Conservation of momentum

For an isolated system of interacting particles, total momentum stays constant; this follows directly from the second and third laws.

Recoil of a gun: gun and bullet start at rest, so after firing their momenta are equal and opposite; the heavier gun moves back much more slowly.

In any collision the momentum lost by one body equals the momentum gained by the other, whatever happens to the kinetic energy.

When one body throws another (for example a person on smooth ice throwing a ball), velocities must be measured relative to the ground before applying conservation.

Momentum is conserved as a vector; in one-dimensional problems keep track of direction with signs.