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March 18th, 2009, 04:23 AM   #1
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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!
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March 18th, 2009, 12:57 PM   #2
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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..
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March 19th, 2009, 12:54 PM   #3
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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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