Physics Help Forum Centroid of a rainbow shape?

 General Physics General Physics Help Forum

 Apr 17th 2011, 06:52 AM #1 Junior Member   Join Date: Mar 2011 Posts: 7 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
Apr 17th 2011, 07:50 AM   #2

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,814
 Originally Posted by Splint 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
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Tags centroid, rainbow, shape

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post ling233 Kinematics and Dynamics 3 Nov 30th 2015 09:15 AM MMM Advanced Mechanics 28 Mar 15th 2015 07:38 AM Apprentice123 Kinematics and Dynamics 6 May 22nd 2009 04:09 PM Apprentice123 Kinematics and Dynamics 1 May 21st 2009 10:59 AM Apprentice123 Kinematics and Dynamics 1 May 21st 2009 10:58 AM