Conservation of Momentum

The law of conservation of momentum states that in an isolated system, the total momentum remains constant if no external forces act on the system.

Mathematical Expression

p⃗total=∑miv⃗i=constant\vec{p}_{total} = \sum m_i\vec{v}_i = constant
m1v⃗1+m2v⃗2=m1v⃗1′+m2v⃗2′m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}'_1 + m_2\vec{v}'_2

Types of Collisions

  • Elastic collisions (kinetic energy conserved)
  • Inelastic collisions (kinetic energy not conserved)
  • Perfectly inelastic collisions (objects stick together)

Applications

  • Rocket propulsion
  • Billiard ball collisions
  • Car crashes
  • Particle physics
  • Space vehicle maneuvers