This is a very general problem, but I'm hoping you can offer some help. I don't need an exceptionally complex answer, just a discussion of the different forces & forms of mechanical energy and what will happen. Ok, you have an half-pipe. The left half has friction, the right side does not. You release a ball on the left side. It rolls down the pipe without slipping, so that when it reached the bottom it has both translational and rotational Kinetic Energy. It then slides up the right (frictionless) side. It will rise to a height less than the initial height because some of the original U(grav) is still in the form of Rotational kinetic energy. (The ball will still be rotating at point of max height on the right side do to lack of friction.) The cylinder then slides back down the half pipe to the bottom. What will happen at the bottom where it reaches the left (friction) side? Thanks for your help!