In ninth grade I did a science fair project where a sliding metal bar was rotated against a lopsided track so that the bar would always be longest on one half and shortest on the other. According to the hypothesis, this was supposed to create an imbalance in centripetal force and create a net motion. What I found out is that the force from the track needed to push the bar back in to its shortened state was opposite the force produced by the bar being extended in the first place, so the whole thing had no net motion.

However, what you have done is what I mentioned in the article as being the "standard" way of doing it. I'm taking another look at whether the assumptions are correct, namely that the system can legitimately be split into one equation for linear momentum and another for angular momentum, or whether because this system combines both there is some nonlinear coupling involved that does not allow for that.

Your equation (1) itself says linear momentum is conserved, the other equations are not needed to say that, but that's the very assumption I called into question in the article. I'll post here again after my re-analysis is finished. Thanks for this document, it's the first time I've seen the standard method explained in full.

It consider a possible value of initial omega and lineal speed in the bar.
And it is also valid for not completely elastic collision.
Hi, Tom:
Get it, test yourself and please replace your old docs to these ones if you test and see it and you realize it is good.

I must say the calculations there are wrong.
I have found the right way to calculate it (please ask me for it if you want to know), and in this case i must correct that linear and angular momentum are both conservated in that process.

Linear and angular momentum are not conservated in other kind of processes, but both are conservated in this one.