centripetal motion (FC)

Question

The law has for 4 shapes

F(c)= m.a(c)

Fc=m×4π²r /T². (He He squared the law for the circumference of a circle so why is it r and not r²)

F(c)= m v²/r.

F(c)= m.4π² r . f². (Why it's Divide by the periodic time at the top while multiplying the frequency at the bottom Is this because the frequency is the reciprocal of the period?

Answer 1

F_C = mv²/r

Now substitute 2πr/T for v

F_C = m/r *(2πr/T)² = m/r * 4π²r²/T² = m4π²r/T² = 4π²mrf² because f = 1/T

The r in the denominator outside of the v² cancels one of the r's in the r² that appears in the numerator from the substitution.