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

 
Physics news on Phys.org
  • #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?
 

FAQ: Finding coordinates of a centroid

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.

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.

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.

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.

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.

Similar threads

Please help me finding this centroid of a graph. Thank you.
Replies
7
Views
3K
Find the coordinates of intersection between tangents and given curve
Replies
15
Views
2K
Verify Green's Theorem in the given problem
Replies
10
Views
1K
Polar coordinates of the centroid of a uniform sector
Replies
5
Views
1K
How should I find the equilibrium points and the general equation?
Replies
3
Views
571
Calculate this Integral around the Circular Path using Green's Theorem
Replies
3
Views
1K
How should I show that these systems have no periodic solutions?
Replies
2
Views
311
Centroid Position of a Lamina Bounded by a Curve
Replies
2
Views
2K
Find Values of Osculating Circle Tangent to a Parabola
Replies
4
Views
792
Solve the attached problem that involves circle and tangent
Replies
2
Views
865

Hot Threads

Recent Insights

Back
Top