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I'm thinking it is either the tension due to the ball, or the ball's centrifugal force. But the thing is, are these two forces the same in the conditions I've set (no gravity, no air resistance)?

After all, the centripetal force would be due to the tension on the ball from the rope. Since the centrifugal force is essentially the opposite of the centripetal force, then it would be equal to the tension on the rope from the ball, right?

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I'm thinking it is either the tension due to the ball, or the ball's centrifugal force.

The outward pointing real force acting on the rope is the tension due to the ball. The ball’s centrifugal force is a fictitious force which acts on the ball and not on the rope, and it only exists in the rotating reference frame.

There is also a centrifugal force acting on the rope in the rotating reference frame, but like all fictitious forces it is proportional to the mass of the object. So assuming the rope is light the force would be small

Dale
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