Originally Posted by mjohnson (Post 12498136)

I still don't see covered anywhere the rotational inertia from the ball - it seems that most of the classic maths assume a point mass that doesn't roll. It'd be fun to see that worked up for a real ball/hoop with nonzero radius. Since it started with no rotation at H1 and ended up rolling with some speed at a lower H2, the speed should be lower that you'd expect based on m*g*(H2-H1) because some of that potential energy went into rotation.

These are dangerous waters... Go too far and you get all into the something which is simultaneously simple and mind-meltingly complicated. I've watched this video numerous times and I get a bit further each time...
https://www.youtube.com/watch?v=Q10_srZ-pbs