Calculating the COM of a Spherical Plot

What is everyone excited for??? More math! Ok, maybe not, but I’ll come back to the electronics projects later (including investigating the Parallax RFID reader, Arduino FIO, and heck, maybe even some more LED fun). In the meantime, let’s get back to math.

What do the volume calculations look like, and how would one go about calculating the center of mass/geometric centroid of a spherical plot? More after the break…
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Calculating the COM of a 3D Surface of Revolution

My current research at Rutgers focuses on identifying the cognitive mechanisms that are employed when perceiving the shape and structure of 3D objects. One of the little problems that I had to overcome was finding out how to calculate the center of mass/gravity of a 3D surface of revolution analytically. Specifically, I needed to calculate the COM for conical frustums with and without an attached part (which was also analytically generated).

Unfortunately, it wasn’t as easy to derive as I assumed, but the steps toward that end are pretty straightforward.  After the break you can see the general equation I ultimately derived for calculating the COM in 3D-space.
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