An object moving in a circle is only doing so because it is forced to. At every moment it's circular motion it's being accelerated toward a center, in this case by our stays. But, at the same time, at every moment the object would much rather travel in a straight line, and will do so if given the chance.
The slinger intends to give the object that chance... BUT wants to choose the moment. The moment, of course is the release of the trigger. As soon as the trigger is released the object will move in a straight line that is perpendicular (90 degrees) to the radius of the circular motion. Simply put, when released, the object will travel along the tangent at any point on the circle.
This isn't surprising considering simple throwing. With a baseball, if you want the ball to go roughly forward, you have to release it at the top of your swing. When you release a frisbee to throw it forward you release it out to the side. In both of these cases the release is 90 degrees from the direction of travel. This is more difficult with the sling because the stays put the slinger at a distance instead of directly holding the object.
But of course the real world is not frictionless so there are three delays you need to consider:
1. Trigger Friction
2. Object/Pouch Friction
3. Weight of the Pouch and Stay
These three factors will delay the moment that the object actually leaves on it's new life as a tangent traveller which means only one thing for the slinger... RELEASE YOUR TRIGGER JUST A FRACTION OF A SECOND BEFORE THIS PERFECT 90 DEGREES.
get your sling on...