# Centre of gravity: Adjusting position

If an object is freely suspended from a pivot, why does the centre of gravity fall directly below that pivot? Would this be the same in non-uniform gravitational fields?

• We define "below" by the direction of gravitational attraction. The center of gravity by definition is along that direction. – Lewis Miller Feb 28 '16 at 22:55

F is the force due to gravity. r is the distance between the point of application of the force and the pivot. $$\theta$$ is the angle between the direction of F and r.
The torque $$\tau$$ is then $$\tau = \mathbf {Fr}\sin\theta$$ When the centre of gravity is exactly below the pivot then the angle, $$\theta=0$$ so $$\tau=0$$. The body stays in equilibrium due to absence of net rotational force and net translational force(the weight of the rod is counteracted by the reaction force of the pivot).