Conservation of linear momentum says the total momentum p⃗ of a closed system (sum of all m_i v⃗_i) stays constant when no net external force acts on it. Mathematically: ∑p⃗_i = constant, and v⃗_cm = (∑m_i v⃗_i)/(∑m_i). That means internal forces change individual momenta but their vector sum doesn’t—impulses between objects are equal and opposite (Newton’s 3rd law), so J⃗ = Δp⃗ for the system only if external impulse is zero. On the AP exam you’ll use this to solve 1- or 2-D collisions or explosions: pick a system with no external force, write ∑p_before = ∑p_after, and solve for unknown velocities. Remember impulse-momentum for short interactions and that perfectly inelastic collisions stick (kinetic energy not conserved). Review the CED keywords (center of mass, impulse, elastic/inelastic) and practice problems on Fiveable (topic study guide: https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0; unit: https://library.fiveable.me/ap-physics-c-mechanics/unit-4).

Momentum stays constant because, inside a closed system, all forces between objects are internal and come in equal-and-opposite pairs (Newton’s 3rd law). When two objects collide they exert impulses on each other: J12 = −J21, so the change in one object’s momentum is exactly balanced by the opposite change in the other’s. Adding those changes gives Δp_total = 0, so the system’s total momentum is conserved. Equivalently, with no net external force the center-of-mass velocity is constant (v_cm = Σp_i / Σm_i), so Σp_i can’t change. On the AP exam you should connect Newton’s third law to impulse (J = Δp) and state the no-net-external-force condition before applying conservation of momentum. For a quick review of the Topic 4.3 ideas and worked examples, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0). For extra practice (1000+ problems), try the unit practice page (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Momentum conserved means the vector sum of all momenta in a chosen system doesn't change unless a net external force acts. Practically: if internal forces (like collision forces) act, they’re equal and opposite (Newton’s 3rd law) so total p = Σmivi is constant and the center-of-mass velocity is constant when external force = 0 (CED 4.3.A). Impulse J = Δp describes how external forces change momentum (4.3.B). Energy conserved is different: total energy (including internal, thermal, chemical, etc.) is always conserved, but mechanical energy (kinetic + potential) is only conserved when no non-conservative work (friction, deformation) happens. In collisions: momentum is always conserved (if isolated), but kinetic energy is conserved only in elastic collisions—in elastic vs inelastic collisions some KE is converted to internal energy (CED keywords: elastic, inelastic, perfectly inelastic). For AP prep, be ready to pick a system and check external forces for momentum problems and to state whether mechanical energy is conserved for collision/interaction questions (see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and more Unit 4 review (https://library.fiveable.me/ap-physics-c-mechanics/unit-4). For extra practice try the AP Physics C problem set (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Use the center-of-mass velocity formula from the CED: v_cm = (Σ m_i v_i) / (Σ m_i). Practically, multiply each object’s mass by its velocity (vector if 2-D), add those momentum terms, then divide by the total mass. Steps: 1. Choose the system (which masses count). 2. For each object compute p_i = m_i v_i (include direction). 3. Sum the momenta Σ p_i and the masses Σ m_i. 4. Compute v_cm = Σ p_i / Σ m_i. Example (1-D): m1 = 2 kg at +3 m/s, m2 = 1 kg at −1 m/s → Σp = 2·3 + 1·(−1) = 5 kg·m/s, Σm = 3 kg, so v_cm = 5/3 ≈ 1.67 m/s. Remember: if net external force = 0, v_cm is constant (useful for collision problems on the AP exam; you only need 1- or 2-D analysis per the CED). For topic review see the Conservation of Linear Momentum study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and try practice problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Use conservation of momentum when the net external force on the system you choose is zero (or negligible) during the interaction. That’s the CED core: internal forces (including impulses in collisions) come in equal-and-opposite pairs, so total momentum of the system is unchanged—Δpsys = Jexternal. Practically that means: - For collisions or explosions (instantaneous interactions), pick the two (or more) objects as your system; if external forces (gravity, friction) act over a much longer time than the collision, you can treat them as zero during the collision and use p_before = p_after. - If external forces aren’t negligible, momentum of the chosen system changes by the external impulse: J = Δp. - The center-of-mass velocity is constant when no net external force acts: v_cm = (Σ m_i v_i)/(Σ m_i). AP tip: problems test 1–2D collisions and explosions (use vector components) and relate impulse and Δp—practice those on the exam (Unit 4 weighting). For a quick refresher see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0). For broader review and lots of practice, check the unit page (https://library.fiveable.me/ap-physics-c-mechanics/unit-4) and practice set (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Saying “momentum is always conserved in all interactions” means momentum isn’t mysteriously created or destroyed—it’s only moved around. For any closed system (one you choose so no net external force acts on it), the vector sum of all individual momenta is constant: Σp_i = constant. Internal forces (including contact forces during collisions) can change one object’s momentum, but Newton’s third law makes those changes equal and opposite, so they cancel in the total. If the system does feel a net external force, the system’s total momentum changes by the external impulse J = Δp. Practically, pick your system so external forces are zero, then use conservation of momentum to relate velocities before and after collisions or explosions and to find v_cm (v_cm = Σm_iv_i / Σm_i). Want to practice problems and AP-style questions on this? See the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and thousands more problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Include friction in your momentum work whenever it provides a net external impulse on the system during the time interval you care about. The CED rule to use: total momentum of a selected system is constant only if the net external force (or net external impulse) on that system is zero (4.3.B.2–3). So ask two quick questions: - What system did you choose? If you select just the colliding objects, contact friction with the ground or a table is external. - Does friction deliver a significant impulse during the interaction time? If yes, momentum of that system changes and you must include the friction impulse (or expand the system to include whatever takes that impulse—e.g., include Earth + surface so the frictional force becomes internal). Examples: two pucks colliding on a nearly frictionless air table → neglect friction, momentum conserved. Same collision on a rough table with large frictional impulse → momentum NOT conserved for just the pucks. During brief collisions, frictional impulse is often small so problems will usually state “negligible friction” so you can apply conservation (4.3.A.4). For more practice and CED-aligned examples, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and lots of practice problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

