Very Simple Uniform Circular Motion Derivation

[planauts]

Homework Statement

This is a very easy derivation (I think), I forgot how to do it though.

How do you derive $$a = \frac{4\pi^2R}{T^2}$$ or $$a = 4\pi^2Rf^2$$?

Homework Equations

The Attempt at a Solution

They both mean the same thing since T is Inverse Frequency but I don't understand how it is derived from $$a = \frac{v^2}{r}$$. I know it uses the Sphere formula...

Thanks,

 

[praharmitra]

Well, if a particle went around a circle of radius R in time T, what would its speed be?

 

[planauts]

Wow, I feel very stupid now lol.

$$\frac{(\frac{2\pi r}{T})^2}{r}$$

Thanks,