A slender metal arch, denser at the bottom than the top, lies along the semicircle y2+z2=1, z>=0, in the yz plane and I'm trying to find its center of mass.
Density, D(x,y,z) = 2-z
I already found the total mass of the metal arch to be 2pi-2
I found the total mass by parameterizing the equation as y=cos(t), z=sin(t) from 0<t<pi and integrating 2-sin(t)dt from 0 to pi.
I'm not sure how to find the center of mass, especially if it's not on the semicircle.
All help is greatly appreciated!