Where is the Center of Mass for a Semicircular Wire?

[physicsss]

A uniform thin wire is bent into a semicircle of radius r. Determine the coordinates of its center of mass with respect to an origin of coordinates at the center of the "full" circle. (The semicircle is in the positive y plane.)

 

[Tide]

What have you done so far?

 

[physicsss]

I've tried to integrate sqrt(r^2-x^2) from -r to r, and then divide it by half the area of the circle...

 

[Tide]

That's a good start! Instead of dividing by half the area of the circle divide by the diameter of the circle instead:

$$\bar y = \frac {\int_{-R}^{R} y dx}{\int_{-R}^{R} dx}$$

Your units would provide a clue!