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Proving centripetal acceleration formula

  1. Oct 10, 2005 #1
    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.
  2. jcsd
  3. Oct 11, 2005 #2

    Andrew Mason

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    Have a look at this link:

  4. Oct 11, 2005 #3


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    What formula are you talking about?

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

    If an object is undergoing uniform circular motion then

    [tex]x = r \cos \omega t[/tex]

    [tex]y = r \sin \omega t[/tex]

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

    Combine the two to obtain

    [tex]a = \frac {v^2}{r}[/tex]

    You can generalize this to "nonuniform" circular motion.
    Last edited: Oct 11, 2005
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