Momentum and its conservation

Key Definition Linear momentum is defined by p = mv and is a vector quantity with SI unit kg m s⁻¹.

Its direction is always the same as the velocity, so a sign convention must be chosen before any one-dimensional calculation.

Doubling the mass or doubling the velocity doubles the momentum, because momentum is directly proportional to each.

Key Definition The principle of conservation of linear momentum states that the total momentum of a closed system remains constant provided no external resultant force acts on it.

This principle follows directly from Newton's second law in the form F = Δp/Δt (the resultant force equals the rate of change of momentum), combined with Newton's third law.

Equal and opposite forces between two interacting bodies act for the same time, so they produce equal and opposite changes in momentum that cancel exactly.

In Edexcel one-dimensional problems, this conservation is applied as:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

A clear positive direction must be stated and the signs of the velocities handled carefully.