3.2.4—Centre of mass

If components have masses m₁,m₂,… and centres at r₁,r₂,…, the combined centre is r̄=(Σmᵢrᵢ)/(Σmᵢ). Each component’s mass must be proportional to its area or volume only when density is common.

Choose a convenient reference point, include holes or removed pieces with negative area when appropriate, and check that the result lies between the extreme positions of positive masses.

A 3 kg block at x=1 m joined to a 1 kg block at x=5 m gives x̄=2 m, not 3 m: the lighter block should shift the centre only modestly.

Equal-sized parts do not imply equal masses when densities differ; never replace mass weights by geometry without checking the model.