Assume a stationary object (point object) on a smooth very large disc at a distance $r$ from its axis perpendicular and passing through the centre. (No external forces apart from gravity and Normal which are equally balanced). Now the disc is rotated with a constant angular velocity.
Now when the object is observed in an inertial frame O, The object remains stationary. But when observed in a non-inertial frame attached to the centre of the disc and rotating along with the disc, there exists a centrifugal force (pseudo force) pointing away from the centre and no force to counter it and hence must be moving away right? Yet this seems to be counter-intuitive to the idea that the object must be rotating in the opposite direction with the same magnitude. The above observation of the rotating frame is also against the observation of the object in the inertial frame where the distance from the centre remains constant.
Where am I wrong?