Center of Gravity & Center of Mass

Center of mass:

The center of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. The center of mass is a function only of the positions and masses of the particles that comprise the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the object. In the case of a loose distribution of masses in free space, such as, say, shot from a shotgun, the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass. In the context of an entirely uniform gravitational field, the center of mass is often erroneously called the center of gravity — the point where gravity can be said to act.
The center of mass of a body does not always coincide with its intuitive geometric center, and one can exploit this freedom. Engineers try to design a sports car's center of mass as low as possible to make the car handle better. When high jumpers perform a "Fosbury Flop", they bend their body in such a way that it is possible for the jumper to clear the bar while his or her center of mass does not.
The center of momentum frame is an inertial frame defined as the inertial frame in which the center of mass of a system is at rest. A specific center of momentum frame in which the center of mass is not only at rest, but also at the origin of the coordinate system, is sometimes called the center of mass frame, or center of mass coordinate system.

Center of gravity:

The center of gravity of a collection of masses is the point where all the weight of the object can be considered to be concentrated. Examples can be seen in my previous post.