What is the velocity of the opposing rod in a hexagon mechanics problem?

[StatusX]

I did the same thing and got the initial value for theta dot to be -9v/10L, which gives the right answer. My Kinetic energy is:

$$T = \frac{2m L^2}{3} (1 + 6 \cos^2 \theta) \dot \theta^2 + 6 L \dot y \cos \theta \dot \theta + 3 \dot y^2$$

But I'm still note sure why it's a good idea to set $p_\theta=0$.