Once you have the coil, you need to set it in motion by adding keyframes.
Go to the first frame press I and select rotation.
Move to a different frame, rotate the coil and set a new keyframe by pressing I again.
Now set the coil to a passive rigid body.
Add the object on the vending machine and the rest of the collision objects. Set all of them, except for the box to be dispensed, as Passive rigid bodies.
Then set your dispensed object as a Rigid body but make it active.
The big problem, as you'll soon see, is that the coil does not work correctly as as rigid body to interact with the dispensed box. The box goes out flying out at at the beginning of the animation.
The issue is that the physics for collision objects and rigid bodies is far from perfect and does not follow the real geometry of the object, but creates like a bounding box: The Coil becomes almost like a big solid object with no gaps in between.
The solution is then to turn the dispensed object into a rigid animated object for part of the interaction to force it to follow the turns of the coil, thus simulating the real motion of a vending machine.
Animate the object so it follows the movement of the coil.
Now all that's left is to animate the animate button. To do that go to a frame where the dispensed object has reached the edge of the dispenser. Hover with the mouse over the animate box and press I to set a key frame, Then move one frame in the time line, uncheck the animate button and press I again to add another keyframe. What you are doing is deactivating the animation settings for the rigid body and letting it act just with the physics engine. Press AltA to cache the physics and watch a preview of the object falling over the edge of the dispenser.
Here's the .blend file