# centroid of a plane area

Discussion in 'Physics' started by logearav, Feb 22, 2012.

1. ### logearav Thread Starter Member

Aug 19, 2011
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0
Revered members,
Please look at my attachment. I need to find the centroid of the plane area. The radius of semi circle at the bottom and top is 3 cm. I dont know how to proceed. Should i use the formula for semicircle or semi ellipse? Help in this regard will be greatly appreciated.

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2. ### MrChips Moderator

Oct 2, 2009
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5,936
Have you done integration as yet?

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3. ### logearav Thread Starter Member

Aug 19, 2011
248
0
I know integration. Just guide me how to proceed Mrchips. Thanks for your reply

4. ### MrChips Moderator

Oct 2, 2009
18,689
5,936
The centroid (or center of mass) along one axis is the sum of each point mass multiplied by its distance from a reference point, then divided by the sum of each point mass.

You can express this as:

$\overline{x} = \frac{\sum{mx}}{\sum{m}}$

The first step would be to find the centroid of a semi-circle.

Do you know how to calculate the area of a circle using integrals knowing the formula for circumference?

circumference = $2\pi r$

If so, calculate the centroid of a semi-circle by dividing the semi-circle into small half rings going out from the center of the circle.

Last edited: Feb 23, 2012