Force calculation: mv2/r, but here mv2r, why? [Proof of F = mv²/R]

F calculation - mv2/r, but here mv2r, why?

From Newton’s second Law, it can be shown that F = ma, where F is the net force acting on a body, m is the mass of the body and a is the acceleration. So to find the centripetal force we must first find the centripetal acceleration for a body undergoing circular motion.

The following is from a previous answer of mine where I derived the centripetal acceleration:

A particle in circular motion follows the graph of x2+y2=r2, where r is the radius of the circular motion. This can be expressed in parametric equations with the time variable, allowing us to see where the particle would be at a specific point in time.

These are:
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Where T is the time period of the motion.
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Where f is the frequency and
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Therefore the parametric equations can be re-written as
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Now we need to find the acceleration for the x and y components of position. We find these by double differentiating each position variable with respect to time.
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Now we just need to find the resultant acceleration.
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Let’s now write this in a different form.
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