To answer your question more clearly (or shall I say with more relative freedom) we can make a few basic assumptions about a particular scenario. These assumptions are not strictly necessary but they make the situation simple enough to only include basic physics
- Your ball is a rigid ball in an isolated stretch of spacetime, with
no other forces (eg. gravity, magnetic fields) acting upon it.
- It is rotating slowly (meaning any point of the ball doesn't reach relativistic speeds)
- The ball is not a quantum scale object.
- The ball is sufficiently small enough so gravitational effects are negligible upon the rotation considered.
- We exclude other types of motion that can happen to the ball or its components like vibration
Then your ball isn't moving anywhere. It is rotating about a static axis in order to conserve its angular momentum. Yes, it has molecules moving in a circular path and the tendency of molecules to move away from the ball at tangential velocity is balanced out by intermolecular forces acting inward. So in the absence of net force centre of the ball keeps stillness (the centre is depicted as a point , and rotation of a point around its own axis is undefined because it is singular), and the molecules of the ball (or any point not in the exact centre of the ball) keep moving in a circular path at a constant angular velocity.
So in essence, while the ball doesn't have external forces acting upon it still has internal intermolecular (and also intra-molecular) forces acting upon every particle of it so as to convert the linear momentum of each particle into angular momentum every instance, hence linear velocity motion of particles are converted to circular motion. That is what rotation is. Every particle is subjected to the external force of other particles residing by it hence the circular motion (due to the gradient of linear velocity along the axis normal to the axis of rotation) of the particles of the rotating rigid body
Important question: Why is there a difference in linear velocity along the axis normal to the axis of rotation?
Answer: Because that is how rotational motion is imparted upon our rotating ball at the start of our motion, that is to make a positive
gradient of linear velocity outward along the axis perpendicular to
the axis of rotation. Physically an one way to do this is by applying
two equivalent yet opposite forces at two exactly opposite points on a
perimeter of a large circle on the ball.
Relevant question: What happens to the molecules at the exact axis of rotation?
Answer: Well, they rotate about the exact axis of the rotation of the ball. But still, parts of them (atoms) will be moving around (means in a circular path not changing the relative position of one point to another point of the ball). If
you zoom in to more than that then there will be quantum effects and
Heisenberg uncertainty comes into play.