For all uniform circular motion, the magnitude of the velocity vector is a constant even though its direction is changing continuously. When this direction points along the same orientation again it can only indicate a complete cycle. However, for the centripetal force to be exactly radial, the instantaneous change in time must be taken to the limit using the formalism of differential calculus such that ∆t ® 0, implying its time independence. In addition to being mass independence the scalar product of centripetal acceleration and radius vector is a constant square of light speed.


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