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AP® Physics C Mechanics
AP Physics C: Mechanics teaches calculus‑based kinematics, Newton’s laws, work‑energy, momentum, and rotation, emphasizing analytical problem solving and fundamental physical relationships and prepares students for the AP exam and future engineering studies.
90
Minutes
40
Questions
3/5
Passing Score
$98
Exam Cost
Who Should Take This
High‑school juniors and seniors who have completed pre‑calculus and are ready for college‑level physics benefit from this certification. It suits aspiring engineers, physicists, and science majors who need a rigorous, calculus‑driven foundation to excel on the AP exam and in subsequent STEM coursework.
What's Covered
1
All five units of the AP Physics C: Mechanics course framework (College Board, effective 2024-present): Unit 1 Kinematics
2
, Unit 2 Newton's Laws of Motion
3
, Unit 3 Work, Energy, and Power
4
, Unit 4 Systems of Particles and Linear Momentum
5
, Unit 5 Rotation
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
20 Activity Formats
Course Outline
64 learning goals
1
Unit 1: Kinematics
2 topics
Motion in One Dimension
- Define displacement, velocity, and acceleration as derivatives of position and velocity functions with respect to time and identify their SI units.
- Derive the kinematic equations for constant acceleration by integrating the acceleration function and apply them to solve one-dimensional motion problems.
- Determine velocity and position as functions of time by integrating non-constant acceleration functions expressed as polynomials or other elementary functions.
- Interpret position-time, velocity-time, and acceleration-time graphs, extracting velocity from slopes, displacement from areas under curves, and acceleration from curvature.
- Analyze free-fall problems with air resistance by setting up and solving first-order differential equations for velocity as a function of time.
Motion in Two Dimensions
- Resolve two-dimensional motion into independent horizontal and vertical components and apply vector addition to displacement, velocity, and acceleration.
- Analyze projectile motion by applying kinematic equations independently to horizontal and vertical components to determine range, maximum height, and time of flight.
- Describe relative motion between reference frames and apply Galilean velocity addition to solve problems involving objects observed from different inertial frames.
- Derive the parametric equations for the trajectory of a projectile launched at an angle and determine the launch conditions that maximize range on level ground.
2
Unit 2: Newton's Laws of Motion
3 topics
Forces and Free-Body Diagrams
- State Newton's three laws of motion and identify the fundamental contact and field forces including gravity, normal force, friction, tension, and spring force.
- Construct free-body diagrams for objects in static and dynamic situations, correctly identifying all forces and resolving them into components along chosen coordinate axes.
- Apply Hooke's law (F = -kx) to analyze the restoring force of ideal springs and determine the force as a function of displacement from equilibrium.
- Identify Newton's third law force pairs and explain why internal forces cannot change the momentum of a system while external forces can.
Applying Newton's Second Law
- Apply Newton's second law (F_net = ma) to determine the acceleration of single objects on horizontal and inclined surfaces with and without friction.
- Analyze connected multi-body systems such as Atwood machines, objects on pulleys, and blocks on surfaces to find acceleration and tension using simultaneous equations.
- Distinguish between static and kinetic friction, apply the friction models (f_s <= mu_s N, f_k = mu_k N), and determine threshold conditions for sliding on inclines.
- Set up and solve the differential equation of motion for objects experiencing velocity-dependent drag forces such as F = -bv and F = -cv^2.
- Determine the terminal velocity of an object experiencing linear or quadratic drag by setting net force equal to zero and solving for the steady-state velocity.
Circular Motion and Gravitation
- Derive the expression for centripetal acceleration (a_c = v^2/r = omega^2 r) and identify the forces providing centripetal acceleration in various circular motion scenarios.
- Apply Newton's second law to uniform circular motion problems including banked curves, conical pendulums, and vertical loops to determine required forces and critical speeds.
- Apply Newton's law of universal gravitation to calculate forces between masses and derive expressions for gravitational field strength as a function of distance.
