The Ward-Leonard system is an electrical control system used in winding systems, such as those in mine hoists, to precisely control the speed of the motor driving the cage. By adjusting the voltage supplied to the motor, the system ensures that the cage does not exceed safe speeds, thus preventing over-speeding, which could lead to accidents. While over-winding, deceleration, and acceleration are important considerations in winding systems, the primary role of the Ward-Leonard system is to regulate speed and prevent over-speeding.
Thus, the correct answer is Over-speeding of the cage.