conservation of momentum

Meaning: Momentum is a vector, p = mv. If the net external force on a system is zero (or negligible during a brief collision), its total momentum does not change. Internal forces are equal and opposite by Newton's third law, so they move momentum between objects without changing the total. Each component (x and y) is conserved separately.

Equation: m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′, where m is mass (kg), v is velocity before the collision (m/s), and v′ is velocity after (m/s). Velocities carry signs for direction. For objects that stick together: m₁v₁ + m₂v₂ = (m₁ + m₂)vf.

On the MCAT: Typical setups are colliding carts, a bullet embedding in a block, gun recoil, a person jumping off a boat, and two-dimensional billiard-ball collisions. You predict a final speed or direction, such as the lighter object recoiling faster. Elastic collisions also conserve kinetic energy; inelastic ones lose some to heat, sound and deformation. In a ballistic pendulum, momentum is conserved in the collision, then mechanical energy is conserved in the swing.

Common confusion: Students think momentum is lost in an inelastic collision because kinetic energy drops. For an isolated system, momentum is conserved in every collision; only kinetic energy depends on the collision type. Also give opposite directions opposite signs.