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circular motion - how to prove/derive v=rw?

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    title says it all
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    You're moving in a circle of radius r, so the distance you travel in one full trip round the circle is 2.pi.r and you're doing it in one time period, T

    speed, v = distance/time = 2.pi.r/T

    w = angular speed, and you complete 2 pi radians in time T, so w = 2pi/T

    so v=rw
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    Thankyou!

    you can have a little dribble of green tomorrow! (alredy repped today ) :p:
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    Heh, thankyou muchly I shall look forward to it :p:
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    or you could use calculus to prove it:

     S = r \theta \to \frac{d S}{dt} = \frac{d (r \theta)}{dt} = r \frac{d \theta}{dt} + \theta \frac{d r}{dt}

    If your moving on a circle, your radius is not changing with time so  \frac{dr}{dt} = 0

    so  v = \frac{dS}{dt} = r \frac{d \theta}{dt} = r \omega
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    (Original post by div curl F = 0)
    or you could use calculus to prove it:

     S = r \theta \to \frac{d S}{dt} = \frac{d (r \theta)}{dt} = r \frac{d \theta}{dt} + \theta \frac{d r}{dt}

    If your moving on a circle, your radius is not changing with time so  \frac{dr}{dt} = 0

    so  v = \frac{dS}{dt} = r \frac{d \theta}{dt} = r \omega
    ahhh clever!

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Updated: December 10, 2007
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