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AP Course

AP Physics C: Mechanics

Updated for the AP Physics C: Mechanics framework effective fall 2024, with calculus-based derivations, labs, quizzes, and practice.

Build calculus-based mechanics with original derivations, experiments, quizzes, and practice sets.

Lessons
Scalars and VectorsDisplacement, Velocity, and AccelerationRepresenting MotionReference Frames and Relative MotionMotion in Two or Three DimensionsSystems and Center of MassForces and Free-Body DiagramsNewton’s Third LawNewton’s First LawNewton’s Second LawGravitational ForceKinetic and Static FrictionSpring ForcesResistive ForcesCircular MotionTranslational Kinetic EnergyWorkPotential EnergyConservation of EnergyPowerLinear MomentumChange in Momentum and ImpulseConservation of Linear MomentumElastic and Inelastic CollisionsRotational KinematicsConnecting Linear and Rotational MotionTorqueRotational InertiaRotational Equilibrium and Newton’s First Law in Rotational FormNewton’s Second Law in Rotational FormRotational Kinetic EnergyTorque and WorkAngular Momentum and Angular ImpulseConservation of Angular MomentumRollingMotion of Orbiting SatellitesDefining Simple Harmonic Motion (SHM)Frequency and Period of SHMRepresenting and Analyzing SHMEnergy of Simple Harmonic OscillatorsSimple and Physical Pendulums
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics C: Mechanics · Unit 4 · Topic 4.3

Conservation of Linear Momentum

Impulse integrals and system momentum describe collisions, center-of-mass motion, and changing-mass models.

1. Topic Lens

Conservation of Linear Momentum is studied through linear momentum. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\vec J=\int\vec F\,dt=\Delta\vec p\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Sum particle momenta to define total system momentum P.
  2. Internal force pairs cancel in the system sum under Newton's third law.
  3. Only net external force remains, so integrating it gives the system momentum change.
\[\vec F_{\text{ext}}=\frac{d\vec P_{\text{system}}}{dt}\]

3. Detailed Visual Model

Pixel diagram for Conservation of Linear MomentumOriginal schematic connecting Conservation of Linear Momentum to Linear Momentum.
Conservation of Linear Momentum: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

A 10 N force acts for 0.20 s in one direction. Find the impulse.

Answer: J=(10)(0.20)=2.0 N·s in the force direction.

Investigation idea: Use high-frame-rate video to reconstruct two-dimensional momentum vectors before and after a collision.

Common trap: Momentum conservation applies to a defined system with negligible external impulse, not automatically to each object.

Checkpoint · Topic 4.3

Explain how conservation of linear momentum supports or limits this conclusion: J=(10)(0.20)=2.0 N·s in the force direction.

Official curriculum reference: College Board AP Physics C: Mechanics course page. The explanation and worked example are independently written for this study site.