Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Center of mass
An experimental method to locate the three-dimensional coordinates of the center of mass begins by supporting the object at three points and measuring the forces, F, F, and F that resist the weight of the object, formula_32 (formula_33 is the unit vector in the vertical direction). Let r, r, and r be the position coordinates of the support points, then the coordinates R of the center of mass satisfy the condition that the resultant torque is zero,
or
This equation yields the coordinates of the center of mass R* in the horizontal plane as,
The center of mass lies on the vertical line L, given by
The three-dimensional coordinates of the center of mass are determined by performing this experiment twice with the object positioned so that these forces are measured for two different horizontal planes through the object. The center of mass will be the intersection of the two lines L and L obtained from the two experiments.