Ex: A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is 0. Determine the acceleration of the cylinder's center of mass, and the minimum coefficient of friction that will allow the cylinder to roll without slipping on this incline. Draw a free-body diagram for the cylinder: f. w cos a W w sin 0 0 Take the torque about the contact point to solve for the acceleration: Tnet = la = Fd a = Ra a R α= 1 = 1cm + Mx² I= MR² MR² + 4 2 F = w sin 0 F = Mg sin 0

Ex: A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is 0. Determine the acceleration of the cylinder's center of mass, and the minimum coefficient of friction that will allow the cylinder to roll without slipping on this incline. Draw a free-body diagram for the cylinder: f. w cos a W w sin 0 0 Take the torque about the contact point to solve for the acceleration: Tnet = la = Fd a = Ra a R α= 1 = 1cm + Mx² I= MR² MR² + 4 2 F = w sin 0 F = Mg sin 0