solid formed by rotating y=sqrt(cos(x)), x=0, y=0 about x-axis w/ uniform density. Find the coordinates of center of mass (x, y, z).

Question

combines calculus volume using integrals and physics center of mass

Answer 1

When the given curve (y=sqrt(cos(x)) ) rotates around  x-axis (when x>0 and y>0) it forms a "hemisphere", which has a "height" Pi/2. Now if we imagine a "hemisphere" standing above x-axis (more exactly x-plane), we can see that the center of mass is the point M(0,0,2/Pi). This is due to having uniform density. 

The body, which comes out as result of rotating the curve y=sqrt(cos(x)) is actually not a hemisphere but ellipsoid.

Coordinates x=0,y=0, z=1/2 can be found by integration as well