Derivation of r (radius) in terms of f (frequency)? Help please.

Okay, so the job I need to do is derive an equation for the radius of an object in terms of its frequency.

These are the equations that we are allowed to use:

v(Linear velocity) = rω
v=2πr/T
ω (angular velocity)=2πf
f (frequency)= 1/T (time period)
T= 2πr/v
a (centripetal acceleration)=v^2/r
F (centripetal force)=mv^2/r

So now.. my attempt:

r= v/ω
= √ar/2πf
= (√(a*(vT/2π))/2πf
2πfr=√(a*(vT/2π)
2πfr^2= a * (vT/2π)
2π * 2πfr^2 = a * vT

…… I’m lost I have so many variables that I need to eliminate and I’m not sure what else to do from here. Help would be very appreciated.

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