My doubt is the following: in a rotating frame of reference you have the centrifugal pseudo force.
When you analyze and object in circular motion (due to a rope) in the rotating frame of reference, the object will experience two forces, a real one due to the tension in the rope is centripetal, and the centrifugal pseudo force. Both forces compensate each other, thus the object, in the rotating frame, remains in equilibrium with no motion.
Now assume there is also another object not attached to a rope, and that the object is stationary in the nonrotating reference frame. But in the rotating reference frame this object will experience only the centrifugal force, so instead of seeing it rotating in the opposite direction than the reference system, we should see it accelerating away due the the centrifugal force.
What is it conceptually wrong with my reasoning?