Thread: Center of Mass

I have two problems here that i cant figure out

EDIT find the center of mass given that the mass is constant

1.)the "triangular" region in the first quadrant between the circle x^2+y^2=9 and the lines x=3 and y =3 (Hint: use geomentry to find the area).


2.) Find the center of mass of a thin plate covering the region between the x-axis and the curve y= 2/x^2. 1<=x<=2 if the plates density ate the point (x,y)
is delta(x)=x^2

(1)You can view the the region as subtracting the rectangle from the quater-circle.

Now the centroid of the rectangle is trivial (1.5,1.5) und the area is 9.

The centroid of a quater-circle is located on the line (that is symettry) and is (a known formula). In this case . Thus the centroid is . Thus, . And has area .

Thus, by the composite centroid formula we have,

hmmm.... my book say's i should get 2/(4-pie).... i think ur #### gives me the c of m of the semicircle... i want to find the c of m of the triangular shape made by the semicircle and x=3 and y=3