Centres of Mass, Summation Method

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For a uniform regular body with symmetry eg a cube, flat triangle, sphere, the centre of mass is in the middle. Unfortunately, most bodies are not regular or uniform. To find the centre of mass of an arbitrary body we must use one of the formulae,

or or same variation of one of these formulae.

For example, we find the centre of mass of the object below. For illustrative purposes, take the density of the second one as half the density of the first.

Mass

Distance of centre of mass from AB

Distance of centre of mass from AC

Moment About AB

Mnment About AC

Small Rectangle

1.5

1

Large Rectangle

8

2.5

Take moments about AB:

Take moments about AC:

The centre of gravity is right from AB and below AC.

The process for the Integral Method is similar.

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