Conservation of Momentum: The total momentum before collision equals total momentum after collision: p₁ᵢ + p₂ᵢ = p₁f + p₂f, where p = mv. This applies to all collision types.
Elastic Collisions: Both momentum and kinetic energy are conserved. Objects bounce off each other. Common in billiards, atomic particles. Formulas: v₁f = [(m₁-m₂)v₁ᵢ + 2m₂v₂ᵢ]/(m₁+m₂) and v₂f = [(m₂-m₁)v₂ᵢ + 2m₁v₁ᵢ]/(m₁+m₂).
Inelastic Collisions: Momentum is conserved but kinetic energy is not. Some energy converts to heat, sound, deformation. The coefficient of restitution (e) measures bounciness: e = |v₂f - v₁f| / |v₁ᵢ - v₂ᵢ|, where 0 ≤ e ≤ 1.
Perfectly Inelastic: Objects stick together after collision (e = 0). Maximum kinetic energy is lost. Final velocity: v_f = (m₁v₁ᵢ + m₂v₂ᵢ)/(m₁+m₂). Examples: tackle in football, clay balls, car crashes where vehicles lock together.
2D Collisions: Momentum is conserved separately in x and y directions. Requires vector addition. Common in billiards at angles, vehicle crashes at intersections, particle scattering experiments.
Applications: Car crash safety (crumple zones designed for inelastic collisions), sports equipment design (baseball bats, tennis rackets), particle physics (collision experiments in accelerators), space exploration (orbital mechanics, docking), ballistics and forensics.