- Analyze orbital motion by combining gravitational force with centripetal acceleration requirements to derive Kepler's third law for circular orbits.
- Design an experiment to measure the acceleration due to gravity using a simple pendulum and evaluate systematic and random sources of uncertainty in the measurement.
3
Unit 3: Work, Energy, and Power
3 topics
Work and the Work-Energy Theorem
- Define work as the line integral of force along a displacement path (W = integral F dot dr) and calculate work done by constant forces using the dot product.
- Calculate work done by variable forces including spring forces and position-dependent forces by evaluating definite integrals over the displacement.
- Apply the work-energy theorem (W_net = delta KE) to relate the total work done on an object to its change in translational kinetic energy.
- Interpret work graphically as the area under a force-displacement curve and use this to solve problems where forces vary with position.
Potential Energy and Conservation of Energy
- Distinguish conservative from non-conservative forces and explain how potential energy functions are defined only for conservative forces through integration.
- Derive gravitational potential energy (U = mgh near Earth's surface and U = -GMm/r for general separations) and elastic potential energy (U = (1/2)kx^2) from force expressions.
- Apply conservation of mechanical energy to solve problems involving gravitational and elastic potential energy transformations where only conservative forces do work.
- Analyze potential energy diagrams U(x) to identify equilibrium positions, turning points, and the nature of equilibrium (stable, unstable, neutral).
- Derive the relationship F(x) = -dU/dx and apply it to determine force from a potential energy function or construct U(x) from a given force expression.
- Calculate escape velocity from a gravitational field by applying conservation of energy with gravitational potential energy U = -GMm/r.
Power and Energy Dissipation
- Define power as the rate of energy transfer (P = dW/dt = F dot v) and calculate instantaneous and average power delivered to or by a system.
- Analyze energy dissipation by non-conservative forces such as friction and drag, accounting for the conversion of mechanical energy to thermal energy.
- Construct an energy bar chart or energy flow diagram for a complex system with multiple conservative and non-conservative forces, tracking all energy transformations.
4
Unit 4: Systems of Particles and Linear Momentum
3 topics
Center of Mass
- Define the center of mass of a system of particles and calculate its position using the mass-weighted average formula for discrete particle distributions.
- Calculate the center of mass of continuous mass distributions (rods, plates, semicircles) by evaluating integrals of position weighted by linear or areal mass density.
- Explain how the center of mass of an isolated system moves at constant velocity when no external forces act, even if internal forces cause individual parts to accelerate.
Impulse and Momentum
- Define linear momentum (p = mv) and state the impulse-momentum theorem as the integral of net force over time equaling the change in momentum of a system.
- Calculate impulse from variable force-time functions using integration and determine the resulting change in velocity of the object.
- Express Newton's second law in its general form (F_net = dp/dt) and apply it to systems where mass varies with time, such as rocket propulsion.
- Interpret force-time graphs to determine impulse and average force during collisions, and explain the physical significance of the impulse area.
Conservation of Momentum and Collisions
- State the conditions under which linear momentum is conserved and apply conservation of momentum to one-dimensional elastic and perfectly inelastic collisions.
- Solve two-dimensional collision problems using conservation of momentum in component form, determining final velocities and scattering angles.
- Compare elastic and inelastic collisions by calculating the kinetic energy before and after the collision and determining the energy converted to other forms.
- Analyze explosion and recoil problems using conservation of momentum to determine the velocities of fragments after separation.
- Design an experiment using a ballistic pendulum or air track to verify conservation of momentum and evaluate the elasticity of collisions from measured data.
5
Unit 5: Rotation
3 topics
Rotational Kinematics
- Define angular displacement, angular velocity, and angular acceleration as derivatives of angular position, and relate them to their translational counterparts via the radius.
- Apply the rotational kinematic equations for constant angular acceleration to calculate angular position, velocity, and acceleration as functions of time.
