Linear Momentum

Linear momentum is mass times velocity, p = mv, a vector that points the same way as the velocity and is measured in kg·m/s. It's especially useful for collisions (brief, strong interactions where outside forces barely matter) and explosions (where forces inside a system push its parts apart).

Impulse is the average force times the time it acts, J = F_avg Δt, and it equals the change in momentum, J = Δp; on a force–time graph it's the area under the curve, and on a momentum–time graph the slope is the net force. That's why airbags and bending your knees reduce the force on you: they stretch out the time it takes to stop.

If the net external force on a system is zero, its total momentum stays the same, so any momentum one object gains, another loses. You use this to find velocities just before and after a collision or explosion, and the system's center of mass keeps moving at a constant velocity. In one dimension you solve these fully; in two dimensions you may set up the momentum equation for each direction and reason about it, but you won't have to solve the equations simultaneously.

In an elastic collision the system's total kinetic energy is the same before and after; in an inelastic collision some of it turns into other forms, such as thermal energy or sound. Momentum is conserved in both kinds when no net external force acts. When the objects stick together and move off as one, the collision is called perfectly inelastic.