Hello!

A slender metal arch, denser at the bottom than the top, lies along the semicircle y^{2}+z^{2}=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!