Find Center of Mass for Semicircular Wire

[Slightly]

Homework Statement

Find the center of mass of a semicircular wire. The wire is a semicircle, but the important thing to realize is that the wire is a closed loop. Think of a solid half disk, and just take the outer edge.
Where is the center of mass? This will be positioned with the center at the origin.
Radius b.

Homework Equations

cm = x1*m+x2*m/total mass

The Attempt at a Solution

What I tried to do was try to stay away from the integrals since there are just wires being used.
For the center of mass of x, it will be at zero because of symmetry.

For y, I used the equation above. With uniform density, the mass will factor out and I will just be left with lengths.

(2b*0 + Pi*b*2*b/Pi )/(2b + Pi*b)... is this right? or would you suggest that I use integrals.

 

[phinds]

Homework Statement

Find the center of mass of a semicircular wire. The wire is a semicircle, but the important thing to realize is that the wire is a closed loop. Think of a solid half disk, and just take the outer edge.

Self-contradictory. Doesn't make sense. Draw a picture.

 

[Slightly]

Here is the picture!

 

[phinds]

That makes sense. The wire is not a semi-circle, it is a semi-circle AND a connecting wire.