# Proving centripetal acceleration formula

1. Oct 10, 2005

### dragon513

Hi I was taught about centripetal accerleration last class, but my teacher didn't tell me why or how this formula works.

So I was wondering if anyone knows a website that has mathematical proof of this formula.

2. Oct 11, 2005

### Andrew Mason

Have a look at this link:

AM

3. Oct 11, 2005

### Tide

What formula are you talking about?

If you mean $a = v^2 / r$ then you may be able to convince yourself with the following:

If an object is undergoing uniform circular motion then

$$x = r \cos \omega t$$

$$y = r \sin \omega t$$

Now just take derivatives and find the speed $v = \sqrt {\dot x^2 + \dot y^2} = \omega r$. Likewise, the acceleration is $a = \omega^2 r^2$.

Combine the two to obtain

$$a = \frac {v^2}{r}$$

You can generalize this to "nonuniform" circular motion.

Last edited: Oct 11, 2005