This unit is ≈17% of the A-Level Physics, across 7 lessons. Full syllabus
Lesson 4 of 7 · Mechanics and materials
Momentum, impulse and collisions
7 min read · about 1 h 40 min with practice3 quick checks≈2% of the testCore: Core: tested on most papers
Reading is free. Sign in to tick off lessons, keep your place and track your mastery.
Momentum questions reward a disciplined method more than any other mechanics topic. The physics is two equations, F=ΔtΔp and “total momentum before = total momentum after”. Nearly every lost mark comes from a sign error or from assuming kinetic energy is conserved. Expect MCQs on units and graphs, 3–5 mark collision and impulse calculations, and a 6-mark extended response on vehicle safety.
By the end you’ll be able to
Define momentum and state the principle of conservation of linear momentum
Use F = Δ(mv)/Δt, including situations where mass changes (jets, water hoses)
Find impulse as the area under a force–time graph and explain safety features that increase impact time
Solve 1-D collision and explosion problems and decide whether a collision is elastic by comparing kinetic energy
Resolve momentum in two dimensions for oblique collisions (Edexcel, IAL, Cambridge extension)
What the exam asks
Definitions (1–2 marks): momentum, impulse, the principle of conservation of momentum, elastic and inelastic collisions.
Force and impulse:F=ΔtΔ(mv), impulse from the area under a force–time graph, rebounds (where the change in velocity is the sum of the speeds), and average force during an impact.
Collisions and explosions: 1-D problems with a sign convention, then a kinetic-energy check to classify the collision.
jets, hoses, rockets and conveyor belts, using .
vii.Check your understanding
3 questions on momentum, impulse and collisions. Every option is explained once you answer.
Sign in to try the quick check
Answers are checked on our side, every option is explained, and your result feeds your mastery for this topic. It’s free.
The first 3 of 10 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.
PromptCard 1 of 3
Define linear momentum and give its unit.
Changing mass:
F=vΔtΔm
Safety: crumple zones, seat belts, airbags and helmets explained with impulse and energy. This is often a 6-mark question, and AQA links it to ethical transport design.
Two-dimensional collisions on some boards (see below).
Core ideas
Momentum
p=mv
Momentum is a vector, measured in kg m s−1, which is equivalent to N s. Its direction matters, so every calculation starts with a positive direction.
Force is the rate of change of momentum
F=ΔtΔ(mv)
This is Newton’s second law in its general form. For constant mass it becomes F=ma. When mass flows at a steady speed (a jet of water, rocket exhaust, sand dropping onto a belt), the force is
F=vΔtΔm
For a fluid jet of density ρ, cross-sectional area A and speed v, the mass arriving each second is ρAv. If the jet is brought to rest, F=ρAv2. The speed appears twice: once in the mass per second and once in the change of velocity.
Impulse
impulse=FΔt=Δ(mv)
Impulse is the area under a force–time graph, even when the force varies. For a triangle it is 21×peak×duration. For a smooth curve, count squares or use trapezia.
Rebounds: a ball hitting a wall at u and rebounding at v has Δp=m(v−(−u))=m(u+v). The speeds add.
Conservation of linear momentum
For a system of interacting bodies, the total momentum stays constant, provided no external resultant force acts on the system.
Collisions: momentum is always conserved (in a closed system). Total energy is always conserved. Kinetic energy is conserved only in a perfectly elastic collision.
Inelastic: some kinetic energy becomes internal energy, sound or deformation. If the bodies stick together, the collision is “perfectly (totally) inelastic” and loses the most kinetic energy that momentum conservation allows.
Explosions (or recoil) starting from rest: the total momentum is zero before, so it is zero after. The pieces move in opposite directions with speeds inversely proportional to their masses. Kinetic energy increases, supplied by chemical or elastic potential energy.
To classify a collision, calculate total Ek before and after. For Cambridge, you should also recall that in a perfectly elastic collision the relative speed of approach equals the relative speed of separation. This is a fast check that avoids the kinetic-energy arithmetic.
A useful link is Ek=2mp2 (explicitly in the Edexcel and IAL specifications). In an explosion from rest the two pieces have equal momentum magnitudes, so the lighter piece carries more kinetic energy.
Two-dimensional collisions
Resolve every momentum into two perpendicular components and conserve each component separately. A special result: when a moving sphere makes a perfectly elastic, glancing collision with an identical sphere at rest, the two move off at 90∘ to each other.
Safety features
For a given change of momentum (fixed by the mass and initial speed), F=ΔtΔp, so increasing the stopping time decreases the average force. An energy view gives the same conclusion: force × stopping distance = kinetic energy lost, so a longer stopping distance means a smaller force. Crumple zones, seat-belt stretch, airbags and helmet foam all lengthen the time and distance of the collision. Airbags also spread the force over a larger area, which reduces the pressure on the body.
Worked examples
Exam technique
Arrow and sign first. Write “→ positive” and put a minus sign on every velocity to the left, including unknowns you find. A negative answer means the object moves the other way. Say so in words.
Before = after, in one line. Write m1u1+m2u2=m1v1+m2v2 with numbers substituted. That line alone usually earns the method mark.
Never assume kinetic energy is conserved unless the question says “elastic”. Use it only to classify or when told.
Rebound questions: the change in velocity is u+v, not u−v.
Graph questions: the area under an F–t graph is impulse; the gradient of a p–t graph is resultant force.
Safety 6-markers: use the chain “same Δp → longer Δt → smaller F → smaller deceleration → less injury”, then name specific features and say how each one increases the time or distance.
Common mistakes
Quick recap
p=mv, a vector; kg m s−1≡N s.
F=ΔtΔ(mv); for jets F=vΔtΔm=ρAv.
Impulse =FΔt=Δp= area under the F–t graph.
Momentum is conserved when no external resultant force acts; total energy is always conserved; kinetic energy is conserved only if the collision is elastic.
Explosions from rest: equal and opposite momenta, speeds inversely proportional to mass, Ek=2mp2.
2-D (not AQA): conserve each perpendicular component separately.
Safety: a longer impact time or distance gives a smaller force for the same change in momentum.