1. The problem statement, all variables and given/known data A hollow cylinder with mass m and radius R stands on a horizontal surface with its smooth flat end in contact the surface everywhere. A thread has been wound around it and its free end is pulled with velocity v in parallel to the thread. Find the speed of the cylinder. Consider two cases: (a) the coefficient of friction between the surface and the cylinder is zero everywhere except for a thin straight band (much thinner than the radius of the cylinder) with a coefficient of friction of μ, the band is parallel to the thread and its distance to the thread a<2R (the figure shows a top-down view); (b) the coefficient of friction is μ everywhere. Hint: any planar motion of a rigid body can be viewed as rotation around an instant centre of rotation, i.e. the velocity vector of any point of the body is the same as if the instant centre were the real axis of rotation. The figure: http://i64.tinypic.com/2ijrv53.jpg 2. Relevant equations 3. The attempt at a solution I have no idea were to start! I know that it is against the forum rules.. but can someone give me only a hint to set up the solution?