PROBLEMS TO BE WRITTEN UP AND TURNED IN AT RECITATION

     This problem is due at your first recitation meeting after MON 4/12.
     It should be written on a single sheet of paper (front and back), or
     if multiple sheets are used, staple them together.  For full credit,
     the work must be neat, with clearly labeled free-body diagrams.  The
     labels must be in BOTH words and symbols.  For each part, you must
     BRIEFLY explain your strategy in words, as well as neatly showing
     your physics equations and math, with proper units. (40 points total)

     FISHBANE - CHAPTER 9
     65. A yo-yo is made from two uniform disks, each with mass M/2 and
         radius R, connected by a light axle of radius r (R>r).  Since
         the axle is nearly massless, 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 between 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 with a force of magnitude F.  
         (a) Assuming the yo-yo rolls without slipping, find the 
             magnitude of the static frictional force on the yo-yo by
             the surface.  (18 points)
         (b) Assuming the yo-yo rolls without slipping, find the
             acceleration of the center of mass of the yo-yo.  State
             magnitude and direction.  (12 points)
         (c) What is the maximum value of F for which the yo-yo will
             roll without slipping? (10 points)