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Why would a physical string be taut if you cut the ball off? I don't think that would work in practice.
I agree that the non-tangent component of the ball's momentum is where the centrifugal bit comes from, there's no magic. They're just labelling it "centrifugal" because it acts in that direction.
I think you're missing the mark with the balanced forces though, that's not what the 3rd law means. Equal and opposite forces can also mean two objects accelerating away from each other.
In this case the acceleration on the ball should ultimately match an imperceptible change in the Earth's wobble, communicated from the string, to the post, to the ground.
If one of those forces, say the force exerted by the post on the ground, is not matched in the 3rd law sense - it just means you have a wobbly post.
useless-
Why would a physical string be taut if you cut the ball off? I don't think that would work in practice.
Because it has mass and thus intertia.
the non-tangent component of the ball's momentum is where the centrifugal bit comes from, there's no magic. They're just labelling it "centrifugal" because it acts in that direction.
It's completely tangential though. The apparent centrifugal force is surely a consequence of making forces neatly balance to zero in a non-inertial reference frame so you can worry about other aspects. It just doesn't exist in the inertial frame.
In this case the acceleration on the ball should ultimately match an imperceptible change in the Earth's wobble, communicated from the string, to the post, to the ground.
But then the model is better described as two masses, ball and earth (or ball and wobbly post), and we might as well have a massless string connecting them. The system rotates around a point on the string. Still simplifies to a single rotating mass.
chez_jay
I'm suspicious of this ball and string. If you cut the ball off, a physical string would still be taut. So I don't think we need the ball to demonstrate the behaviour, and so we can simplify the model to a single rotating rigid body, with mass and thus inertia. So the two bodies bit doesn't seem to be relevant.
I don't see any room for a centrifugal force in this model, it's just inertia. There doesn't need to be balanced forces at any point on the body, as it's all rotating and thus accelerating.
Edit: Going back to the original ball and string, I suspect that visualising a force transmitted through the string to the ball is implicitly constructing a non-inertial reference frame.