9.1Momentum and Its Conservation

Impulse and Momentum — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 3 of 5 1 quiz

📚 American System Physics Hub / Topical Revision

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Lesson summary

Define momentum and impulse and state their units.Momentum = mass × velocityp = mv (kg·m/s).Impulse = force × timeFΔt (N·s).Impulse = change in momentumFΔt = Δp = mvf − mvi.Resultant force = change in momentum ÷ time takenF = Δp/Δt (N).1 N·s = 1 kg·m/s.Area under a force–time gra…

Momentum is a vector
Newton's second law can be written F = Δp/Δt
Rearranging gives FΔt = Δp
Momentum and kinetic energy are different
Momentum (p)
Impulse–momentum theorem

Part 1 of 7Key ideas

1Momentum

Momentum mass × velocity

p = mv (kg·m/s).

2Impulse

Impulse force × time

FΔt (N·s).

3Impulse

Impulse change in momentum

FΔt = Δp = mv_f − mv_i.

4Resultant force

Resultant force change in momentum ÷ time taken

F = Δp/Δt (N).

1 N·s = 1 kg·m/s.

Area under a force–time graph = impulse (N·s).

For the same Δp, increasing Δt decreases the average force.

A ball rebounding with the same speed has Δp = 2mv (twice the momentum it arrived with).

Part 2 of 7Learning objectives

Define momentum and impulse and state their units.

What the symbols mean:

Apply the impulse–momentum theorem, F = Δp/Δt.

What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s⁻¹); FΔt is the impulse (N s)

Find impulse from the area under a force–time graph.

Explain how safety features reduce injury using impulse.

Part 3 of 7Essential knowledge

Essential knowledge

9.1 Impulse and Momentum concept map: Momentum = mass × velocity, Impulse = force × time, Impulse = change in momentum, Resultant force = change in m, Momentum is a vector — Visual guide to the key ideas explained in this lesson.

Momentum measures how hard it is to stop a moving object; it depends on both mass and velocity. A slow truck and a fast bullet can have similar momentum.

Momentum is a vector

Momentum is a vector direction matters. In one dimension use + and − signs for opposite directions.

Newton's second law can be written F

Δp/Δt

the resultant force equals the rate of change of momentum. For constant mass this is the same as F = ma.

Rearranging gives FΔt = Δp

Rearranging gives FΔt = Δp the impulse of the force equals the change in momentum (impulse–momentum theorem).

Impulse can be increased either by a larger force or by applying it for longer – e.g. following through in golf or tennis increases contact time and so the ball's final momentum.

When stopping an object, Δp is fixed. Spreading the stop over a longer time reduces the average force; this is the principle of airbags, crumple zones, seat belts, padded gym floors and bending knees on landing.

On a force–time graph, the area under the curve is the impulse. For a varying force, the average force is the impulse divided by the time.

When an object bounces back, the change in momentum is larger than when it just stops, because the velocity changes sign: Δp = m(v_f − v_i) with opposite signs.

The unit N·s equals kg·m/s, showing impulse and momentum are the same kind of quantity.

Momentum and kinetic energy are different

Momentum and kinetic energy are different momentum is a vector (kg·m/s), KE is a scalar (J). Two objects can have equal momentum but different KE.

Part 4 of 7Process & sequence

Choose a positive direction and write it down.

Write initial and final velocities with signs (a rebound reverses sign).

Calculate initial momentum p_i = mv_i and final momentum p_f = mv_f.

Find the impulse Δp = p_f − p_i.

Divide by the contact time to find the average force F = Δp/Δt.

State magnitude, unit (N or N·s) and direction.

How an airbag reduces injurywrite these steps in this order; each step is a marking point.

In a crash the person's momentum must fall to zero – Δp is fixed.

The airbag lets the head decelerate over a longer time Δt.

Since F = Δp/Δt, a longer Δt means a smaller average force.

The force is also spread over a larger area, lowering pressure.

Smaller force and pressure mean less injury.

Part 5 of 7Worked examples

−3.0 N·s

A 0.15 kg ball moving at 20 m/s is caught and stopped in 0.050 s. Find the impulse and the average force on the ball.

Take the ball's initial direction as +.
Δp = m(v_f − v_i) = 0.15 × (0 − 20) = −3.0 N·s (3.0 N·s opposite to the motion)
F = Δp/Δt = −3.0/0.050 = −60 N, i.e. 60 N opposite to the ball's motion.

825 N ≈ 830 N

A 0.060 kg tennis ball arrives at 25 m/s and leaves in the opposite direction at 30 m/s. Contact time 4.0 ms. Find the average force.

Take the leaving direction as +v_i = −25 m/s, v_f = +30 m/s.
Δp = 0.060 × (30 − (−25)) = 0.060 × 55 = 3.3 N·s
F = 3.3/0.0040 = 825 N ≈ 830 N in the direction the ball leaves.

A 1200 kg car speeds up from 10 m/s to 25 m/s. What impulse acted on it? If this took 6.0 s, what was the average resultant force?

Δp = 1200 × (25 − 10) = 1.8 × 10⁴ N·s
F = 1.8 × 10⁴/6.0 = 3.0 × 10³ N forwards.

Part 6 of 7Summary

Momentum p = mv is a vector, unit kg·m/s.

Impulse = FΔt = Δp, unit N·s.

Force = rate of change of momentum.

Longer stopping time → smaller force (airbags, crumple zones).

Watch signs: a rebound gives a large change in momentum.

Part 7 of 7Compare: Compare

Safety features and impulse
Feature	What it changes	Effect on force
Airbag	Increases stopping time of head	Smaller average force
Seat belt (stretches slightly)	Increases stopping time; spreads force	Smaller force and pressure
Crumple zone	Increases collision time	Smaller force on occupants
Bending knees on landing	Increases time to stop	Smaller force on legs
Helmet foam	Increases time head takes to stop	Smaller force on skull

In each case Δp is fixed by the situation; only Δt can be changed.

Momentum vs kinetic energy
Property	Momentum	Kinetic energy
Formula	p = mv	KE = ½mv²
Unit	kg·m/s	J
Scalar/vector	Vector	Scalar
Conserved in all collisions (closed, isolated)?	Yes	Only in elastic collisions

Key terms

Command terms

Identify / Describe (FRQ)

A short, specific statement; describing requires relevant characteristics, not a single word.

Explain / Justify (FRQ)

Give the cause-and-effect reasoning or evidence; a restated fact does not score.

Calculate

Show setup, substitution and the answer with units.

Predict

State the expected outcome; add a reason only if asked to justify.

MCQ technique

Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Momentum (p) · Impulse · Impulse–momentum theorem · Change in momentum (Δp) · Resultant (net) force · Newton's second law (momentum form) · Force–time graph · Average force · Crumple zone · Velocity (v) · Vector quantity

Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).

Use precise vocabulary, never “it/stuff/things”.

Show units and working in calculations.

In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

the airbag absorbs the momentumthe airbag increases the time taken to stop, so the rate of change of momentum (force) is smaller

momentum = mass × speedmomentum = mass × velocity (it is a vector)

impulse is a forceimpulse is force × time, equal to the change in momentum (N·s)

change in momentum = mv − mu without signschoose a positive direction; a rebound velocity is negative

force = change in momentumforce = change in momentum ÷ time taken

Last updated: 18 October 2026