(Solved): A solid cylinder with radius \( 0.35 \mathrm{~m} \) and mass \( 8 \mathrm{~kg} \) has rolled acros ...

A solid cylinder with radius \( 0.35 \mathrm{~m} \) and mass \( 8 \mathrm{~kg} \) has rolled across the floor and into a wall. When it strikes, it has an angular speed \( \omega_{0}=9 \mathrm{rad} / \mathrm{s} \). The coefficient of friction between the cylinder and both the floor and wall, \( \mu=0.5 \). How long until the cylinder comes to rest? Assume zero rebound from the wall. Specify your answer in seconds to 3 decimal places.