Proving centripetal acceleration formula

[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.

Thanks in advance.

 

[Andrew Mason]

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.

Thanks in advance.

Have a look at this link:

AM

 

[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.