$7)$ A flat$-$face radial follower has a lift of $4$ cm $.$ The follower rises first $1$ cm at constant acceleration for $\backslash (60^\{\backslash$circ$\}\backslash )$ cam rotation and then rises $2$ cm at constant velocity for the next $\backslash (60^\{\backslash$circ$\}\backslash )$ of cam rotation. After a dwell for $\backslash (45^\{\backslash$circ$\}\backslash )$ of cam rotation, the follower returns with simple harmonic motion for the next $\backslash (90^\{\backslash$circ$\}\backslash )$ of cam rotation followed by a dwell. Determine the minimum base circle radius of the cam, and the minimum length of the follower face. The minimum radius of curvature of the cam profile must be at least $5$ cm $.$