The Center of Mass
of an object (of mass m) is the single point
that moves in the same way as a point mass (of mass m) would move when subjected to the same external forces
that act on the object. That is, if the resultant force
acting on an object (or system of objects) of mass m is F
, the acceleration
of the center of mass of the object (or system) is given by acm
If the object is considered to be composed of tiny masses m1, m2, m3, and so on, at coordinates (x1,y1,z1), (x2,y2,z2), and so on, then the coordinates of the center of mass are given by
where Σ = sigma, the sequence of
Xcm = Σ(xi * mi) / Σ(mi)
Ycm = Σ(yi * mi) / Σ(mi)
Zcm = Σ(zi * mi) / Σ(mi)
where the sums extend over all masses composing the object. In a uniform gravitational field, the center of mass and the center of gravity coincide.
For the integration method of center of mass, check out Center of Mass: Part Two.