Momentum and impulse

Why do airbags save lives? Why does a boxer roll with a punch? Why does catching a fastball sting less when you pull your glove back? One quantity answers all three — and it's the last one this course needs.

Momentum: mass in motion

$p = mv$

Momentum is velocity weighted by how much matter carries it — a vector, in kg·m/s. A 2000 kg car at 1 m/s and a 100 kg linebacker at 20 m/s carry the same momentum; stopping either takes the same total effort.

Impulse: how momentum changes

Multiply both sides of F = ma by time instead of distance (that was the energy move) and you get the momentum version of the second law:

$F\,\Delta t = \Delta p$

The product F·Δt is the impulse. To change momentum by a fixed amount, you choose the trade: a huge force for an instant, or a gentle force sustained. The total is the same; the peak force is not.

That trade is the physics of every safety device:

Nothing reduces the momentum you must shed — only how long you take to shed it is negotiable.

Why momentum is conserved

Here's the third law's payoff. When two objects collide, A pushes B and B pushes A — equal forces, opposite directions, same contact time. So the impulses are equal and opposite, and whatever momentum B gains, A loses to the decimal:

$\Delta p_B = -\Delta p_A$

The total momentum of the pair never changes — not approximately, not on average: exactly, at every instant of the crunch. No outside force, no change in total momentum.

Why this matters

Inside a collision, forces are violent, brief, and unknowable — F = ma is useless there. But the total momentum sails through untouched, which means you can connect "before" to "after" while skipping the crunch entirely. That's the final lesson.