I have a bit of a strange problem.

I'm working on a game engine that will incorporate jumping between ropes.
I was going to put this in the games forum, but I want to use proper maths, rather than trickery to achieve it, so I thought I'd be better off here.

I have the character running around, so I have gravity, inertia, values for speed and direction, swing radius, etc. But I don't know how to calculate the rotational velocity based on the 'incoming' velocity. To be honest, I don't know where to start. Should I constrict the character to a cirular path, or do it manually with trig?

I also need to be able to exit the swing and keep the same velocity and direction upon exit, but I think I know how that's done. It's just calculating the initial speed as he grabs the vine.

I'd provide some data, but there's not much I've got so far that would relate, if you know what I mean.