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Centres of Gravity of a Lamina

We can find the distance of the centre of gravity from a line of a point by taking moments about the point for each part of the lamina. We equate this to the moment of the lamina as a whole and solve the equation to find the distance of the centre of gravity from the axis.

The lamina below has uniform density, so the centre of gravity of P is at the centre of P and the centre of gravity of Q is at the centre of Q.

Taking moments about AB, we can draw up the table:

Section

Distance of centre of gravity from AB

Area

Distance * Area

P

Q

Lamina

Taking moments about A'B':

Section

Distance of centre of gravity from A'B'

Area

Distance * Area

P

Q

Lamina