A spool with inner radius R = 5 ft is made to roll without slip over a horizontal rail as...

A spool with inner radius R = 5 ft is made to roll without slip over a horizontal rail as shown. If the cable on the spool is unwound in such a way that the free or vertical portion of cable remains perpendicular to the rail, determine the angular acceleration of the spool and the acceleration of the spool’s center O. The vertical component of the velcocity of point A is υA = 12 ft/s, and the vertical component of its acceleration is aA = 2 ft/s2.

Figure P6.94