Momentum and its change

Momentum

• The momentum of a body is the product of its mass and its velocity vector: p = m v; it is a vector quantity pointing in the direction of the velocity.
• Its unit is kg·m/s in the absolute system, and g·cm/s in the centimetric (C.G.S.) system.
• The change of momentum is the final momentum minus the initial one: Δp = m v₂ − m v₁.
• In motion along a straight line choose one direction as positive; velocities in the opposite direction enter the calculation with a negative sign.

Worked example

1. A body of mass 2 kg moves at 3 m/s to the right, strikes a wall and returns at 5 m/s to the left. Taking right as positive: v₁ = +3, v₂ = −5, so Δp = 2(−5) − 2(3) = −10 − 6 = −16 kg·m/s, i.e. a change of 16 kg·m/s directed to the left.
2. Note that the change is not 2 × (5 − 3) = 4; ignoring the reversal of direction is the standard error.