The center of mass of a system of particles is the point at which the system's whole mass can be considered to be concentrated for the purpose of calculations. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the object (but not necessarily in contact with it). 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.
The center of mass is often called the center of gravity, but this is only true in a system where the gravitational forces are uniform. For example, on the Earth, differences in the pull of gravity may safely be ignored.Barycenter may refer to the center of mass but is most commonly used when referring to the point at which the gravitational forces exerted by two objects are equal.
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