3.2.2—Centre of mass

For particles of masses mᵢ at positions xᵢ, the centre of mass satisfies x̄=Σmᵢxᵢ/Σmᵢ, with the same weighted-average rule applied independently to y-coordinates.

Heavier masses pull the centre towards them. Set an origin and sign convention first; coordinates may be negative, and the centre can lie outside the material for a separated system.

Masses 2 kg at x=0 and 6 kg at x=4 m have x̄=(2·0+6·4)/8=3 m, much nearer the larger mass.

The centre of mass is not always the geometric centre and is not necessarily a point inside an irregular or multi-part object.