Momentum: What Collisions Conserve

The other conserved quantity

Momentum is moving mass, sign and all. Its superpower: in any collision, explosion or push-off, the total momentum of the participants is identical before and after — always, even when the crash is violent, sticky and energy-wasting. Deep down this is Newton’s third law wearing a ledger: the equal-and-opposite forces trade momentum between the partners, so the sum cannot move.

That is why recoil is not optional. A rifle fires a light, fast bullet forward; the rifle must carry the same momentum backward. A rocket is continuous recoil. Two skaters pushing off split zero momentum into two opposite shares — the lighter one leaves faster, in exact inverse proportion to mass.

Impulse: momentum’s price in time

Stopping always costs the same Δp; how it feels depends on the time you take. Airbags, crumple zones, bent knees on landing, catching a ball with soft hands — all the same trick: stretch Δt so F shrinks. Hit a windscreen instead and Δt is milliseconds, so F is enormous. Safety engineering is largely the art of buying time.

Two kinds of collision

• Elastic — the partners bounce and kinetic energy survives too (billiard balls, nearly). Equal masses trade velocities outright: the cue ball stops dead and the target leaves with its speed.
• Inelastic — the partners crumple or stick; kinetic energy partly becomes heat and deformation. Momentum is conserved regardless. Two equal cars in a head-on at equal speeds: total momentum zero before, zero after — a combined wreck at rest, all that KE spent on the metal.

That split is the exam-day compass: momentum always survives; kinetic energy only in elastic collisions. When a problem says “they stick together”, momentum is the only law you need.