I'm going to assume that this is a DC geared motor. What's the voltage, current and speed of rotation?
A problem with timing a motor for precise rotation, is that due to changes in supply voltage, load, friction, and temperature, the stop-position will creep over time. A stop-position sensor/switch will resolve this. Also, geared motors slow down when the power is removed, not stop abruptly. A braking mechanism will solve this.
Attached are a couple of possible circuits.
The concept is that the dispensing wheel has cams that open a stop-switch at each position.
When the ball triggers the 555 monostable, it turns on the motor for a brief period, enough to move it beyond the stop-switch. With the 555 timed out, the motor continues to rotate until the next stop cam opens the stop-switch and stops the motor. The motor is controlled by a relay that either provides power, or shorts a resistor across the motor winding, braking the rotation. One circuit uses a laser pointer LED and photo transistor to trigger the 555, the other used a microswitch.
Ken