Suppose a cylinder is on a plane inclined 30 degrees above the horizontal, lying so that it is ready to roll.
a. draw an extended free-body diagram for the cylinder. make sure to label forces appropriately.
b. write down the three equations of motion that govern the linear and rotational motion of the cylinder. recall that i_cyl = [1(mr^2)]/2, and make sure to substitute in all known quantities and use the standard symbols for unknown quantities.
c. what constraints can be applied to the above equations to ensure that there is rolling without slipping?
d. given the equations and constraints above, what is the minimum coefficient of static friction that will allow perfect rolling?
e. what is the magnitude of the acceleration of the cylinder in the direction going down the inclined plane?