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Math Help - Conical pendulum and changing angle

  1. #1
    Senior Member Mukilab's Avatar
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    Conical pendulum and changing angle

    If the mass is changed hanging on a conical pendulum, will theta change?
    I understand that the time period is independent of the mass, but theta is also dependent on the radius and height of the conical pendulum, which will surely change when the mass changes?

    Also, if you are given the angular speed of the pendulum (omega or w) how can you test if the string of the pendulum is strong enough to support the mass?
    Surely you don't need to use omega and just see if the string can freely support a weight of (mg/cos[theta]) where m is the original weight and g is gravity

    Please refer to this diagram #
    http://upload.wikimedia.org/wikipedi...ndulum.svg.png
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  2. #2
    MHF Contributor
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    Re: Conical pendulum and changing angle

    Quote Originally Posted by Mukilab View Post
    If the mass is changed hanging on a conical pendulum, will theta change?
    I understand that the time period is independent of the mass, but theta is also dependent on the radius and height of the conical pendulum, which will surely change when the mass changes?

    Also, if you are given the angular speed of the pendulum (omega or w) how can you test if the string of the pendulum is strong enough to support the mass?
    Surely you don't need to use omega and just see if the string can freely support a weight of (mg/cos[theta]) where m is the original weight and g is gravity

    Please refer to this diagram #
    http://upload.wikimedia.org/wikipedi...ndulum.svg.png
    It appears that the mass has no effect on $\theta$. It does of course affect the tension.

    If you know both the mass and the angular velocity you can calculate the tension.

    $T=\dfrac{m}{L \omega^2}$

    Note that T must increase as $\theta$ does and so ensuring that the string doesn't break when the pendulum is at rest won't ensure it won't break when moving.

    Conical pendulum - Wikipedia, the free encyclopedia
    Last edited by romsek; March 23rd 2014 at 03:46 PM.
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