# What is the centroid of a C-shape?

• nobodyuknow
In summary, the conversation is about finding the centroid of a shape with given dimensions. The formula for finding the centroid is discussed and the attempt at a solution is given. The confusion about the shape's centroid not being on the shape itself is clarified with the example of a doughnut having its centroid at the center.

## 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?

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?

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

CWatters said:
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).

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.

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

## 1. What is the centroid of a C-Shape?

The centroid of a C-Shape is the point where all the individual centroids of its constituent shapes intersect, and it is the geometric center of the shape.

## 2. How is the centroid of a C-Shape calculated?

The centroid of a C-Shape can be calculated by dividing the shape into smaller, simpler shapes and using the formula for finding the centroid of each individual shape. The centroid of the C-Shape can then be determined by finding the intersection point of these individual centroids.

## 3. What is the significance of the centroid in a C-Shape?

The centroid in a C-Shape is important because it is the point where the shape is in perfect balance. This means that if the shape was supported at its centroid, it would not tip over or rotate when subjected to external forces.

## 4. How does the location of the centroid affect a C-Shape?

The location of the centroid can greatly affect the behavior of a C-Shape when subjected to external forces. If the centroid is closer to one side of the shape, it will tend to tip over more easily in that direction. However, if the centroid is located at the center of the shape, it will be more stable and resistant to tipping.

## 5. Can the centroid of a C-Shape be outside of the shape itself?

No, the centroid of a C-Shape will always be located within the boundaries of the shape. This is because the centroid is the point where the shape is in perfect balance, and if it was located outside of the shape, it would not be in equilibrium.