Momentum

Momentum — the product of an object's mass and its velocity:

p = m v

with momentum in kg m/s, mass in kg and velocity in m/s. Momentum is a vector, so it carries the direction of the velocity, and in one dimension that means a sign.

Conservation of momentum — in a closed system, the total momentum before an event equals the total momentum after it:

total momentum before = total momentum after

This holds for collisions and explosions alike, provided no external force acts.

Setting up a collision problem:

1. Choose a positive direction and state it.
2. Work out the total momentum before, treating anything moving the other way as negative.
3. Set it equal to the total momentum after.
4. Solve.

Example: a 2 kg trolley at 3 m/s right strikes a stationary 4 kg trolley and they stick together. Momentum before = 2 × 3 + 4 × 0 = 6 kg m/s. After, the combined mass is 6 kg, so 6 = 6v and v = 1 m/s right.

Explosions start with zero total momentum, so the fragments must carry equal and opposite momenta. A rifle recoils for exactly this reason: the bullet's forward momentum is matched by the rifle's backward momentum.

Force and momentum — a resultant force changes momentum, and the specification expresses this as:

F = (m v − m u) / t

which is the rate of change of momentum. It is the same physics as F = ma, written so the change in momentum is explicit.

Why crumple zones work. They increase the time over which a collision brings the car to a stop. The change in momentum is fixed by the mass and the speed, so a longer time means a smaller force — and the force is what injures people. Airbags, seatbelts, crash mats and bending lamp posts all do the same job.