Final answer:
In a rotating tube, the ball moves outward due to inertia in an inertial frame, which is explained by the absence of a centripetal force, and within the tube's frame, it's explained by a fictitious force called the centrifugal force.
Step-by-step explanation:
When a ball is placed inside a rotating tube and the tube is rotated, the ball tends to move outward. This phenomenon can be understood from two different frames of reference: the inertial frame (a non-rotating reference frame) and the rotating frame of reference.
In an inertial frame, the force that appears to push the ball outward is actually the absence of a force acting to change the ball's straight-line motion. This effect is due to the ball's inertia, which causes it to move in a straight line because no external force is acting on it. As the tube rotates, the ball wants to continue moving in a straight line (tangentially to the circle), which makes it seem as if it's being pushed outwards. This is not a real force acting on the ball but rather a lack of centripetal force.
From within the rotating frame, we use a fictitious force called the centrifugal force to explain the ball's movement outward. This force is an apparent force that seems to act on all masses in a rotating system. The trajectory of the ball, as seen by an observer inside the rotating frame, would be curved, as the ball seems to move away from the center. The ball's path curves because the rotating system itself is accelerating, and without a real force to keep the ball moving in a circle (centripetal force), it seems to be flung outwards.