Problem

Some pipe sections of radius r and mass m are being unloaded and placed in a row against a...

Some pipe sections of radius r and mass m are being unloaded and placed in a row against a wall. The first of these pipe sections, A, is made to roll without slipping into a corner with an angular velocity ω0 as shown. Upon touching the wall, A does not rebound but slips against the ground and against the wall. Modeling A as a uniform thin ring with center at G and letting μg and μw be the coefficients of kinetic friction of the contacts between A and the ground and between A and the wall, respectively, determine an expression for the angular velocity of A as a function of time from the moment A touches the wall until it stops. Hint: Using the methods learned in Chapter 7, we can show that the friction forces at the ground and at the wall are constant.