Question

Find the centroid of the shaded part in terms of R.
Where R is the radius of the bigger semicricle.

Answer 1

i think x coordinate is 0 by symmetry

Answer 2

integrating this in terms of x and y looks difficult , changing to polar coordinates looks easier

Answer 3

to find the y coordinare of the centroid

Answer 4

you can also solve this problem using moments of inertia and the parallel axis theorem