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

[Dr.D]

The momentum conjugate to theta is the partial of T wrt theta-dot, and since theta-dot and y-dot are both initially zero, that gives zero for the initial value of this expression.

 

[StatusX]

No, they aren't initially zero. In the problem, a push is given to the bottom rod, which makes both dy/dt and d\theta/dt non-zero, although (for some reason I don't fully understand) only makes p_y non-zero, not p_\theta.

 

[Dr.D]

If the force is nonimpulsive, then this makes the acceleration of the bottom rod nonzero, but its initial velocity is still zero.

 

[StatusX]

The point of the problem is that the bottom rod is initially (ie, just after the force has been applied for some short time, providing some non-zero impulse) moving at speed v. The initial velocity of all the rods is non-zero, and the question is to find how they are related. Sorry if that wasn't clear.

 

[Dr.D]

I worked it on through assuming that this is an impulsive force, and I concluded that the post impulse value of theta-dot is -(9*V)/(11*L) and the speed of the top bar is (2*V)/11.

I don't think those are the result you had said were the given answers, but that is what I got never the less. Have you been able to work out a better result?

 

[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.