|MadSci Network: Physics|
the relevant quantity to see whether the proton can split apart in a circular accelerator is not the centrifugal force as such, but the difference of the centrifugal force within the proton. The proton has an approximate diameter of r_p = 1fm = 10^-15 m. The radius of LHC is, as you have stated, r = 4300m. The quotient of the centrifugal force at opposite ends of the proton is given by (r+ 2 r_p)/r, which is approximately 1. So the proton will stay stable while going around in the LHC.
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