In the case of a ball on the earth's surface the forces acting on it are the normal force, the force of gravity, and a sideways inertial force due to centripedal acceleration caused by the earth's rotation. The magnitude of the inertial force is its mass times the acceleration that I wrote about earlier:

, and the component of that force acting horizontally to the earth's surface is

. There is no string here, so nothing to oppose that force, and consequently the ball begins to roll according to

, where T = torque acting on the ball (which is the force described above times the radius of the ball:

), I is the moment of inertia of the ball, and alpha is the resulting rotational acceleration of the ball.

Of course in real life no ball is absolutely smooth and the surface of the earth is not absolutely smooth, so the small amount of torque created on the ball by the earth's rotation is insignificant.