Momentum & collisions

A table tennis ball flies towards you: no problem, you catch it easily. A medicine ball at the same speed: much harder to stop. And a rolling shopping trolley is easier to stop than a rolling car. Apparently moving things carry something that depends on two factors: how heavy they are and how fast they are. Physics calls exactly this something momentum.

Momentum: mass times velocity

The momentum $p$ of an object is simply its mass times its velocity. A football of $0.4$ kg flying at $10$ m/s has a momentum of $0.4 \cdot 10 = 4$ kilograms times metres per second, written $4$ kg·m/s for short. A car of $1000$ kg rolling at just $1$ m/s still reaches $1000$ kg·m/s. That is why even something slow can be dangerous if it is heavy enough. The larger the momentum, the more force or time you need to stop the motion.

Collisions: momentum is conserved

When two objects collide, something remarkable happens: the total momentum stays the same, as long as no extra force acts from outside. It can only pass from one object to the other, but it cannot vanish. You can see this directly in billiards: the white ball hits a resting ball of the same mass dead centre, almost stops itself, and the ball it hit rolls on with almost the same speed. The momentum has merely changed owner. You can even calculate with this: a cart of $4$ kg at $3$ m/s has a momentum of $12$ kg·m/s. If it hits a resting cart of $2$ kg and the two lock together, $6$ kg share that momentum: they roll on together at $2$ m/s. Always mind the direction as well: two equally large momenta running in exactly opposite directions add up to zero.

So why do crumple zones and airbags save lives? In a crash the car's momentum has to be brought to zero, there is no way around that. But you do have a choice about the time: the longer the braking takes, the smaller the force at every moment. A crumple zone folds up and stretches the impact over a longer time. An airbag does the same for your head: instead of stopping hard and abruptly, you are slowed down softly and over a longer time.