Linear Momentum

4. Linear Momentum — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 8 parts Lesson 1 of 13 3 quizzes

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Lesson summary

4. Linear Momentum — AP PHYSICS 1 notes: Use momentum, impulse and conservation of momentum to analyse collisions and explosions and explain safety features.Linear momentum — p = mv, a vector in the direction of the velocity, in kg·m/s.Constancy — momentum stays constant unless a…

Centre of mass
Force–time graph
Momentum–time graph
Favg = Δp/Δt
Safety devices
System choice

Part 1 of 6Momentum

Linear momentum

Linear momentum p = mv, a vector in the direction of the velocity, in kg·m/s.
What the symbols mean: p = momentum (kg m s⁻¹) · m = mass (kg) · v = velocity (m s⁻¹)

Constancy

Constancy momentum stays constant unless a net external force acts.

Centre of mass

Centre of mass v_cm = Σp/Σm, unchanged when no external force acts.

Part 2 of 6Impulse

Impulse

J = FΔt = Δp, the net force times its time of action.
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)

Force–time graph

Force–time graph area under the curve is the impulse, found by area for a variable force.
- (change in momentum)

Momentum–time graph

Momentum–time graph the slope is the net force.

From rest

From rest area of the F–t graph gives Δp, so v = Δp/m.

Example

Example a racket acts on a tennis ball for about 5 ms.

Part 3 of 6Why longer collision time reduces force

Favg

Δp/Δt

for a given change in momentum a longer time gives a smaller average force.

Safety devices

Safety devices seat belts, airbags and crumple zones increase the collision time.

Force–time graph

Force–time graph lower peak and wider base but the same area, the same impulse.

Part 4 of 6Conservation of momentum

1Law

Law total momentum of a system changes only through a net external force, so it is conserved when the net external impulse is zero.

2System choice

System choice include the interacting objects inside the system.

3Two objects

Δp_A = −Δp_B.

4Two dimensions

Two dimensions resolve into x and y components and conserve each separately.

5Collision then swing

Collision then swing momentum applies only to the horizontal direction just after the collision.

Part 5 of 6Collisions

Type	Momentum	Kinetic energy	Notes
Elastic	Conserved	Conserved	Relative speed of approach equals relative speed of separation
Inelastic	Conserved	Decreases
Perfectly inelastic	Conserved	Decreases the most	Objects stick: m₁v₁ + m₂v₂ = (m₁ + m₂)v

Part 6 of 6Explosions

Momentum

Momentum the initial momentum (often zero) is conserved; there is no external impulse during separation.

Pieces

Pieces carry equal and opposite momentum.

Kinetic energy

Kinetic energy increases because stored potential energy is released.

Energy after

Energy after a collision followed by a swing or slide can be combined with energy conservation afterwards.

Key terms

Term	Meaning
Momentum	Product of mass and velocity, p = mv.
Impulse	Net force times time; equals change in momentum.
Conservation of momentum	Total momentum constant with no net external impulse.
Elastic collision	Collision in which kinetic energy is conserved.
Inelastic collision	Collision in which kinetic energy is not conserved.
Centre of mass	Point that moves as if all mass were concentrated there.

Avoid these mistakes

Forgetting that momentum is a vector so direction (sign) matters.

Using conservation of momentum when a net external impulse acts on the chosen system.

Assuming kinetic energy is conserved in every collision.

Believing a crumple zone changes the impulse — it changes the time and so the force.

Applying the horizontal momentum equation to a vertical swing after a collision.

Last updated: 14 October 2026