What do I need to know for AP Physics 1 Topic 4.3?
Topic 4.3 Conservation of Linear Momentum: Linear momentum of a system remains constant when the net external impulse on that system is zero or negligible during the interval of interest.
- Choose an appropriate system, distinguish internal from external forces, write vector momentum before and after interactions, and justify when conservation applies.
- Practice target: 42 original MCQs and 4 original FRQs for this exact topic.
- Course alignment: current AP Physics 1 framework for the 2026–27 school year and May 2027 exam.
Conservation of Linear Momentum
Linear momentum of a system remains constant when the net external impulse on that system is zero or negligible during the interval of interest.
Linear momentum of a system remains constant when the net external impulse on that system is zero or negligible during the interval of interest.
What you need to understand before calculating
Choose an appropriate system, distinguish internal from external forces, write vector momentum before and after interactions, and justify when conservation applies.
This page explains the key vocabulary where it is used. Internal links are for deeper study, not a requirement for understanding the sentence you are reading.
Key terms explained on this page
These terms are defined here before they are used in the calculations. A deeper internal link is optional where one exists; the reader does not need to leave this page to understand the current explanation.
Isolated system
For momentum analysis, an isolated system is one whose net external impulse is zero or negligible during the interval of interest.
Real example: Two carts colliding on a nearly frictionless track can be treated as isolated during the short collision.
Deeper lesson: Isolated systemInternal versus external force
Forces between objects inside the system are internal and cancel in the total-system momentum change; outside interactions are external.
Real example: The forces two colliding carts exert on each other are internal when both carts are inside the system.
Deeper lesson: Internal versus external forceTranslate the physics into a representation
AP Physics 1 frequently asks you to move between words, diagrams, graphs and equations. Use this representation as a reasoning anchor, then explain what each labeled quantity means in this topic.
Core concepts with real physical examples
| Concept | Meaning | Real example 1 | Real example 2 |
|---|---|---|---|
| Isolated-system model | Momentum is conserved when external impulse is zero/negligible. | Two carts collide on a nearly frictionless track. | Two skaters push apart while horizontal external impulse is negligible. |
| Internal forces | Forces between objects inside the system cannot change total system momentum by themselves. | Collision forces between two carts are internal to the two-cart system. | Explosion forces among fragments are internal if all fragments are included. |
| External impulse | External forces can change total system momentum. | Friction from the floor changes the momentum of a sliding-box-only system. | A wall exerts external impulse on a ball-only system during a bounce. |
| Vector conservation | Momentum conservation must preserve direction/sign or components. | In one dimension, east can be positive and west negative. | In two dimensions, conserve x and y momentum separately. |
| Recoil/explosion | Objects can gain opposite momenta while total remains fixed. | A stationary firework explodes into fragments with vector-sum momentum zero. | A person jumps from a stationary boat and the boat recoils. |
Equations and relationships: variables, units, conditions, examples
| Relationship | Variables & SI units | When to use it | Real example |
|---|---|---|---|
| Σp⃗_i = Σp⃗_f | momentum: kg·m/sAll symbols used here: p and P_system = momentum (kg·m/s); m or M = object/total system mass (kg); v = object velocity (m/s); v_cm = center-of-mass velocity (m/s); J_ext = external impulse (N·s); subscripts i/f = initial/final; object subscripts identify members of the system. | Isolated-system momentum conservation. | For two carts, m1v1i+m2v2i=m1v1f+m2v2f. |
| ΔP⃗_system = J⃗_ext | P: kg·m/s; J_ext: N·sAll symbols used here: p and P_system = momentum (kg·m/s); m or M = object/total system mass (kg); v = object velocity (m/s); v_cm = center-of-mass velocity (m/s); J_ext = external impulse (N·s); subscripts i/f = initial/final; object subscripts identify members of the system. | General statement including external impulse. | If external impulse is zero, ΔP_system=0. |
| Σp_x conserved; Σp_y conserved | component momentum: kg·m/sAll symbols used here: p and P_system = momentum (kg·m/s); m or M = object/total system mass (kg); v = object velocity (m/s); v_cm = center-of-mass velocity (m/s); J_ext = external impulse (N·s); subscripts i/f = initial/final; object subscripts identify members of the system. | Two-dimensional isolated interactions. | Explosion fragments require separate x and y balances. |
Worked physical reasoning
Cart collision
Situation: Two carts collide on a low-friction track.
Physics: Choose both carts as the system; interaction forces are internal and momentum is approximately conserved.
Person and boat
Situation: A person walks/jumps one way from a floating boat.
Physics: With negligible horizontal external impulse, the boat gains opposite momentum.
Ball and wall
Situation: A ball bounces from a wall.
Physics: Ball-only momentum is not conserved because the wall provides external impulse; ball+wall+Earth can be a larger system.
AP scope and boundary
Always justify conservation using the system and net external impulse, not merely by saying “it is a collision.”
