A small mass, $m,$ is on the rough wall of a rotating cylinder of radius $r.$ The coefficient of static

friction is $.$ i$)$ Obtain the kinematics in cylindrical coordinates; ii$)$ Draw a general the FBD of the

particle $($in a random motion against the wall$).$ iii$)$ Write Newton's Law for the particle. iv$)$ Obtain

the minimum angular velocity of the cylinder, $,$ such that the particle will not slide down the

wall of the cylinder.