Momentum and Its Conservation

Momentum

Momentum is the measure of a body's mechanical motion: p = m·v, its unit is kg·m/s.

Impulse of a Force

The impulse of a force is equal to the change in the body's momentum:

F·Δt = Δp = m·v₂ − m·v₁

Newton's second law in terms of momentum: F = Δp/Δt.

Conservation Law

• In a closed system, momentum is conserved: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'.
• In an inelastic collision, the bodies move together: m₁v₁ + m₂v₂ = (m₁ + m₂)·u.
• In an elastic collision, both momentum and kinetic energy are conserved.
• Jet propulsion (a rocket) is based on the conservation of momentum.

Collision	Momentum	Kinetic energy
Elastic	conserved	conserved
Inelastic	conserved	not conserved

Example: a 3 kg body moving at 4 m/s collides with a stationary 1 kg body and they move off together. u = 12/4 = 3 m/s.

Momentum is a vector quantity: direction must be taken into account. For a ball bouncing back from a wall, Δp = m·v − (−m·v) = 2mv.