I first saw this seven years ago as a placement exam for college, and I still don’t know the full answer (although the version I saw was with *no* slipping).

A yo-yo lies on the floor. It’s made out of an inner disc of radius r and an outer disc of radius R. Its mass is m. There’s a (massless) string wound around its inner disc. You pull the string with force F and angle θ with respect to the horizontal direction. What is the acceleration of yo-yo? Assume the yo-yo rolls with slipping.