This was a question on a test that I couldn't figure out. You have a hoop, mass M, moment of inertia MR2, and an initial angular velocity ω. It is dropped onto a plane with kinetic coefficient of friction μ. What will be its linear velocity when it stops slipping and rolls away smoothly if it doesn't bounce? Conservation of energy can't be used since it must lose energy to friction. I'm lost on where to even start. Maybe work is extracted from the hoop as it is slipping in an amount of the friction force times the circumferential distance of the slip. This energy, which comes from the rotational kinetic energy of the hoop, must be lost to heat, but at the same time some will be translated into translational kinetic energy, and I don't know how much. Does anyone know how to do this?