centre of mass of polygon | Physics Library

Let A₁A₂…A_n be an n-gon which is supposed to have a constant surface-density in all of its points, M the centre of mass of the polygon and O the origin. Then the position vector of M with respect to O is

∑ _i=1ⁿ −−→
OAi

(1)

We can of course take especially O = A₁, and thus

∑n ∑n −A−−→M = 1- −A−−A→ = 1- −−A −→A . 1 n 1 i n 1 i i=1 i=2

In the special case of the triangle ABC we have

(

(2)

The centre of mass of a triangle is the common point of its medians.

Remark. An analogical result with (2) concerns also the homogeneous tetrahedron ABCD,

−−→ 1 −→ −→ −−→ AM = --(AB + AC + AD ), 4

and any n-dimensional simplex (cf. the midpoint of line segment: −−→
AM = 1
2 −→
AB ).

"centre of mass of polygon" is owned by pahio.
(view preamble)