Fake forces on rotating frames of reference.

[House]

Suppose we have a rotating frictionless disk and there is a rotating observer on the center of it. Furthermore, suppose a very small ball on the disk's edge. Now we clearly know that the ball is not moving but the rotating observer sees the ball following a circular path with an angular velocity ω opposite of the one of his frame of reference. He now has to explain that movement and, since he is in a non-inertial frame, he has to introduce some non Newtonian forces. Accepting that the ball has a relative velocity v_r in the non-inertial frame, the question is:
Is there a centifugal force and a Coriolis force acting on the ball? Or does the ball have to "physically" be included on the disk?

 

[House]

Update: The math says that the rotating observer measures a force given by: F = mω×(ω×r) which is towards the center of the circular motion. Is that it?

 

[A.T.]

Now we clearly know that the disk is not moving...

I assume you mean the ball is at rest in the inertial frame of reference.

Accepting that the ball has a relative velocity v_r in the non-inertial frame, the question is: Is there a centifugal force and a Coriolis force acting on the ball?

Yes, both are acting in opposite directions, and their net effect is the inwards centripetal force, that matches the circular movement in the rotating frame.