|When a ball swings in a horizontal circle at the end of a string, what's the force on the ball pulling it straight? What's the force pulling it out?
Let's neglect gravity, which isn't important in this horizontal motion problem. When a ball swings in a circle at the end of a string, there is only one force on it and that force is inward (toward the center of the circle). We call such a force a centripetal force, meaning toward the center. There are many kinds of centripetal forces and the string's force is one of them. As for the ball's tendency to travel in a straight line, that's just the ball's inertia. With no forces acting on it, it will obey Newton's first law and travel in a straight line. There is no real force pulling the ball outward. But a person riding on the ball will feel pulled outward. We call this feeling a fictitious force. Fictitious forces always appear in the direction opposite an acceleration. In this case (an object traveling in a circle) the outward fictitious force is called centrifugal "force." But remember that it's not a real force; it's just the object's inertia trying to make it go in a straight line.