Center of Gravity

Every rigid body is, at bottom, a collection of a great many point masses, and each of these individual point masses experiences its own small gravitational pull towards the center of the Earth. Because any everyday-sized rigid body is minuscule compared to the size of the Earth, all of these countless individual gravitational pulls act, to excellent approximation, as parallel forces, all pointing in the same (locally "downward") direction.

The resultant of all these parallel individual weights always acts through one single, fixed point (relative to the body) — this point is called the center of gravity of the body (with respect to Earth). Formally: the center of gravity of a body is the point at which the entire weight of the body may be taken to act, whatever the body's position or orientation happens to be.

Relation to center of mass. The center of gravity coincides exactly with the center of mass of a rigid body whenever the gravitational field is uniform across the entire body — a condition that holds to outstanding accuracy for any object of ordinary, everyday, or even continental scale on Earth's surface (the field genuinely varies only over truly enormous, planetary-scale distances). The deeper concept of a gravitational field itself is developed fully in a later unit on gravitation.

Locating the center of gravity of an irregular lamina. Two complementary practical methods exist:

1. By pivoting. The lamina is supported on a fine pivot at various trial points, by trial and error, until a point is found where the lamina stays perfectly horizontal when released. At that point, the pivot's upward normal reaction force exactly cancels, and acts along the same vertical line as, the downward weight acting through the center of gravity — so the net torque on the lamina, about every point, is exactly zero, and it remains in static equilibrium (horizontal). …