4.7 Centre of Gravity and Centre of Mass
An object is composed of a large number of small particles. Each particle is acted upon by the gravitational force directed towards the centre of the Earth. As the object is small compared to the Earth, the value of g can be taken as uniform over all particles. Therefore, each particle experiences the same force mg.
The sum of the gravitational forces acting on all particles is equal to the total weight of the object:
w = M g
Where M = ∑m is the mass of the object.
lightbulbCentre of gravity is that point where the total weight of the body appears to be acting.
If a body is supported at its centre of gravity, it stays there without rotation. The centre of gravity of an object of regular shape lies at its geometrical centre.
Table 4.1: Centre of Gravity of Some Shapes
| Object | Centre of Gravity |
|---|---|
| Square, Rectangle | Point of intersection of the diagonals |
| Triangle | Point of intersection of the medians |
| Round plate | Centre of the plate |
| Sphere | Centre of the sphere |
| Cylinder | Centre of the axis |
| Metre rule | Centre of the rod |