Use a defined system and a named quantity to track transfers, distinguish changing parts from conserved totals, and check the conditions of energy and momentum balances.
Key knowledge
For a fixed collection of classical particles whose internal forces satisfy Newton's third law, zero net external force keeps the total linear momentum constant.
Values and equations
P = Σᵢ mᵢvᵢ; F_external,net = 0 ⇒ dP/dt = 0
P
Total vector linear momentum kg m s⁻¹
mᵢ
Mass of particle i kg
vᵢ
Vector velocity of particle i m s⁻¹
F_external,net
Vector sum of external forces N
t
Time s
Conditions and scope
Use an inertial frame and a fixed collection of particles.
Internal forces obey equal-and-opposite pairing; all external forces are included in the total.
Sources · 7
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
OpenStax 9.3: summed forces, fixed system and zero net external force.
2026-10-10 · Classical linear-momentum conservation under stated conditions only; relativistic field momentum and other conserved quantities are outside scope.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Agreement within this scope
Classical total vector momentum remains constant when external resultant force vanishes and internal force pairs cancel.
The isolation condition is essential; momentum of a colliding subsystem can change through external forces.
A nonrelativistic neutron of mass m and kinetic energy E scattered elastically from a free stationary nucleus of mass M retains E′/E=(η²+1+2ηcosθ_cm)/(η+1)², η=M/m. Thus αE≤E′≤E with α=[(η−1)/(η+1)]²; light targets can transfer a larger fraction of energy. If scattering is isotropic in the center-of-momentum frame, E′ is uniform on that interval and the mean logarithmic decrement is ξ=1+αlnα/(1−α), with ξ=1 at η=1.
Nonrelativistic energy and momentum balance constrain the energy transfer; isotropic angular probability is a separate scattering assumption.
For a constant-mass Newtonian particle in an inertial frame, linear momentum is p=mv and net-force impulse over an interval is J=∫F_netdt=p_f−p_i. For a fixed many-particle system, the external impulse changes total momentum when internal force pairs cancel. A large collision force over a short time is governed by the impulse, not force magnitude alone.
This relation concerns the stated impulse and momentum transfer claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
When external impulse is negligible, total momentum is conserved through a Newtonian collision. An elastic collision also preserves total translational kinetic energy; an inelastic collision does not. In a perfectly inelastic collision two bodies stick and have common final velocity (m₁v₁+m₂v₂)/(m₁+m₂). Their translational kinetic-energy decrease becomes other forms of energy rather than destroying total energy.
This relation concerns the stated elastic and inelastic collisions claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Learning guidance · 3 / 3
Preserved learning suggestions. They are not proof, empirical evidence or mandatory prerequisites.