- Relate the tangential velocity, centripetal acceleration, and tangential acceleration of a point on a rotating rigid body to the angular quantities and radius.
Torque and Rotational Dynamics
- Define torque as the cross product of position and force vectors (tau = r x F) and calculate the torque about a specified axis for various force configurations.
- Calculate the moment of inertia of systems of discrete point masses about a given axis and apply the parallel-axis theorem to shift to offset axes.
- Derive the moment of inertia of continuous bodies (uniform rods, disks, cylinders, spheres) by evaluating the integral I = integral r^2 dm over the mass distribution.
- Apply Newton's second law for rotation (tau_net = I alpha) to calculate the angular acceleration of pulleys, wheels, and other rigid bodies subject to multiple torques.
- Analyze static equilibrium of rigid bodies by requiring that both the net force and net torque about any point equal zero, and solve for unknown forces.
- Solve combined translational and rotational dynamics problems where a rope or string connects a translating mass to a rotating pulley.
Rolling Motion and Angular Momentum
- Explain the rolling-without-slipping constraint (v_cm = R omega) and analyze how it couples translational and rotational motion on inclines and flat surfaces.
- Apply energy conservation including both translational and rotational kinetic energy to determine the speed of rolling objects at the bottom of inclines.
- Define angular momentum for rigid bodies (L = I omega) and for particles (L = r x p) and state the conditions under which angular momentum is conserved.
- Apply conservation of angular momentum to analyze systems where moment of inertia changes, including collapsing stars, spinning figure skaters, and rotational collisions.
- Derive the angular impulse-angular momentum theorem (integral tau dt = delta L) and apply it to problems involving impulsive torques.
- Design an experiment to measure the moment of inertia of a disk or ring using energy conservation on an inclined plane and compare the result to theoretical predictions.
- Construct an integrated argument demonstrating the analogy between translational and rotational quantities (force/torque, mass/moment, velocity/angular velocity, momentum/angular momentum).
Scope
Included Topics
- All five units of the AP Physics C: Mechanics course framework (College Board, effective 2024-present): Unit 1 Kinematics (12-18%), Unit 2 Newton's Laws of Motion (20-25%), Unit 3 Work, Energy, and Power (15-25%), Unit 4 Systems of Particles and Linear Momentum (10-16%), Unit 5 Rotation (14-20%).
- Kinematics: motion in one and two dimensions, displacement, velocity, and acceleration as derivatives and integrals of position and velocity functions, projectile motion, and relative motion.
- Newton's laws: forces including gravity, friction (static and kinetic), normal force, tension, and spring force; free-body diagrams; application of Newton's second law using differential equations; circular motion and centripetal acceleration.
- Work, energy, and power: work as the integral of force over displacement, kinetic energy and the work-energy theorem, potential energy (gravitational and elastic), conservation of mechanical energy, non-conservative forces, and power as the rate of energy transfer.
- Systems of particles and linear momentum: center of mass and its motion, impulse-momentum theorem, conservation of linear momentum, elastic and inelastic collisions in one and two dimensions.
- Rotation: rotational kinematics using angular displacement, velocity, and acceleration; torque; moment of inertia and parallel-axis theorem; rotational dynamics (Newton's second law for rotation); rolling motion; angular momentum and its conservation.
- Calculus-based problem solving including differentiation, integration, and differential equations applied to physical systems throughout all units.
- Experimental skills including design, data collection, graphical analysis, linearization techniques, and uncertainty estimation.
Not Covered
- Electricity, magnetism, optics, thermodynamics, and modern physics topics covered in AP Physics C: Electricity and Magnetism or AP Physics 2.
- Advanced mathematical methods beyond single-variable calculus, including partial differential equations, linear algebra, and vector calculus beyond dot and cross products.
- Fluid mechanics, wave mechanics, and sound beyond what is required for mechanical systems.
- Lagrangian and Hamiltonian mechanics, non-inertial reference frame analysis, and graduate-level analytical mechanics.
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