$13-59.$

The $2-$kg spool $S$ fits loosely on the inclined rod for which the coefficient of static friction is ${}_s=0\mathrm{.}2.$ If the spool is located $0\mathrm{.}25m$ from $A,$ determine the maximum constant speed the spool can have so that it does not slip up the rod.

Hints: $1)$ Solve for max linear speed of S and $2)$ As you draw your FBD$/$kinetic diagrams, think closely about the direction of the axes for the spool particle. Are they based on the geometry of the arm, or the geometry of the spool's path?