need help with dynamics of multi-part space colonies

I can't answer your question, but that's never stopped me before, so here goes.

I've played around with the idea of counterrotating cylinders joined end-to-end. I imaging something like an elevator car between them, except that instead of going up and down it races around the circumference in the direction opposite rotation. It keeps on accelerating, except of course it's actually decelerating, until it's stopped, and then keeps right on doing that so that it's actually accelerating in the opposite direction. It matches speed with the other cylinder and a door opens, letting you step out into another world.

A more advanced design might actually have multiple bands between the cylinders, each rotating a few KmPH slower, and then a few KmPH faster in the other direction. With practice, one would be able to walk from one to the other, with one's weight lessening and then increasing again. There might be a double-wide recreational band right at the 0G midpoint.