The first thing we are going to do before entering fully into the definition of the term barycenter is to discover its etymological origin. In this case, we can state that it is a word of Greek origin since it is the result of the sum of two components of that origin:
-The noun “baros”, which can be translated as “gravity” or “weight”.
-The name “kentron”, which is synonymous with “stinger”.
The concept is used in the field of physical to name the center of gravity of something. In the field of geometry, the center of gravity is the point at which the medians belonging to a triangle intersect.
The center of gravity of a physical body, when it presents a uniform density, is coincident with its Mass center. The same is true when the matter it is distributed in the body symmetrically.
To understand precisely what the center of gravity is, therefore, it is important to know what the ideas of gravity center and center of mass. The center of gravity is called the point of application of the force resulting from the sum of the forces of gravity that have incidence on the different sectors of the body. In a material body, this center of gravity is called the center of gravity.
The center of mass, on the other hand, is the geometric point that acts dynamically as if the force resulting from external forces were applied to it. When there is uniformity in the density or the material distribution respects certain properties (such as symmetry), the center of mass coincides with the center of gravity (and, therefore, with the center of gravity).
For the geometry, the center of gravity of the surface that is contained in a plane figure is a point that, with any line that crosses it, allows the segment in question to be divided into two parts that have the same moment with respect to this line.
In addition to all the above, we can indicate these other important aspects:
-The center of gravity of a segment is the exact center of it.
-The center of gravity of a tetrahedron, for example, is the point at which the segments that connect each vertex with what is the isobaricenter intersect. This we have to show that it is a barycenter that stands out for the fact that all the masses are equal to each other.
-If what we want is to know the center of gravity of a triangle, we have to state that this will be the intersection of what the three medians of said geometric figure are.
-You have to know that when calculating the aforementioned center of gravity you can use the incorporation of what are partial center of gravity. That is, by regrouping points.
-On the other hand, it should not be overlooked that the center of gravity will not change if we proceed to multiply what all the masses are by the same factor.
-A simple and fast way to calculate the center of gravity of a geometric shape is by using a ruler and a compass.