4.1 Momentum and Impulse

Momentum defined

Momentum (p) is a vector quantity equal to p = mv, mass times velocity, measured in kg·m/s. It points in the same direction as an object's velocity. Momentum describes how hard it is to stop a moving object — a heavy truck moving slowly can have the same momentum as a light car moving fast.

Impulse and the impulse-momentum theorem

Impulse (J) equals J = FΔt, the product of net force and the time it acts, also equal to the area under a Force vs. time graph. The impulse-momentum theorem states J = Δp, so impulse causes a change in momentum. This explains why airbags reduce injury: increasing Δt decreases the average force for the same Δp.

Vector nature and direction

Because momentum and impulse are vectors, direction matters — bouncing off a wall involves a larger Δp than sticking to it, since velocity reverses sign. Always assign a positive direction and treat velocities/forces opposite to it as negative when calculating Δp = m(v_f − v_i).

Key terms

Momentum (p)

p = mv; a vector quantity describing mass in motion, measured in kg·m/s.

Impulse (J)

J = FΔt; the product of net force and time interval, also equal to the area under a Force vs. time graph.

Impulse-momentum theorem

J = Δp; the impulse on an object equals its change in momentum.

Why increasing Δt matters

For a fixed impulse (Δp), a longer time interval Δt results in a smaller average force — the principle behind airbags and padding.

Vector nature of momentum

Momentum and impulse have direction; reversing velocity (like a bounce) produces a larger magnitude change in momentum than stopping.

Try an AP-style question

What is the momentum of a 3 kg ball moving at 4 m/s?

1. 24 kg·m/s
2. 0.75 kg·m/s
3. 7 kg·m/s
4. 12 kg·m/s