Momentum

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Every moving object has momentum. It depends on mass and velocity. Momentum is a vector, so direction matters: choose one direction as positive and give the opposite direction a minus sign.

In a closed system, where no external forces act, the total momentum before an event equals the total momentum after it. This is conservation of momentum. It works for collisions and for explosions, where objects start at rest and move apart with equal and opposite momentum.

A force changes momentum. Force equals the rate of change of momentum. If the same change of momentum takes a longer time, the force is smaller. Air bags, seat belts, crumple zones, gymnasium mats and cycle helmets all work this way.

Rules to remember

momentum = mass × velocity (p = mv); unit kg m/s.
Closed system: total momentum before = total momentum after.
Objects that stick together: m₁u₁ + m₂u₂ = (m₁ + m₂)v.
Explosion from rest: total momentum stays zero, so the two momenta are equal in size and opposite in direction.
force = change in momentum ÷ time taken (F = mΔv/Δt).
Longer time for the same change in momentum means a smaller force.

Common mistake

Students add the momenta of objects moving in opposite directions as if both were positive. Give one direction a minus sign before adding.

Worked example

A passenger of mass 70 kg is travelling at 15 m/s when the car crashes. An air bag brings the passenger to rest in 0.25 s. What is the average force on the passenger? Compare it with stopping in 0.050 s without the air bag.

Change in momentum = m × Δv = 70 × 15 = 1050 kg m/s.
With the air bag: F = 1050 ÷ 0.25 = 4200 N.
Without it: F = 1050 ÷ 0.050 = 21 000 N, which is five times larger.

Answer: 4200 N with the air bag, compared with 21 000 N without it.

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