# Centroid of a C-Shape

## Homework Statement

http://prntscr.com/fcbm8

Find the centroid - All dimensions are in mm

## Homework Equations

xbar = (A1X1+A2X2) / (A1+A2)

Similarly for Ybar I assume

## The Attempt at a Solution

I got the y co-ordinate to be 20.428mm, and would assume that the x coordinate would be 5mm.

Is this right?

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CWatters
Homework Helper
Gold Member
You can divide the shape into three rectangular parts several different ways but I used two vertical lines in the obvious places. I assumed the origin is in the bottom left corner.

xbar = (A1X1+A2X2+A3X3) / (A1+A2+A3)

= (700*5 + 800*30 +400*30) / (700+800+400)
= 20.789

ybar = (A1Y1+A2Y2+A3Y3) / (A1+A2+A3)

= (700*35 + 800*10 + 400*65) / (700+800+400)
= 30.789

This is what confused me, does this mean the centroid is not on the shape itself?

CWatters
Homework Helper
Gold Member
In this case yes. Where would the centroid of a doughnut be?

HallsofIvy
Homework Helper
In this case yes. Where would the centroid of a doughnut be?
In the center, of course. That's what the "centroid" is- the geometric center. If you were to represent the doughnut as two circled in the in the xy-plane, centered at the origin with radii r and R, and then have other circles as the thickness of the doughnut, the centroid would be at (0, 0, 0).

CWatters