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rock.freak667

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## Homework Statement

I need to get the centroid of this shape

http://img713.imageshack.us/img713/5607/section.jpg [Broken]

it's a semi-circular section basically. On the left most side, the distance from the origin to to where it cuts the y-axis is 'R' and the distance from the x-axis to the end of the upper arc is 'r'.

## Homework Equations

[tex]I_x = \int y^2 dA[/tex]

[tex]I_y= \int x^2 dA[/tex]

[tex]A \bar{x}= \int xy dA[/tex]

[tex]A \bar{y} = \int y dA[/tex]

## The Attempt at a Solution

I just need to know if my integrals are set up properly

The equation of the entire circle would have been x

^{2}+y

^{2}=R

^{2}.

[tex]A= \int y dx = \int_{0} ^{r} \sqrt{R^2-x^2}[/tex]

Assuming my 'A' is correct

dA=y dx

[tex] A \bar{x} = \int xy dA = \int xy^2 dx = \int_{0} ^{r} x(R^2-x^2) dx[/tex]

my object is symmetrical about the x-axis so [itex]\bar{y} = 0[/tex]

[tex]I_x = \int y^2 dA = \int y^3 dx = \int_{0} ^{r} (R^2-x^2)^{\frac{3}{2}}dx[/tex]

[tex]I_y = \int x^2 dA = \int x^2 y dx = \int_{0} ^{r} x^2\sqrt{R^2-x^2)dx[/tex]

I think my limits may be wrong, but the integrands should be correct.

Also, if someone can just link me to a site with the centroid and second moment of area of this shape that would be helpful as I don't need to actually derive it in my report, I just need to use the result.

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