- #1

geoffrey159

- 535

- 72

## Homework Statement

Find the center of mass of an equilateral triangle with side ##a##

## Homework Equations

## \vec R = \frac{1}{M} \int \vec r \ dm ##

## dm = \frac{M}{A} dx dy ##

## A = \frac{\sqrt{3}}{4}a^2 ##

## The Attempt at a Solution

I set a pair of orthogonal axis ##(\vec x,\vec y)## so that one side of the triangle lies on the ##x## axis, and one vertex is at the origin.

I find the following position for the center of mass:

##R_x = \frac{1}{A} (\int_0^{\frac{a}{2}}\int_0^{\sqrt{3}x} x \ dy\ dx + \int_\frac{a}{2}^{a}\int_0^{\sqrt{3}(a-x)} x \ dy\ dx ) = \frac{a}{2}##

##R_y = \frac{1}{A} (\int_0^{\frac{a}{2}}\int_0^{\sqrt{3}x} y \ dy\ dx + \int_\frac{a}{2}^{a}\int_0^{\sqrt{3}(a-x)} y \ dy\ dx ) = \frac{a}{2\sqrt{3}}##

Do you think it is correct?