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The reactive force is the ball causing the tension in the string
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.
chez_jay-
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.
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I'm suspicious of this ball and string. If you cut the ball off, a physical string would still be taut.
Sort of. The point of a ball on the end of a string is that you can simplify the system and ignore the elasticity of a string, air resistance, etc. It's a point mass (the ball) on the end of a light inelastic string.
If you take away the ball then you have to come up with something that is the mass at the end of the string. The natural thing would be to consider splitting the string into two halves, and that the half furthest from the anchor point is a mass that replaces the ball for the sake of the setup.
useless
Greenbank
I thought the middle bit of the Wikipedia article was reasonably clear:
IOW:
The second form of Newton's 3rd law is
The two bodies are the ball and the string
The centripetal force is the string pulling the ball towards the centre of rotation
The reactive force is the ball causing the tension in the string
Both of those are visible in an inertial reference frame, although the directions are constantly changing