You pick a system because conservation of momentum only applies to that system when the net external force on it is zero. If you include only the interacting objects (an isolated system), all forces between them are internal and their total momentum is constant—any momentum lost by one object is gained by another (CED 4.3.A.3, 4.3.B.2). If you choose a different system that includes something exert­ing an external force (ground, Earth, launcher), that external impulse changes the system momentum (CED 4.3.B.3). Choosing the system also determines the center-of-mass velocity you can use: v_cm = Σ m_i v_i / Σ m_i and v_cm is constant when no net external force acts (CED 4.3.A.1). For collision problems on the AP exam, pick the smallest isolated system that makes momentum conserved (usually the colliding bodies) so you can apply Σp_before = Σp_after; include external impulses otherwise. For a quick review, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and more practice problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

In both collisions and explosions, total linear momentum of an isolated system is conserved because internal forces come in action–reaction pairs (Newton’s 3rd law). The difference is how momentum is redistributed: - Collision: two (or more) bodies collide; their individual momenta change but the vector sum stays the same if no net external force acts. Energy may be conserved (elastic) or not (inelastic, perfectly inelastic). Use p_total = Σm_iv_i before = Σm_iv_i after to solve velocities immediately before/after (1–2D quantitative on the exam). - Explosion: one object breaks apart (internal forces push fragments apart). The fragments’ momenta sum to the pre-explosion momentum (often zero if the parent was at rest), so fragments recoil in ways that conserve the system’s center-of-mass velocity (v_cm constant when external forces ≈ 0). Remember: whether momentum changes depends on your chosen system—external forces transfer momentum to/from the surroundings (CED 4.3.A–B). For a focused review, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and practice problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Yes—momentum can be conserved even when kinetic energy isn’t. Momentum conservation depends only on there being no net external force on the chosen system (CED 4.3.B.2). By Newton’s third law, internal forces between colliding objects produce equal and opposite impulses, so the total momentum stays constant (CED 4.3.A.3.i–iii). Kinetic energy, however, can change because some kinetic energy can be converted into other forms (heat, sound, deformation) during inelastic collisions. Quick examples: - Perfectly elastic collision—both momentum and kinetic energy conserved. - Inelastic collision—momentum conserved, kinetic energy not conserved (some lost to deformation). - Perfectly inelastic—objects stick together; momentum still conserved, KE drops the most. On the AP exam you should (a) pick your system so external forces are zero, (b) apply p_total_before = p_total_after to find velocities, and (c) only invoke kinetic-energy conservation for elastic collisions (CED Topic 4.3 and 4.4). For a focused refresher, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0). For more practice problems, use the Unit 4 page (https://library.fiveable.me/ap-physics-c-mechanics/unit-4) or the practice set (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Newton’s third law (every force has an equal and opposite partner) is the reason momentum can be conserved inside a closed system. When two objects interact, the force object A exerts on B, F_AB, and the force B exerts on A, F_BA, are equal in magnitude and opposite in direction. That means the impulses they deliver are equal and opposite (J_AB = Δp_B and J_BA = Δp_A with J_AB = −J_BA), so any momentum lost by one object is gained by the other—the total momentum ∑p_i doesn’t change if there’s no net external force (CED 4.3.A.3 and 4.3.B.2). Pick your system so external forces are zero (or negligible) and you can apply p_before = p_after to solve collisions or explosions (CED 4.3.A.4). For a quick topic review, see the Conservation of Linear Momentum study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0). For extra practice problems, try