Finding coordinates of a centroid

In summary, the conversation discusses finding the coordinates of the centroid for a region bounded by two curves using the formulas for center of mass in x and y variables. The individual is having trouble setting up the integral and is confused about the range for y. They also mention adjusting for density in the y-variable equation.
  • #1
hahaha158
80
0

Homework Statement



Find the exact coordinates of the centroid for the region bounded by the curves x=5-y^ 2 and x=0

I am not sure about this one because it uses dy instead of dx i think.

I tried to set it up like this

x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]

This does not give me the right answer, can anyone help? I have no trouble solving it if it gives me a region bounded by y=x (for example), but i think that the centre of mass in y-variable means that Mx and My are reversed?

Very confused, thanks for any help you can give

Homework Equations



x=My/A
y=Mx/A


The Attempt at a Solution

 
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  • #2
hahaha158 said:
x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]
Why the 0.5 at the front?
Also, you have the wrong range for y.
 
  • #3
haruspex said:
Why the 0.5 at the front?
Also, you have the wrong range for y.

i added the 0.5 because i tried using the My equation for centre of mass in y-variable whch is density/2∫[f(y)^2-g(y)^2]dy from a to b. Would the range be -5^.5 to 5^.5?
 

Related to Finding coordinates of a centroid

1. What is a centroid?

A centroid is the geometric center of a shape or object. It is the point at which all the individual points of the shape balance each other out, making it the center of gravity or balance.

2. How do you find the coordinates of a centroid?

To find the coordinates of a centroid, you need to take the average of all the x-coordinates and the average of all the y-coordinates of the points that make up the shape. This will give you the x-coordinate and y-coordinate of the centroid.

3. Can the centroid be located outside of the shape?

Yes, the centroid can be located outside of the shape. This can happen if the shape is not symmetrical or if it has irregularly distributed points.

4. What is the significance of finding the centroid of a shape?

Finding the centroid of a shape can be useful in many applications, such as engineering and architecture. It can help determine the center of mass and balance of an object, which is important for stability and structural integrity.

5. Are there different methods for finding the centroid of a 3-dimensional shape?

Yes, there are different methods for finding the centroid of a 3-dimensional shape, depending on the shape's complexity. One method is to divide the shape into smaller, simpler shapes and find the centroid of each of those shapes. Another method is to use mathematical equations specific to certain shapes, such as the centroid formula for a cone or sphere.

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