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Centre of gravity definition

The centre of gravity of a body is the point where the whole weight of the body seems to act.

The centre of gravity of a regular body is at its centre.

The centre of gravity of an irregular body can be outside the body itself.

If a body is hanging freely, its centre of gravity will always be vertically below the pivot.

A beam is placed on a pivot with a weight at one end. The centre of gravity acts to the right of the pivot and so causes a moment.

If the ruler is in equilibrium, we can use the principal of moments to calculate the weight of the ruler $$\Tblue{W}$$ \begin{gather*} 0.7 \um \times 100 \text{ N} = 0.5 \um \times \Tblue{W} \\ \Tblue{W} = \dfrac {0.7 \um \times 100 \text{ N}} {0.5 \um} = 140 \text{ N} \end{gather*}

The clockwise moment caused by the centre of gravity cancels out the anti-clockwise moment caused by the weight.
The clockwise moment caused by the centre of gravity cancels out the anti-clockwise moment caused by the weight.