axis theorem.11 min answer β
- How do angular position, velocity and acceleration describe rotation, and how does calculus link them just as it does for linear motion?Topic 5.1 Rotational Kinematics: define angular position, velocity and acceleration as derivatives, apply the constant-angular-acceleration equations, and use integration for variable angular acceleration.10 min answer β
- What is torque as the rotational effect of a force, and how do the lever arm and the cross product determine its magnitude and sense?Topic 5.3 Torque: define torque as the product of force and lever arm, compute it as and as a cross product, and combine torques about an axis.10 min answer β
Unit 6: Energy and Momentum of Rotating Systems
Module overview β- What is angular momentum, and how does an angular impulse from a torque change it, both for rigid bodies and for particles moving in a straight line?Topic 6.3 Angular Momentum and Angular Impulse: define angular momentum for rigid bodies and particles, relate net torque to its rate of change, and use the angular impulse-momentum theorem.11 min answer β
- When is angular momentum conserved, and how do we use its conservation to analyze a spinning system whose rotational inertia changes or that is struck by a moving object?Topic 6.4 Conservation of Angular Momentum: state that angular momentum is conserved when the net external torque is zero, and apply it to changing rotational inertia and rotational collisions.11 min answer β
- How does gravity provide the centripetal force for orbits, and how do energy and angular momentum conservation describe circular and elliptical satellite motion?Topic 6.6 Motion of Orbiting Satellites: derive the speed and period of a circular orbit, find the orbital energy, and apply conservation of energy and angular momentum to elliptical orbits and Kepler's laws.11 min answer β
- What is the rolling-without-slipping condition, and how do we combine it with energy and force methods to analyze rolling bodies?Topic 6.5 Rolling: state the rolling-without-slipping constraints on velocity and acceleration, analyze the role of friction in rolling, and apply energy and dynamics methods to rolling bodies.11 min answer β
- What is the kinetic energy of a rotating body, and how do translational and rotational kinetic energy combine for a body that both moves and spins?Topic 6.1 Rotational Kinetic Energy: define rotational kinetic energy as , combine it with translational kinetic energy for a moving, spinning body, and use it in energy conservation.10 min answer β
- How does a torque do work as a body rotates, and how do the rotational work-energy theorem and rotational power parallel their translational forms?Topic 6.2 Torque and Work: compute the work done by a torque as the integral of torque over angle, apply the rotational work-energy theorem, and define rotational power as .10 min answer β
Unit 7: Oscillations
Module overview β- What defines simple harmonic motion, and why does a linear restoring force lead to the differential equation whose solution is sinusoidal?Topic 7.1 Defining Simple Harmonic Motion: identify simple harmonic motion as arising from a linear restoring force, derive the defining differential equation, and recognize its sinusoidal solution.10 min answer β
- How does energy move between kinetic and potential forms in an oscillator, and how does conservation of energy fix the speed at any displacement?Topic 7.4 Energy of Simple Harmonic Oscillators: express the kinetic, potential and total energy of an oscillator, apply conservation of energy to relate speed and displacement, and find the speed at any position.10 min answer β
- How are frequency, period and angular frequency related, and how do they depend on the physical properties of the mass-spring and pendulum oscillators?Topic 7.2 Frequency and Period of SHM: relate period, frequency and angular frequency, and determine them for the mass-spring system and the simple pendulum from the system properties.10 min answer β
- How do the sinusoidal expressions for position, velocity and acceleration describe an oscillator, and how do we extract amplitude, phase and the maxima from them?Topic 7.3 Representing and Analyzing SHM: write the sinusoidal position, velocity and acceleration of an oscillator, relate their amplitudes and phases, and read the motion from graphs and initial conditions.11 min answer β
- How do the simple and physical pendulums undergo simple harmonic motion at small angles, and how do we derive their periods using rotational dynamics?Topic 7.5 Simple and Physical Pendulums: derive the small-angle period of the simple pendulum and the physical pendulum using the rotational form of Newton's second law and the small-angle approximation.11 min answer β