term "center of gravity" is used not only in mechanics and in the calculation of the motion of celestial bodies, but also everyday life.Just people do not always think about what the laws of nature manifested in a given situation.For example, skaters in the pairs figure skating actively using the center of mass of the system when to spin, holding hands.
Earlier, before the opening of Newton's law of gravity, it was believed that the Earth and all the planets of the system revolve around the central star - the sun.That is, the location of the center point coincides with the physical center of the star.Theoretically, it was possible.But then Newton proved that the objects are mutually attracted to each other - not just the sun influences the planet, but also affects the latest star.Since the formula contains not only the square of the distance, but the mass, the interaction forces are unequal.The result is that the center of mass of the mechanical system "Earth-Sun" is not located in the middle of the star, and is offset relative to the physical center.Therefore this point revolve around the Earth, and the Sun itself.
center of mass allowed to assume first, and then brilliantly confirm the existence of the system of the star Sirius satellite unobtrusive.Watching the movement of the stars, an astronomer noticed her strange undulating bias.It turned out that Sirius - a double star.They revolve around the center of mass, which causes fluctuations seen.
center of mass does not depend on the type of connection objects: magnetic field, the rope, the cane.Imagine two balls with masses m1 and m2, connected with one another light metal rod length L. This part of the momentum imparted to the ball m1, and be passed m2.Now, if we throw this bunch of balls in the air at an angle, the flight only at first glance seem erratic although the balls "somersault", changing its position, some common point on the rod moves as it should - on a parabolic trajectory.This is the center of mass.It is not necessarily located in the object.For example, in the example with the stars it is located in the void.In the calculations, it is believed that the total mass of all the objects is concentrated at this point, it is accompanied by the vector of external forces.If you tell any body system momentum is in full compliance with the laws of conservation of energy-momentum of its value at the center of mass is equal to zero.If considered in isolation from external influences system, the motion of its center of mass at a constant speed.Accordingly, in this case we can speak of an inertial reference system.
concept of the center of mass is also used in designing ships.It is necessary to take into account not just two bodies and a huge number and all lead to a common denominator.Errors in the calculation of mean lack of stability of the ship, in one case, he is too immersed in water, risking to sink at most minor waves;and the other is too elevated above sea level, creating the danger of revolution on its side.By the way, that's why every thing on board should be in place, provided calculations: the most massive at the bottom.
center of mass is used not only in relation to celestial bodies and the design of mechanisms, but also in the study of "behavior" of the particles of the microworld.For example, many of them are born in pairs (electron-positron).With the original rotation and subject to the laws of attraction / repulsion, they can be considered as a system with a common center of mass.
For simple systems to calculate the position of the point of the center of mass is quite easy.To do this, you need to sum up the work of each body weight on the radius vector, and the resulting value is divided by the total weight.