When you spin an object around a fixed point, a sling for example, does the object at the end build up energy that causes it to shoot out quickly when released?
Yes. As you whip the object around on a string, you are doing work on it. You do this by making subtle movements with your hand, exerting forces that aren’t exactly toward the center of the circle. When you do this, the object begins to travel faster and faster, so its kinetic energy increases. Traveling in a circle doesn’t change this kinetic energy because kinetic energy is proportional to speed squared, and doesn’t depend on direction. Finally, when you let go of the string, the object stops circling and begins to travel in a straight line. It carries with it all the kinetic energy you gave it by whipping it about.