A yo-yo is made from two uniform disks, each with mass M/2 and radius R, associated by a light axle of radius r(R>r). Since the axle is nearly mass less, the total mass of the yo-yo is M. A light, thin string is wound several times around the axle. The yo-yo is placed on a rough horizontal surface; the coefficient of static friction among the yo-yo and the surface is mu_s. The string is held so that it exits the yo-yo horizontally on the lower side of the stem. The string is then pulled horizontally by a force of magnitude F.
a) Assuming the yo-yo rolls without slipping, discover the magnitude of the static frictional force on the yo-yo by the surface.
b) Assuming the yo-yo rolls without slipping, discover the acceleration of the center of mass of the yo-yo. State direction and magnitude.
c) What is the maximum worth of F for which the yo-yo will roll without slipping?