the AP Physics C practice bank (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Think of momentum p = mv as “how much motion” an object has. Impulse J is the way you change that motion: J = Δp. In symbols: J = ∫Fnet dt, and for a constant force that’s J = FΔt = m(vf − vi). So impulse is the time-integral of force; its effect is a change in momentum. Two quick AP-C points from the CED: Newton’s third law makes impulses between interacting objects equal and opposite (Ji on A = −Jj on B), so internal impulses cancel and total momentum of a closed system is conserved if the net external force is zero. That’s why you can use conservation of momentum to find velocities before/after collisions (1–2D on the exam). If external impulse acts, Δpsystem = Jexternal. Want more examples and practice problems (collisions, impulse-momentum theorem)? Check the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and browse 1000+ practice questions (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Internal vs. external forces matter because only external forces change a system’s total momentum. Internal forces are forces objects in your chosen system exert on each other (e.g., the impulse between two colliding carts). By Newton’s 3rd law those internal impulses are equal and opposite, so they cancel in the sum and can’t change the system’s total momentum—momentum is just transferred between parts (CED 4.3.A.3 and 4.3.B.1). External forces act on the system from outside (gravity, a push, friction). A nonzero net external force gives a net impulse J = Δp for the whole system, so total momentum changes (CED 4.3.A.3.iii and 4.3.B.2). Practically: pick your system so unwanted external forces are negligible (then p_total is conserved) or include surroundings if they matter. For AP exam collisions, you’ll usually choose the colliding bodies as the system so internal forces cancel and total momentum before = after (see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and unit review (https://library.fiveable.me/ap-physics-c-mechanics/unit-4)). For lots of practice, try the AP Physics C problems (https://library.fiveable.me/practice/ap-physics-c-mechanics).

Step-by-step: solve any collision with conservation of linear momentum 1) Pick your system and check external forces. If net external force ≈ 0, total momentum is conserved (CED Topic 4.3). For AP, analyze quantitatively in 1 or 2 dimensions only. 2) Draw a clear diagram, define +/– directions, label masses (m1, m2) and initial velocities (v1i, v2i). Use components if 2D. 3) Write momentum conservation for the system: m1 v1i + m2 v2i = m1 v1f + m2 v2f (vector form; use x,y components separately in 2D). 4) Use collision type to add equations: perfectly inelastic → v1f = v2f (stick together). Elastic → also conserve kinetic energy: 1/2 m1 v1i^2 + 1/2 m2 v2i^2 = 1/2 m1 v1f^2 + 1/2 m2 v2f^2. Partially inelastic → use coefficient of restitution if given. 5) Solve the algebraic system for unknown final velocities (substitute components when needed). 6) Check limits (momentum vector conserved, energy behavior matches collision type) and units. Want practice? Review Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and do problems at (https://library.fiveable.me/practice/ap-physics-c-mechanics).

The center-of-mass velocity stays constant because the net external force on the system determines the rate of change of the system’s total momentum. Mathematically: p_total = Σ p_i = M v_cm. By Newton’s second law for a system, dp_total/dt = ΣF_ext. If ΣF_ext = 0, then dp_total/dt = 0 so p_total is constant, and since M is constant v_cm = p_total/M is constant. Internal forces (between parts of the system) can change individual p_i, but by Newton’s third law those internal impulses are equal and opposite and cancel in Σp_i, so they don’t change p_total. That’s exactly the CED statement 4.3.A.1–4.3.A.3: pick a system with zero net external force and total momentum (and thus v_cm) is conserved. For more practice and examples tied to the AP CED, see the Topic 4.3 study guide (https://library.fiveable.me/ap-physics-c-mechanics/unit-4/3-conservation-of-linear-momentum/study-guide/qWLd3tCmiQRSZKv0) and the unit practice set (https://library.fiveable.me/practice/ap-physics-c-mechanics).