Momentum (HT only)

Because momentum is a vector, directions matter when adding it up: momentum in opposite directions has opposite signs. For example, if two marbles roll towards each other and collide, the total momentum of the system (accounting for direction) is exactly the same just after the collision as it was just before.

Newton's Second Law can also be written in terms of momentum: force equals the rate of change of momentum.

A large change in momentum happening over a very short time produces a large force — this is why a hard, sudden stop (e.g. in a car crash) can cause serious injury: the change in momentum is large and the time taken is very short, so the force on the passengers is large.

Vehicle safety features work by increasing the time over which a change in momentum happens, which reduces the force experienced:

• •Seatbelts stretch slightly under large forces, increasing the time taken for the wearer to decelerate to a stop and so reducing the force on their body (compared with being stopped instantly by the windscreen).
• •Crumple zones at the front and rear of a car deform and compact during a collision, absorbing energy and increasing the time taken for the car itself to stop, which reduces the deceleration and force felt by passengers.
• •Air bags inflate instantly in a crash, giving the head/body a softer surface to decelerate against over a longer time than hitting the steering wheel or dashboard directly, reducing the force on the neck and head.