My Math Forum Centre of gravity in a hemisphere

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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: 6,641 Thanks: 625 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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# relation between centre of gravity and centre of a hemisphere

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