EXAMPLE 34' A Rolling Cylinder Problem radius starts from and rolls down the incline at an angle of A solid cylinder of mass m and rest the acceleration of the center 3.4.2. The static coefficient is u,. the cylinder rolls without to solve mass ac, and the angular acceleration Assume that slipping. Use two approaches Assume also that the cylinder rolls ithout moment equation wi the problem: (a) the moment about G. (b) the slipping . (c)Obtain the frictional condition required for the cylinder to roll without Solution The friction force is F and the force is N normal The free body diagram is shown in the figure. The force equation in the r direction is mg sin 6- F maa, In the y direction. N- mg cost If the cylinder does not bounce, then ao, 0 and thus from (2. mg cost igure 3.4.2 A cylinder mg ling down an inclined plane. mg (b) (a)