1. The problem statement, all variables and given/known data We consider a yo-yo rolling down an incline, sloping with angle θ relative to horizontal. The yo-yo starts a distance d up the incline. The string is attached to a hook further up the incline, in such a way that it unwinds as the yo-yo rolls down. The yo-yo can be thought of as three uniform discs: a small one of mass m and radius r, sandwiched between two larger ones, each of mass M and radius R. The string is initially wrapped around the smaller middle disc. The string unwinds without slipping. To start with, we will assume that there is no friction between the yo-yo and the incline. a) Is it possible to roll down without slipping on the incline? Why/why not? (Carefully think of the rolling-without slipping conditions). b) What is the speed of the yo-yo when it reaches the bottom of the incline? c) What is the acceleration of the yo-yo? The angular acceleration? How large is the string tension? Now imagine that we turn on kinetic friction between yo-yo and incline, with a coefficient µk. d) What is then the speed at the bottom of the incline? (Tricky! Carefully consider the motion of the point of application). For each question, provide an algebraic expression. 2. Relevant equations α = R∝ ν = Rω τ (torque) = I∝ Moment of Inerta (of uniform disc) = MR2 h = d⋅sinθ Fgx = Mg⋅sinθ Fgy = Mg⋅cosθ 3. The attempt at a solution a) For the yo-yo (disc) to not slide down, we need friction on the surface, right? But in the problem info it says that we assume there are no friction between the yo-yo and the incline. Does that mean that in this case, it is not possible to roll down without sliding?