Center of mass
Overview
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the center of mass or barycenter of a system is the average
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

location of all of its mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

. In the case of a rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...

, the position of the center of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space, such as shot
Lead shot is a collective term for small balls of lead. These were the original projectiles for muskets and early rifles, but today lead shot is fired primarily from shotguns. It is also used for a variety of other purposes...

from a shotgun
Shotgun
A shotgun is a firearm that is usually designed to be fired from the shoulder, which uses the energy of a fixed shell to fire a number of small spherical pellets called shot, or a solid projectile called a slug...

or the planets of the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

, the position of the center of mass is a point in space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

among them that may not correspond to the position of any individual mass.

The use of the mass center often allows the use of simplified equations of motion, and it is a convenient reference point for many other calculations in physics, such as angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

or the moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...

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