Overview
What you’ll learn
- Calculate momentum as p = mv, including its unit and its vector nature.
- Use impulse = FΔt = Δ(mv) to describe what a force acting over a time does to momentum.
- Apply conservation of momentum to one-dimensional collisions and recoil problems.
- Use F = Δp/Δt to relate force to how quickly momentum changes.
- Explain crash-safety design using longer collision times and smaller forces.
Syllabus checklist (0625)
Statements are paraphrased and grouped by tier. Core is studied by everyone; Supplement is examined on the Extended papers only.
Supplement — Extended candidates only
- 1.6Define momentum as mass × velocity; recall and use the equation p = mv.
- 1.6Define impulse as force × time for which the force acts; recall and use the equation impulse = FΔt = Δ(mv).
- 1.6Apply the principle of the conservation of momentum to solve simple problems in one dimension.
- 1.6Define resultant force as the change in momentum per unit time; recall and use the equation F = Δp/Δt.
In 30 seconds
- 1Momentum p = mv — mass × velocity, measured in kg m/s; it is a vector, so direction (and a negative sign) matters.
- 2Impulse = FΔt = Δ(mv): a force acting for a time changes an object’s momentum by exactly that amount, measured in N s.
- 3In any collision or explosion with no outside forces, the total momentum stays constant — momentum before = momentum after.
- 4F = Δp/Δt: the same momentum change hurts less when it takes longer, which is the whole idea behind air bags and crumple zones.
- 5Momentum is always conserved, but kinetic energy usually is not — some becomes heat and sound in a crash.
Notes · 1 of 4
What momentum is
Momentum is mass in motion: p = mv, with direction built in.
Momentum is defined as mass × velocity:
Momentum explains why a small fast bullet can matter as much as a slow heavy trolley: both mass and velocity count, and doubling either doubles the momentum.
Notes · 2 of 4
Impulse: force acting over time
Force × time is the momentum change it produces.
Push a trolley with a steady force and its velocity — and so its momentum — grows. The longer you push, the more momentum it gains. Impulse is defined as force × time for which the force acts, and it equals the change in momentum:
Notes · 3 of 4
Conservation of momentum
In every collision, the total momentum before equals the total momentum after.
The principle of conservation of momentum: when no external force acts, the total momentum of the objects before an interaction equals the total momentum after. Objects can collide and stick, bounce apart, or fly apart from rest (a recoil or explosion) — the total is unchanged every time.
- 1Choose a positive direction
Say "right is positive" and give every velocity its sign.
- 2Total before
Add up m × v for every object before the collision.
- 3Total after
Write the same sum for after, with the unknown velocity as a letter.
- 4Equate and solve
Set before = after and solve. Check the answer makes sense (a struck object should move away in the push direction).
Notes · 4 of 4
Force as rate of change of momentum
F = Δp/Δt links crashes, air bags and crumple zones.
A resultant force changes an object’s momentum. Define the resultant force as the change in momentum per unit time:
This is the physics of safety design. Crumple zones collapse in a crash, stretching the stopping time from milliseconds to tenths of a second. Air bags cushion the head the same way, and seat belts stretch slightly. The car’s Δp is fixed by the crash; the design only changes Δt — and so the force on the passengers.
Revise
Key terms
The words examiners expect you to use precisely.
- Momentum
- Mass × velocity, p = mv, in kg m/s; a vector pointing along the velocity.
- Impulse
- Force × time for which the force acts, FΔt; equal to the change in momentum, in N s.
- Conservation of momentum
- With no external force, the total momentum before an interaction equals the total afterwards.
- Collision
- An interaction in which moving objects exert forces on each other for a short time.
- Recoil
- The backward motion of an object that throws mass forwards, keeping the total momentum at zero.
- Rate of change of momentum
- Δp/Δt — equal to the resultant force acting on the object.
Show 2 more key termsShow fewer key terms
- Crumple zone
- A part of a vehicle designed to collapse in a crash, lengthening the collision time and cutting the force.
- Elastic collision
- A collision in which kinetic energy is conserved as well as momentum (rare in everyday life).
Revise
Common mistakes
Where students most often lose marks in this topic — and what to do instead.
Mistake: Quoting the unit of momentum as N or kg m.
Momentum is mass × velocity, so its unit combines theirs.
Instead: The unit of momentum is kg m/s (the same as the newton-second, N s).
Mistake: Treating momentum as a scalar and adding speeds without directions.
Momentum has a direction — it is a vector, like velocity.
Instead: Choose a positive direction; velocities (and momenta) opposite to it are negative.
