Find the center of mass of a hemisphere of radius R.
R_cm = (rho/M) Integral[ (vector r) dv]
dv = r^2 Sin[theta] dr d[theta] d[phi]
The Attempt at a Solution
In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should be:
r^3 Sin[theta] dr d[theta] d[phi]
Well, that's what I would expect... I keep ending up with 3R/4, but other sources have it as 3R/8, and I see that the volume element dv is written with an extra Cos[theta] which I do not understand..........
I have no problem integrating over volumes in E&M problems, so I do not get why this is such an issue for me.