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There are two formulas that represent centripetal force, $F_c=mv^2/r$ and $F_c=m\omega^2r=4\pi^2f^2mr$. Which one is correct under which circumstances?

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    $\begingroup$ It depends on what is kept constant. $\endgroup$
    – Qmechanic
    Commented Mar 8, 2020 at 20:11

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Both are correct. They are equivalent.

In constant circular motion velocity $v$, radius $r$ and frequency $f$ are related by $$v = 2\pi r f.$$

And therefore is $$\frac{mv^2}{r}=4\pi^2 rmf^2.$$

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