According to the laws of physics, in order to keep an object moving in circular motion, its velocity constantly changes direction. Whenever velocity changes, you have acceleration. Specifically, you have centripetal acceleration — the acceleration needed to keep the object moving in circular motion. The centripetal acceleration always points inward along the radius toward the center of the circle. At any point, the velocity of the object is perpendicular to the radius of the circle.
If the string holding the ball in the figure breaks at the top, bottom, left, or right position you see in the illustration, which way would the ball go? If the velocity points to the left, the ball would fly off to the left. If the velocity points to the right, the ball would fly off to the right. And so on. That’s not intuitive for many people, but it’s the kind of physics question that may come up in introductory courses.
The velocity of an object in circular motion is always at right angles to the radius of the object’s path. At any one moment, the velocity points along the tiny section of the circle’s circumference where the object is, so the velocity is tangential to the circle.