About particle to barbell collision

OKAY!
I have made the doc.
here

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.

Yeah, hang on, I've been preoccupied finishing up a website for a client, but I ran your equations, just haven't had time to do a write up on it. The equations produce the solutions, so your math is correct.

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.

http://montalk.net/newton/newtonmath.html -- there is the corrected version. I just included a screenshot of your article, then added my own quick analysis and discussion. Thanks for working this out. It looks like there's no fooling classical physics using classical means. Maybe quantum / magnetic / chaotic methods - since they are the level from which classical rules arise, can break those same rules.

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.