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March 18th, 2009, 05:23 AM  #1 
Newbie Joined: Mar 2009 Posts: 9 Thanks: 0  Centre of gravity in a hemisphere
I have a hemisphere with radius a. The density of a point P in the hemisphere is proportional with the distance from that point to the symmetry axis of the hemisphere. Than I get the question, how to determine the location of centre of gravity in the hemisphere? I am totally stuck, any little hint of what to do will be appreciated! 
March 18th, 2009, 01:57 PM  #2 
Newbie Joined: Mar 2009 Posts: 9 Thanks: 0  Re: Centre of gravity in a hemisphere
If somebody could help me find an expression for the density of a point P in the hemisphere, that would have been of great help..

March 19th, 2009, 01:54 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,686 Thanks: 661  Re: Centre of gravity in a hemisphere
If you set up the problem (integration) in cylindrical coordinates (r,z,A) where dV=rdrdzdA, then the density is simply kr at all points. The angle A is integrated over a full circle, while r and z have lower limits of 0 and upper limit defined by r^2 + z^2 = a^2, where a is the radius of the hemisphere.


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