# Barycentre

From Citizendium

In geometry, the **barycentre** or **centre of mass** or **centre of gravity**^{[1]} of a system of particles or a rigid body is a point at which various systems of force may be deemed to act. The gravitational attraction of a mass is centred at its barycentre (hence the term "centre of gravity"), and the (classical) angular momentum of the mass resolves into components related to the rotation of the body about its barycentre and the angular movement of the barycentre.

The barycentre is located as an "average" of the masses involved. For a system of *n* point particles of mass located at position vectors , the barycentre is defined by

For a solid body *B* with mass density at position , with total mass

the barycentre is given by

## Notes

- ↑ In physics, the centres of mass and gravity describe two slightly but importantly different concepts: While the centre of mass is defined like above as a spatial average of masses, the centre of gravity can be expressed similarly as a spatial average of the forces involved: Hence, and are generally only identical if the gravitational field (as expressed in terms of the acceleration ) is constant for all , such that . The point on which forces may be deemed to act is then naturally and not .