Finding center of mass and torque for a bent uniform wire

[Tom McCurdy]

Problem here:
http://www.quantumninja.com/hw/random/problem4.jpg

I was trying to figure out how to go about this problem. So far I have come up with

center of mass=
$$\frac{L}{4}cos\frac{\beta}{2}$$

Torque=t
$$\sum t=I\alpha$$

 

[Davorak]

Are you sure this is right
$$cm = \frac{L}{4}cos\frac{\beta}{2}$$
If $\beta$ goes to zero then the cos will go to one and you will be left with $\frac{L}{4}$ which does not seem right to me for a stright rod.

 

[Tom McCurdy]

I thought that was right

 

[Tom McCurdy]

Actually maybe it would be
L/4*cos(b/2)+L/2
center of mass
$$\frac{L}{4}cos\frac{b}{2}+\frac{L}{2}$$

 

[Davorak]

I am sorry you are right. If beta goes to zero the rod becomes lengh of L/2 and the center of mass would the be a L/4.

 

[Tom McCurdy]

Which one is right the first or 2nd one