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Pendulum in non inertial frame

  1. Nov 12, 2013 #1
    1. The problem statement, all variables and given/known data
    A pendulum is placed on a rotating platform which rotates with angular velocity ω around an axis, at equilibrium the angle between vertical and pendulum is θ
    θ= 20 degrees
    ω= 10 1/s
    how far is the pendulum placed from the axis


    2. Relevant equations
    [itex]a_c=\frac{v^2}{R}=\omega^2R[/itex]



    3. The attempt at a solution
    the frame is non inertial so effective g is [itex]\sqrt{g^2 + \omega^2R}[/itex]

    I'm not really sure where to go from here, i thought about doing
    [itex] \omega=\sqrt{\frac{g}{l}}=\sqrt{\frac{g^2 + \omega^2R}{l}}[/itex] and solving for R however [itex]l[/itex] isn't given so i'm not really sure where to go next, any ideas?

    Thanks, Luke
     
  2. jcsd
  3. Nov 12, 2013 #2
    You are wrong considering a mathematical pendulum instead of conic one.

    So you may write down (T is a funicular force):
    $$
    m a_c = m ω^2 R = T sinθ
    $$
    $$
    0 = T cosθ - m g
    $$
     
  4. Nov 12, 2013 #3
    Ah ok, so:

    [itex]Tcos\theta=mg (1)
    Tsin\theta=m\omega^2R (2) [/itex]


    doing (2)/(1) gives

    [itex]R=\frac{gtan\theta}{\omega^2}[/itex]

    plugging in the numbers gives 0.036m, is this correct?
     
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