1.2 Barycentre, Centre of weight gravity, centre of gravity, centre of mass
The barycentre is one among the many centre points of a geometric figure; this is valid at any point of history.
The centre of a falling body, when we refer to ancient times (from Archimedes to Galileo), its definition is slightly different for each author (Archimedes, Pappus, Stevin), is the centre point such that if a body was hanging from it, the body wouldnt lose balance.
The centre of weight gravity, when we refer to modern and contemporary ages, is the point where the gravitational force (weight) is applied; it is also called barycentre.
The centre of mass, during modern and contemporary times, is the point in which the static moment of every axis passing through it is zero. In this peculiar case in which the distribution of the mass is uniform, the centre of mass corresponds to the geometrical barycentre of the figure considered; thus, the reference axis is called barycentric axis.
During the ancient time, since the weight of bodies was considered unalterable, the centre of weight gravity used to match the geometrical barycentre.
In the peculiar case of uniform mass distribution, it is underlined that the centre of mass matches with what was called centre of weight gravity during ancient times.
During modern and contemporary times, even if it was known that the gravity force (weight) of a body was alterable, how could they name it centre of gravity or barycentre? Moreover, how could they believe that the centre of mass corresponded to the centre of gravity?
The centre of mass corresponds to the geometrical barycentre exclusively when the mass distribution is uniform.
If we treat the simple case of uniform mass distribution, also when there is a symmetry, the centre of gravity never matches with the centre of mass. The classical example is the circle in which the centre of mass corresponds to the centre of the circle, but the centre of gravity lies beneath it and therefore cannot be the barycentre.
The rate of distance between the centre of gravity and the centre of mass peaks on the earths surface, diminishing with altitude. Moreover, it increases with:
a) mass growth;
b) density reduction;
c) shape, growing from the sphere to the cylinder to the cube.
All of this is the consequence of my scientific discovery: The shape of solid bodies.
The love for the Pursuit of the Truth and Knowledge, regardless of The shape of solid bodies, has led me to new insights about:
a) buoyant bodies;
b) hanging/rotating bodies.