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

Thanks in advance.

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- Thread starter dragon513
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- #1

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

Thanks in advance.

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Andrew Mason

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Have a look at this link:dragon513 said:

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

Thanks in advance.

AM

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Tide

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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.

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.

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