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Suppose I have a rigid ball in space and I give it a spin. I know that it will keep on spinning at the same angular speed as long as it doesn't interact with anything outside. But since it is spinning, something must be exerting a force, say , on a particle at the surface of the ball towards the centre. How is that force provided?

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The chemical bonds between the constituent particles of the ball are what would be holding it together. You can imagine that for any particle in ball at some radius $r$, the adjacent particles (at that same radius $r$) will exert a restorative tug whenever the first particle is displaced. The symmetry of the adjacent particles guarantees that the net force will be central one (i.e. the ball stays together as it spins).

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