AP Physics C: Mechanics study plan

Derive the constant-acceleration kinematics equations from a = dv/dt and v = dx/dt, then use them to solve for unknown displacement, velocity, time, or acceleration in one-dimensional problems.

Construct and interpret position-, velocity-, and acceleration-versus-time graphs, extracting slope and signed area to translate between the three quantities, including turning points and sign changes.

Resolve projectile motion into independent horizontal and vertical equations and solve for range, apex height, and time of flight, including launches from a nonzero height and from a moving platform.

Integrate a time-dependent acceleration a(t) analytically to obtain v(t) and x(t) for non-constant acceleration, applying initial conditions correctly and checking units of each term.

Draw complete free-body diagrams that name every force, its source object, and its direction, for single bodies and for systems of two or three connected bodies.

Apply Newton's second law in component form to blocks on inclines, Atwood-style pulley systems, and stacked masses, solving symbolically before substituting numbers.

Distinguish static from kinetic friction, decide whether an object slips by testing the static-friction limit, and compute the friction force from the normal force and coefficient in each regime.

Set up uniform circular motion problems by identifying the specific physical force that supplies the centripetal acceleration in each geometry, including horizontal circles, banked curves, and conical pendulums.

Model linear drag by writing m(dv/dt) = mg − bv, solving the differential equation for v(t), and identifying terminal speed from the steady-state condition dv/dt = 0.

Analyze motion under a Hooke's-law restoring force qualitatively and quantitatively, including how a constant external force shifts the equilibrium position without changing the oscillation frequency.

Apply Newton's third law to identify action-reaction pairs and explain why such a pair can never cancel on a single body.

Compute gravitational force and field strength for point masses and spherical bodies, and combine Newton's law of gravitation with the circular-orbit condition to relate orbital speed, radius, and period.

Compute work done by constant and variable forces using W = ∫F·dr, including work by springs, gravity, friction, and forces applied at an angle to the displacement.

Apply the work-energy theorem to relate net work to the change in kinetic energy, and use it to find speeds and displacements that are awkward to obtain from Newton's laws alone.

Apply conservation of mechanical energy with and without non-conservative forces, computing the energy dissipated by friction from the change in total mechanical energy.

Calculate instantaneous and average power from P = dW/dt and P = F·v, and interpret potential-energy curves to locate equilibrium points and classify each as stable, unstable, or neutral.

Apply the impulse-momentum theorem, including force-time graph areas, to determine changes in momentum for constant and time-varying forces.

Use conservation of linear momentum in one and two dimensions, writing separate component equations for explosions and off-axis collisions.

Classify collisions as elastic or perfectly inelastic by accounting for kinetic energy, then solve for unknown final velocities in each case and check the result for physical plausibility.

Locate the center of mass of continuous bodies by integration and describe how the center of mass of a system moves under external forces.

Analyze variable-mass systems such as a rocket by applying momentum conservation to an ejected mass element and deriving the resulting thrust relation.

Compute torque about a chosen axis using τ = r × F, including the sign convention and the perpendicular-distance interpretation of the lever arm.

Calculate moments of inertia by integration for rods, disks, and hoops, and apply the parallel-axis theorem to relocate the axis of rotation.

Apply the rotational form of Newton's second law, Στ = Iα, to pulleys with mass, hinged rods, and multi-body systems that combine translation and rotation.

Analyze rolling without slipping by linking translational and rotational kinematics (v = ωR, a = αR) and identifying which friction force is responsible for the constraint.

Compute rotational kinetic energy and the work done by a torque, then apply the work-energy theorem to rotating and rolling bodies.

Apply conservation of angular momentum to systems whose moment of inertia changes, such as a spinning skater or a collapsing rotating cloud, and to collisions that impart spin.

Solve rolling problems that include both translation and rotation, distinguishing rolling with slipping from rolling without slipping and accounting for energy dissipated while slipping.

Calculate angular impulse from ∫τ dt and relate it to the change in angular momentum for a rigid body.

Write and solve the differential equation for simple harmonic motion, d²x/dt² = −ω²x, and extract amplitude, angular frequency, and phase constant from stated initial conditions.

Relate period and frequency to mass and spring constant for a mass-spring oscillator and to length for a small-angle pendulum, stating the limits of the small-angle approximation.

Convert among position, velocity, and acceleration in simple harmonic motion using their phase relationships, and track the exchange between kinetic and potential energy over a full cycle.

Identify simple harmonic motion in displaced-equilibrium systems such as a floating block or a cylinder rolling in a curved bowl, and determine the effective angular frequency for each.

Re-solve the previously missed problems from weeks 1 through 7 to close out the error log and confirm that each concept tag has been retired.