Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_49

3/49 A small object \( A \) is held against the vertical side of the rotating cylindrical container of radius \( r \) by centrifugal action. If the coefficient of static friction between the object and the container is \( \mu_s \), determine the expression for the minimum rotational rate \( \dot{\theta} = \omega \) of the container which will keep the object from slipping down the vertical side.