A stone tied to a string is whirled in a circle. As it was revolving, the rope suddenly snaps. Then:

When an object moves along a circular trajectory, its velocity at any given instant is directed along the geometric tangent drawn at that point. The tension in the string provides the required centripetal force to alter direction continuously. The moment the string snaps, this centripetal constraint drops to zero, and due to directional inertia, the stone flies off straight along the tangent line.