Common mistakes—and the corrected physics
| Incorrect idea | Correct understanding |
|---|---|
| Momentum is conserved for each object in a collision. | It is the total momentum of an isolated system that is conserved. |
| Internal forces must be zero for conservation. | Internal forces can be large; their paired effects do not change total system momentum. |
| Momentum conservation requires kinetic energy conservation. | Momentum can be conserved in inelastic collisions where K decreases. |
Master this topic beyond a formula list
This checkpoint combines the current AP Physics 1 content boundary with representation, experiment/data reasoning, real situations and cross-topic transfer.
2026–27 mastery checklist
- Apply momentum conservation when net external impulse on the selected system is zero or negligible over the interaction interval.
- Distinguish internal action-reaction forces from external forces using the system boundary.
- Relate conserved system momentum to constant center-of-mass velocity.
- Solve quantitative one-dimensional conservation problems and use vector/semicontitative reasoning for two-dimensional cases within current scope.
Must-not-miss relationship
If J_ext ≈ 0, P_i = P_f. Also P = Mv_cm, so the center-of-mass velocity of an isolated constant-mass system remains constant.
Symbols & SI units used on this topic: p and P_system = momentum (kg·m/s); m or M = object/total system mass (kg); v = object velocity (m/s); v_cm = center-of-mass velocity (m/s); J_ext = external impulse (N·s); subscripts i/f = initial/final; object subscripts identify members of the system.
Two anchor situations
Two carts collide on a low-friction track: their individual momenta change but the pair’s total momentum is approximately conserved.
A person jumps from a stationary boat; person and boat acquire opposite momenta while the system center of mass follows the external-force motion.
Diagram / graph / equation / claim
Build a before/after momentum-vector diagram and a system-boundary diagram before writing the conservation equation.
How to test the physics
Use two-carts collision data to compare total momentum before/after with experimental uncertainty and decide whether conservation is supported.
Current AP Physics 1 treatment is fully quantitative/qualitative in one dimension and semiquantitative in two dimensions; simultaneous-equation solving for full 2D unknowns is not required.
Use momentum conservation together with energy classification to distinguish elastic and inelastic collisions.
Connect to Topic 4.4 collision classificationGo beyond memorizing the equation
This topic now combines model selection, physical intuition, a worked transfer problem, graph/data analysis, answer verification, and the four current AP free-response reasoning modes.
Choose the model before calculating
Define a system for which external impulse is zero or negligible over the interaction interval, then write total initial momentum equal to total final momentum by component.
Why the physics works
Internal interaction forces exchange momentum between system members but cancel in the system total, leaving only external impulse able to change total momentum.
Solve this before opening the solution
A 1 kg cart moving right at 6 m/s sticks to a 2 kg cart initially at rest. Find their common final velocity.
Reveal complete reasoning
Solution: Initial momentum=6 kg·m/s. Final mass=3 kg, so v_f=6/3=2 m/s right.
Physics check: The final speed lies between the initial cart speeds, which is reasonable for a sticking collision with one cart initially at rest.
What should you plot?
Across repeated isolated interactions, plot total final momentum versus total initial momentum.
What does the graph mean?
Data should cluster near a line of slope 1 through the origin.
How this exact topic can appear in each current FRQ mode
If J_ext ≈ 0, P_i = P_f. Also P = Mv_cm, so the center-of-mass velocity of an isolated constant-mass system remains constant.
Build a before/after momentum-vector diagram and a system-boundary diagram before writing the conservation equation.
Use two-carts collision data to compare total momentum before/after with experimental uncertainty and decide whether conservation is supported.
Use momentum conservation together with energy classification to distinguish elastic and inelastic collisions.
State why external impulse is negligible, conserve momentum by component, and do not assume kinetic energy is also conserved.
Continue with the exact topic question banks
Use the focused banks for skill practice. The five full model papers are reserved for whole-exam simulation.
Topic 4.3 quick review
What is the definition I should know first?
Linear momentum of a system remains constant when the net external impulse on that system is zero or negligible during the interval of interest.
What should I identify before using an equation?
Choose an appropriate system, distinguish internal from external forces, write vector momentum before and after interactions, and justify when conservation applies.
Where do I practice this exact topic?
Use the 42-MCQ and 4-FRQ Topic 4.3 banks linked directly on this page.
Where Topic 4.3 appears in AP-style released work
These are original topic summaries and alignment notes, not reproduced College Board question text. One released FRQ can legitimately connect to several topics.
Colliding disks, momentum vectors and center of mass
Links system center of mass, vector momentum and graphical representation.
Translation Between RepresentationsMoving cart, dropped block and collision energy
Combines momentum/collision reasoning with translational kinetic-energy accounting.
Mathematical RoutinesDisk-block collision, impulse and momentum conservation
Connects impulse, momentum and collision reasoning.
Qualitative / Quantitative TranslationRecent public FRQs are the safest format reference. Older released questions can still contain excellent physics, but the course and exam changed; use the atlas alignment notes before treating a legacy question as a current-format simulation.