Centroid of a C-Shape

nobodyuknow

1. The problem statement, all variables and given/known data

http://prntscr.com/fcbm8

Find the centroid - All dimensions are in mm

2. Relevant equations

xbar = (A₁X₁+A₂X₂) / (A₁+A₂)

Similarly for Ybar I assume

3. 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?

CWatters

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

Best show your working as my answer is quite different.

nobodyuknow

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

CWatters

In this case yes. Where would the centroid of a doughnut be?

HallsofIvy

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

I know. I was using it as an obvious example for the OP to think about. eg a shape that has a centroid that's not on the surface of the shape.

nobodyuknow

Yeah, I was probably thinking more about a centroid of a mass, but even then, there's still the donut which proves me redundant.