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Math Help - Mechanics Problem

  1. #1
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    Mechanics Problem

    I did
    \tan \theta = \frac{r}{h} where r is the radius
    so h \tan \theta = r

    T \cos \theta = mg where T is the tension
    T = \frac{mg}{\cos \theta}
    using the standard circular motion result
    T \sin \ theta = m \omega ^2 r
    mg \tan \theta = m \omega ^2  h \tan \theta

    giving \omega^2 = \frac{g}{h}

    where did i go wrong ?
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  2. #2
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    Quote Originally Posted by bobak View Post
    I did
    \tan \theta = \frac{r}{h} where r is the radius
    so h \tan \theta = r

    T \cos \theta = mg where T is the tension
    T = \frac{mg}{\cos \theta}
    using the standard circular motion result
    T \sin \ theta = m \omega ^2 r
    mg \tan \theta = m \omega ^2  h \tan \theta

    giving \omega^2 = \frac{g}{h}

    where did i go wrong ?
    The only thing wrong is that there are two horizontal forces on the ring: not just a component Tsin(θ) from the RA section of the string but also the tension T in the RB section of the string.
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  3. #3
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    Silly me. Thank a lot Opalg.
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