Talk:Barycentre

Centre of mass != Centre of gravity in physics

I am not sure about the exact definition (or usage) of either of the terms in geometry (Euklidean or otherwise) but in physics, they describe two slightly but importantly different concepts: The centre of mass is always, as described in the current version of the page,

${\bar {\mathbf {x} }}_{m}=\left(\sum _{i=1}^{n}m_{i}\right){\bar {\mathbf {x} }}=\sum _{i=1}^{n}m_{i}\mathbf {x} _{i}.\,$

Similarly, the centre of gravity can be expressed as an "average" of the forces $F_{i}$ involved:

${\bar {\mathbf {x} }}_{F}=\left(\sum _{i=1}^{n}F_{i}\right){\bar {\mathbf {x} }}=\sum _{i=1}^{n}m_{i}a_{i}\mathbf {x} _{i}.\,$

Hence, ${\bar {\mathbf {x} }}_{m}$ and ${\bar {\mathbf {x} }}_{F}$ are generally only identical if the gravitational field (as expressed in terms of the acceleration $a_{i}$) is constant for all $\mathbf {x} _{i}$, such that $F_{i}=am_{i}$. Naturally, ${\bar {\mathbf {x} }}_{F}$, not ${\bar {\mathbf {x} }}_{m}$, is the point on which forces "may be deemed to act".

However, I am not sure whether these distinctions should be made in the present (geometry-focused) article because I do not remember having seen the use of "barycentre" (or centroid, for that matter) in either of these two physical contexts. --Daniel Mietchen 09:53, 27 November 2008 (UTC)

Centroid is a purely mathematical concept. As for the other 2, the Greeks didn't distinguish weight & mass, so we can't decide the meaning by etymology. Peter Jackson 12:18, 27 November 2008 (UTC)

The point I was trying to make was that for an inverse-square law such as gravitation, the resultant gravitational of a body or system is equal to the gravitational force exerted by a point mass at the barycentre. However I'ld be happy to split off a page of Centre of gravity (physics) and restrict this one to the mathematical concept of centre of mass. Richard Pinch 18:09, 27 November 2008 (UTC)

If barycentre is defined by the formula, then your statement is only exactly true for a spherically symmetric distribution (& even then only in Newtonian gravity, not general relativity). It's approximately true at large distances. Peter Jackson 18:40, 27 November 2008 (UTC)

I was certainly not aiming to be relativistic! But all the more reason to take the physical aspect to its own page. Richard Pinch 19:54, 27 November 2008 (UTC)

I provisionally deleted the mention of physics in the intro (it might come back in a different place once the article has been expanded) and added Centre of gravity (physics) to Centre of gravity (disambiguation). Don't plan to work on it anytime soon, though. --Daniel Mietchen 11:09, 28 November 2008 (UTC)

Barycentre is not a normal mathematical term, which is centroid. Centre of mass & centre of gravity are distinct physical concepts, as you say. Does barycentre have any use? Perhaps this one should be the disambiguation. Peter Jackson 15:49, 28 November 2008 (UTC)

mass/weight

I don't know about barycentre, but I do know that centre of gravity is the daily-life term for centre of mass, in the same way as weight is the daily-life term for mass. In 1901 the CIPM advised not to use "weight" and "center of gravity" for mass and center of mass anymore, but to no avail, it is still common parlance everywhere outside physics.--Paul Wormer 17:08, 28 November 2008 (UTC)

So let's have an article centre of gravity that starts out by referring the reader to centre of mass ... Peter Jackson 11:33, 1 December 2008 (UTC)