$(35$ pts$)$ The $\backslash (4-\backslash$mathrm$\{$kg$\}\backslash )$ uniform disk in the figure below is at rest when the $\backslash (30-\backslash$mathrm$\{$N$\}\backslash )$ force is applied to the center of the disk for a period of $1\mathrm{.}5$ s $,$ after which the force drops to zero. During the $1\mathrm{.}5$ s period, friction is insufficient to prevent the disk from slipping. Determine the time when slipping stops and the corresponding angular velocity of the disk.