# Centroid,centre of mass and centre of gravity

monty37
may i know what is the difference between centroid,centre of gravity and centre of mass
of a body?is it necessary that all the points coincide?

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Those all mean the same thing.

davieddy
may i know what is the difference between centroid,centre of gravity and centre of mass
of a body?is it necessary that all the points coincide?

Take a triangle for example.

The centroid is the mean position of elements of area.
The centre of mass is the mean position of elements of mass.
In a uniform gravitaional field, the force of gravity on the triangle
can be taken as acting through the centre of mass.

But if the mass per unit area of the triangle varied, the centre of mass
would not (usually) coincide with the centroid.

Note also that the assumption that the earth's gravity is the same
as if its mass were all located at the centre is only true because of
its spherical symmetry.

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"centroid" is a purely mathematical, geometric concept- the geometric center of a body. It can be calculated as the center of mass of an object with constant density. "Center of mass" and "center of gravity" are the same- although the concepts are slightly different: the concept "center of gravity" strictly speaking requires, as davieddy said, a uniform gravitational field while "center of mass" does not. But they are exactly the same point on an object.

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