Question

A thin plate lies in the region between the circle x^2+y^2=4 and the circle x^2+y^2=1 above the x axis. Find the centroid. For the second part, same question except the region in the first quadrant instead of above x axis. For part a, I figured out bar x is 0, and I tried to integrate for bar y but it didn't work.

Answer 1

4 r/3pi is the semicircle
do the outer one, then subtract the inner one.
See for example:
http://en.wikipedia.org/wiki/List_of_centroids

Answer 2

http://mathworld.wolfram.com/Semicircle.html

look at integration for weighted mean, then divide by area. pi r^2/2