centroid of a plane area

Thread Starter

logearav

Joined Aug 19, 2011
243
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.
In fact i have no clue as to how to proceed. Please help
 

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MrChips

Joined Oct 2, 2009
30,712
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.
 
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