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Old Apr 17th 2011, 06:52 AM   #1
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Centroid of a rainbow shape?

Hi,

I'm trying to find out the formula to calculate the centroid of a semicircular surface with a smaller semicircular cut out (rainbow shape).

I drew the shape in a CAD program which showed the centroid to be 64.988mm. The outer radius is 125mm (centroid 53.05mm) and the inner 75mm (centroid 31.83mm). I used 4r/3Pi to find each centroid but I'm not sure about how to get the final centroid. Anyone tell me the formula?

Thanks
Splint
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Old Apr 17th 2011, 07:50 AM   #2
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Originally Posted by Splint View Post
Hi,

I'm trying to find out the formula to calculate the centroid of a semicircular surface with a smaller semicircular cut out (rainbow shape).

I drew the shape in a CAD program which showed the centroid to be 64.988mm. The outer radius is 125mm (centroid 53.05mm) and the inner 75mm (centroid 31.83mm). I used 4r/3Pi to find each centroid but I'm not sure about how to get the final centroid. Anyone tell me the formula?

Thanks
Splint
In this case the center of mass is going to be the centroid of the object. Thus
R = (integral) r dm
where R and r are vectors. In this case you have an enormous simplification...by symmetry you know it is going to be somewhat above the where the center of the (semii)circle would be. So your integral will be
Y = (integral) Y dm

Use the (I presume) uniform area density to change the dm to a dA and go from there.

-Dan
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