4.1.4Linear Momentum

Impulse–Momentum Theorem — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 5 of 13 1 quiz

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Lesson summary

4.1.4 Impulse–Momentum Theorem — AP PHYSICS 1 notes: Apply the impulse–momentum theorem to find velocity changes, forces and contact times in collisions.J = Δp — the impulse of the net force equals the change in momentum: FnetΔt = mvf − mvi.Origin — multiply Fnet = Δp/Δt by Δt.Ve…

Elastic bounce at equal speed
Long contact
Person landing
Longer contact time
Follow-through
Rockets and jets

Part 1 of 7Statement

J = Δp

J = Δp the impulse of the net force equals the change in momentum: F_netΔt = mv_f − mv_i.

Origin

Origin multiply F_net = Δp/Δt by Δt.

Vectors

Vectors the sign of each velocity matters, so choose a positive direction first.

Direction

Direction the change in momentum points along the net force.
- (a ball hitting a wall travelling east gets a westward impulse)

Part 2 of 7Solving problems

Draw a sketch, choose the system and a positive direction.

Write the initial and final momenta with signs.

Find Δp = p_f − p_i.

Equate to FΔt and solve for the force, time, speed or mass.

Part 3 of 7Collision examples

1Bounce

Bounce final velocity has the opposite sign, so |Δp| = m(|v_f| + |v_i|).

2Elastic bounce at equal speed

Elastic bounce at equal speed impulse 2mv, compared with mv for a ball that sticks.

3Long contact

Long contact include gravity in the net force; the surface must support the weight too.

4Person landing

Person landing ground force F = mg + Δp/Δt (up positive), so bent knees increase Δt and lower the force.

Part 4 of 7Safety and sports

Longer contact time

Longer contact time reduces the average force for a fixed Δp.
- (helmets, moving the hands back when catching)

Follow-through

Follow-through increases the time of the force, increasing Δp and ball speed for the same average force.

Rockets and jets

Rockets and jets thrust equals the rate at which momentum is given to the exhaust.

Part 5 of 7Choosing a method

Method	Use when
Impulse and momentum	A time is given or asked for, or the velocity changes direction
Work and energy	A distance is given or asked for, such as stopping distance
Newton's second law and kinematics	The acceleration itself is wanted at an instant

1Braking with constant force F

Braking with constant force F t = mv/F and d = mv²/(2F), so d = vt/2.

2Parallel

Parallel net work changes kinetic energy whereas net impulse changes momentum.

Part 6 of 7Checks

Units

N·s must equal kg·m/s.

Varying force

Varying force the impulse is the area under the F–t graph and the theorem still applies.

Part 7 of 7More from the specification

1Automotive crumple zones on an inclined slope

Automotive crumple zones on an inclined slope vehicular crumple zones deform progressively to reduce impact forces during downhill collisions along a slope.

2Inertia

Resistance of an object to changes in its motion.

3Force-time graph

A graph whose area is the impulse.

4External force

Force from the surroundings.

5Linear momentum

The product of mass and velocity.

6Crumple zone

Car structure that lengthens collision time and lowers force.

Key terms

Term	Meaning
Impulse–momentum theorem	Net impulse equals change in momentum, FΔt = Δp.
Elastic bounce	Rebound in which the speed is unchanged.
Follow-through	Prolonging contact to increase impulse.
Thrust	Forward force from expelling mass backward.

Avoid these mistakes

Using the same sign for velocities before and after a bounce.

Forgetting that the ground force must also support the weight.

Using the impulse of a single force when the theorem needs the net force.

Mixing grams, milliseconds and SI units.

Believing a longer collision time reduces the change in momentum — only the force is reduced.

Last updated: 15 October 2026