What is the center of mass?

The term "center of mass" is used not only in mechanics and in calculating the motion of celestial bodies, but also in everyday life. Just people do not always think about what kind of laws of nature are manifested in this or that situation. For example, skaters in pair skating actively use the center of mass of the system, when they unwind, holding hands.

Before, before the discovery of the laws of gravitation by Newton, it was believed that the Earth and all the planets of the system rotate around the central star - the Sun. That is, the location of the central point coincides with the physical center of the star. Theoretically, it was quite possible. But then Newton proved that objects are mutually attracted to each other - not only does the Sun affect the planet, but the latter also affects the star. Since the formula involves not only the square of the distance, but also the mass, the forces of interaction are unequal. As a result, it turns out that the center of mass of the "Earth-Sun" mechanical system is not located in the middle of the star, but is shifted relative to the physical center. Therefore, around this point both the Earth and the Sun rotate.

The center of mass allowed us to first assume, and then brilliantly confirm the existence in the star system of Sirius of an unobtrusive satellite. Observing the motion of the star, the astronomer drew attention to its strange undulating displacements. It turned out that Sirius is a double star. They revolve around the center of mass, which causes the observed oscillations.

The center of mass is completely independent of the type of connection of objects: magnetic fields, rope, rod. Imagine two balls with masses m1 and m2, connected to each other by a light metal rod of length L. Due to this part of the momentum imparted to the ball m1 will be transmitted and m2. If we now throw this bundle of balls at an angle into the air, then the flight will seem at first glance messy: although the balls "tumbling", changing their position, a certain common point on the rod moves as it should, along a parabolic trajectory. This is the center of mass. It does not have to be in the object itself. For example, in the example with stars, it is located in the void. When performing calculations, it is assumed that the total aggregate mass of objects is concentrated precisely at a given point, the vectors of external forces are also applied to it. If we impart an impulse to any body of the system, then, in full accordance with the laws of conservation of the pulse energy, its value at the point of the center of mass will be zero. If we consider a system isolated from external influences, the motion of its center of mass occurs at a constant rate. Accordingly, in this case we can talk about the inertial frame of reference.

The concept of the center of mass is also used in the design of ships. It is necessary to take into account not just two bodies, but a huge number of them and all lead to a single denominator. Errors in the calculations mean the lack of stability of the ship: in one case it will be excessively immersed in water, at the risk of going to the bottom with the smallest waves; And in the other too elevated above sea level, creating the danger of a coup on the side. By the way, that's why every thing on board should be in its place, provided by calculations: the most massive at the very bottom.

The center of mass is used not only for celestial bodies and for designing mechanisms, but also for studying the "behavior" of microworld particles. For example, many of them are born in pairs (electron-positron). Possessing the original rotation and obeying the laws of attraction / repulsion, they can be viewed as a system with a common center of mass.

For simple systems, it is quite easy to calculate the position of the center of mass point. For this, it is necessary to sum the products of the mass of each body by the radius vector, and divide the obtained value by the total mass.