Center of Mass of a Rigid Body

Consider a bulk object, such as a bat, thrown spinning through the air at some angle. Every part of the bat is undergoing a complicated combined motion, tumbling end over end as it also arcs through the air — so does every point of the bat trace out the familiar parabolic path of projectile motion? The answer is no: only one special point traces a perfect parabola, while every other point traces a more complicated, looping path around that one point.

That one special point, whose motion is exactly the simple parabolic motion of a single thrown particle, is called the center of mass (CM) of the body. Formally, the center of mass of a body is defined as the point at which the entire mass of the body may be imagined to be concentrated, for the purpose of describing the body's translational motion — this single point genuinely represents the behaviour of the whole extended, possibly tumbling, body. …