A headwind can cut a plane's momentum by 5,000 units and both answers are right
Momentum is simply mass multiplied by velocity, yet it underpins almost all of mechanics. In a closed system its total never changes, whether objects bounce apart, stick together or explode. Strangely, its measured value depends on who is watching, so two observers can disagree about the number and both be correct.
The letter p for momentum echoes the Latin pellere, to push or drive. Because velocity has a direction, so does momentum, and its SI unit, the kilogram metre per second, works out the same as a newton-second. A model airplane weighing 1 kilogram heading due north at 1 metre per second carries 1 kilogram metre per second of momentum, also pointing north. For a group of particles, the momenta just add up as vectors.
Newton's second law, in its original sense, says that the net force on a body equals how fast its momentum changes. Speed that same 1-kilogram plane from rest to 6 metres per second in 2 seconds and the change is 6 units, delivered at 3 per second, which matches a force of 3 newtons. The third law adds that interacting objects exert equal and opposite forces, so whatever momentum one gains the other loses. That holds however complicated the interaction, in elastic or inelastic collisions and in explosions alike.
Frame of reference matters. An aircraft of 1,000 kilograms flying at 50 metres per second has 50,000 units of momentum; meet a 5-metre-per-second headwind and its ground speed drops to 45, with momentum of 45,000. Neither calculation is wrong. Within any inertial frame, conservation still holds, a consequence of a deep symmetry: the laws of physics do not change from place to place.
The idea stretches far beyond billiard balls. Momentum is conserved, in modified forms, in special and general relativity, electrodynamics and quantum field theory. In quantum mechanics it becomes an operator, bound to position by the Heisenberg uncertainty principle. For fluids and deformable solids, a momentum-per-volume version produces the Navier–Stokes and Cauchy momentum equations.
Source: Momentum