Show 8 more mistakesShow fewer mistakes
Mistake: Using mass in grams or speed in km/h in p = mv.
The equation needs SI quantities to give kg m/s.
Instead: Convert grams to kilograms and km/h to m/s before multiplying.
Mistake: Forgetting to add the masses after objects couple together.
The combined object carries the mass of both, so its velocity is found using the total mass.
Instead: After sticking: (m₁ + m₂)v = total momentum before.
Mistake: Saying momentum is "lost" in a crash.
Momentum is transferred to the surroundings (Earth, debris) — the total is always conserved.
Instead: It is kinetic energy, not momentum, that turns into heat and sound in a crash.
Mistake: Believing safety features "reduce the impulse" of a crash.
The momentum change Δp of the passenger is fixed by the crash itself.
Instead: Air bags and crumple zones increase the collision time, so F = Δp/Δt is smaller — same Δp, longer Δt.
Mistake: Computing F = Δp/Δt with the final momentum instead of the change.
The equation needs Δp — final momentum minus initial momentum, with signs.
Instead: Stopping a ball: Δp = 0 − mv, so the magnitude is mv but the direction reverses.
Mistake: Assuming the total kinetic energy is conserved in every collision.
Only momentum is always conserved; KE usually decreases.
Instead: In a stick-together collision, check momentum conservation only unless told the collision is elastic.
Mistake: Dropping the minus sign on a recoil velocity.
The minus sign carries the physics: the recoiling object moves opposite to the thrown mass.
Instead: Keep the sign through the algebra and state the recoil direction in words in the answer.
Mistake: Assuming the heavier object always has the larger momentum.
Momentum depends on mass and velocity together — a fast, light object can out-momentum a slow, heavy one.
Instead: Compare the products p = mv, not the masses alone.
Check yourself
Quick quiz
20 questions with instant explanations. About 5 minutes.
Question 1 of 3
- Question 1: current question
- Question 2: not answered
- Question 3: not answered
Calculate momentum
What is the momentum of a 1200 kg car travelling at 15 m/s?
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Practise
Topical questions
12 exam-style questions with model answers and mark schemes.
A set of structured and calculation questions matched to this topic, in three tiers, each with a model answer, mark scheme and examiner tip.
Practise topical questionsExam practice
Practice paper
A 30-mark paper set out like a Cambridge paper, with a separate mark scheme. Give yourself 40 min.
Question paper
Topic 3 Practice Paper
30 marks · 40 min · 6 pages
10 multiple-choice questions and structured questions with answer lines. Topic 3: Momentum (Supplement content: p = mv, impulse, conservation, F = Δp/Δt).
Mark scheme
PROTopic 3 Practice Paper — mark scheme
Answers · Marking points · 3 pages
Model answers with a mark for each creditworthy point — for marking at home or in class.
Which paper covers this topic?
Paper 1 / 2
Multiple choice (45 min, 40 marks)
Core and Extended versions
Paper 3 / 4
Theory, short and structured (1 h 15, 80 marks)
Core and Extended versions
Paper 5 / 6
Practical test or Alternative to Practical (40 marks)
Experimental skills
Want a full paper? Try the Paper 2-style multiple choice, Paper 4-style structured or Paper 6-style practical sets.
Questions
Frequently asked questions
What equations do I need for IGCSE Physics momentum?
Three: p = mv for momentum, impulse = FΔt = Δ(mv) for a force acting over a time, and F = Δp/Δt for force as the rate of change of momentum. Plus the principle: total momentum before = total momentum after.
Why is momentum conserved but kinetic energy sometimes is not?
Momentum is a vector and the forces in a collision are internal and equal-and-opposite, so the total cannot change. Kinetic energy is a scalar that can be transferred to heat and sound when objects deform, so it usually falls unless the collision is perfectly elastic.
How do I handle two objects moving in opposite directions?
Choose one direction as positive and attach minus signs to everything moving the other way. Add the signed momenta before and after, then solve; the sign of your answer gives its direction.
Do air bags reduce the impulse of a crash?
No — the impulse (the passenger’s momentum change) is fixed by the crash. Air bags increase the time over which that change happens, so by F = Δp/Δt the force on the passenger is smaller.
Is momentum on the Core papers for IGCSE Physics?
No. Momentum is Supplement-only in the 0625 syllabus, so it is examined in Paper 2 (multiple choice) and Paper 4 (theory) for Extended candidates, not in Papers 1 and 3.
Up next
Topic 4: Energy, work and power