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AP Physics C: Mechanics

One lesson for each of the course’s 41 topics, in the order the course teaches them. The first 3 units are free for everyone; the rest come with the AP Physics C: Mechanics plan. Read a lesson, try its quick checks, then practice the topic with exam-style questions.

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Kinematics

Unit 1Free5 lessons
  1. 1.1Scalars and VectorsTell scalars from vectors, write any vector in unit-vector notation or as magnitude and direction, and add vectors by components.
  2. 1.2Displacement, Velocity, and AccelerationFind displacement, average velocity and average acceleration, then get instantaneous velocity and acceleration by differentiating and integrating.
  3. 1.3Representing MotionMove between motion diagrams, graphs, equations and words, read slopes and areas off motion graphs, and use the constant-acceleration equations.
  4. 1.4Reference Frames and Relative MotionConvert positions and velocities between reference frames by adding or subtracting vectors, and explain why inertial observers agree on acceleration.
  5. 1.5Motion in Two or Three DimensionsSplit two-dimensional motion into independent components, solve projectile problems with the 1D equations, and handle nonuniform acceleration by calculus.

Force and Translational Dynamics

Unit 2Free10 lessons
  1. 2.1Systems and Center of MassChoose a system, decide when it can be modeled as one object, and locate its center of mass for particles, symmetric shapes and nonuniform rods.
  2. 2.2Forces and Free-Body DiagramsIdentify every force on an object by naming what exerts it, draw a free-body diagram the way the AP exam requires, and turn it into component equations.
  3. 2.3Newton’s Third LawPair every force with its third-law partner, explain why internal forces can't move a system's center of mass, and find the tension in ideal and massive ropes.
  4. 2.4Newton’s First LawFind a net force by vector addition, use zero net force to solve equilibrium problems, and tell which frames of reference Newton's laws hold in.
  5. 2.5Newton’s Second LawUse a = ΣF/m to find accelerations and unknown forces, including connected objects and time-varying forces, and design an experiment that tests the law.
  6. 2.6Gravitational ForceUse Newton's law of gravitation and the field g = GM/r², tell true weight from apparent weight, and find gravity inside and outside a uniform sphere.
  7. 2.7Kinetic and Static FrictionFind the normal force, decide whether friction is static or kinetic, get its size and direction, and use it in Newton's second law, including stacked blocks.
  8. 2.8Spring ForcesApply Hooke's law with the right direction, read a spring constant off data, tell ideal from nonideal springs, and combine springs in series or parallel.
  9. 2.9Resistive ForcesSet up Newton's second law with a drag force -kv, solve it by separating variables, find terminal velocity, and sketch the exponential v(t), a(t) and x(t).
  10. 2.10Circular MotionFind centripetal and tangential acceleration, identify which forces supply the centripetal part (loops, banked curves, conical pendulums), and use Kepler's third law.

Work, Energy, and Power

Unit 3Free5 lessons
  1. 3.1Translational Kinetic EnergyCompute an object's kinetic energy from its mass and speed, predict how it scales, and explain why it is a scalar that depends on the observer's frame.
  2. 3.2WorkCalculate the work done by constant and variable forces with dot products, integrals and graph areas, and use the work-energy theorem to find speeds.
  3. 3.3Potential EnergyDefine potential energy for a system, compute it for springs and gravity, find conservative forces from the slope of U(x), and locate stable and unstable equilibria.
  4. 3.4Conservation of EnergyChoose a system, decide which energies it holds and whether its mechanical energy is constant, and use energy conservation to find speeds, heights and stopping points.
  5. 3.5PowerCalculate average and instantaneous power, use P = F·v for forces on moving objects, and predict how power scales with speed and force.

Linear Momentum

Unit 4With the plan4 lessons
  1. 4.1Linear MomentumCompute an object's momentum as a vector, compare it with kinetic energy, and decide when a collision or explosion model applies to an interaction.
  2. 4.2Change in Momentum and ImpulseUse net force as the rate of change of momentum, find impulse from a force-time integral or graph area, and apply the impulse-momentum theorem.
  3. 4.3Conservation of Linear MomentumChoose a system whose total momentum is constant, use the center-of-mass velocity, and solve for velocities right before and after collisions and explosions.
  4. 4.4Elastic and Inelastic CollisionsClassify a collision as elastic, inelastic or perfectly inelastic from kinetic energy, and combine momentum with energy to solve two-stage collision problems.

Torque and Rotational Dynamics

Unit 5With the plan6 lessons
  1. 5.1Rotational KinematicsDescribe a spinning rigid system with angular position, velocity and acceleration, solve constant-α problems, and read rotation graphs.
  2. 5.2Connecting Linear and Rotational MotionTurn angular displacement, velocity and acceleration into the distance, speed and tangential acceleration of any point on a rotating rigid system, and back.
  3. 5.3TorqueFind the torque a force exerts about a pivot using the perpendicular component, the lever arm, or the cross product, and draw force diagrams for rigid systems.
  4. 5.4Rotational InertiaCalculate rotational inertia from I = Σmr² and I = ∫r² dm, derive it for rods, hoops and disks, and move between axes with the parallel axis theorem.
  5. 5.5Rotational Equilibrium and Newton’s First Law in Rotational FormDecide when a rigid object's angular velocity stays constant, and use zero net torque with zero net force to solve beams, hinges and balances.
  6. 5.6Newton’s Second Law in Rotational FormUse net torque = Iα to find angular acceleration, pair it with F = ma for pulleys and unwinding spools, and measure rotational inertia from a graph.

Energy and Momentum of Rotating Systems

Unit 6With the plan6 lessons
  1. 6.1Rotational Kinetic EnergyFind the kinetic energy of a spinning rigid system with ½Iω², split total kinetic energy into translation and rotation, and use it in energy problems.
  2. 6.2Torque and WorkCalculate the work a torque does as an object turns, from τΔθ, an integral, or the area under a torque-angle graph, and link it to rotational kinetic energy.
  3. 6.3Angular Momentum and Angular ImpulseFind the angular momentum of a spinning rigid system and of an object moving past a point, and use angular impulse and torque graphs to find how it changes.
  4. 6.4Conservation of Angular MomentumDecide when a system's angular momentum stays constant, and use that to solve spin-up, coupling, and pivoted-collision problems.
  5. 6.5RollingLink a rolling object's translation and rotation, split its kinetic energy, and decide when friction does or doesn't remove energy, with or without slipping.
  6. 6.6Motion of Orbiting SatellitesUse energy and angular momentum conservation to find speeds, energies, and escape speed for satellites in circular and elliptical orbits.

Oscillations

Unit 7With the plan5 lessons
  1. 7.1Defining Simple Harmonic Motion (SHM)Tell simple harmonic motion apart from other repeating motion by its force law, find the equilibrium position, and show a system obeys a = -ω²x.
  2. 7.2Frequency and Period of SHMRelate period, frequency and angular frequency, use T = 2π√(m/k) and T = 2π√(ℓ/g), and predict how a period changes when mass, stiffness, length or g change.
  3. 7.3Representing and Analyzing SHMSolve the SHM differential equation with x = A cos(ωt + φ), get velocity and acceleration from it, and read extrema and zeros off equations and graphs.
  4. 7.4Energy of Simple Harmonic OscillatorsTrack kinetic and potential energy through an SHM cycle, use E = ½kA² to find speeds and amplitudes, and predict what changing the amplitude does.
  5. 7.5Simple and Physical PendulumsDerive the period of a physical pendulum from rotational dynamics and the small-angle approximation, apply T = 2π√(I/mgd), and use pendulum data to find g.

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