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Pendulum suspended from Horizontal rotating hoop

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A massless hoop is suspended horizontally and is free to rotate about a vertical axis through its center with a constant angular velocity (omega). Attached to the edge of the hoop is a simple pendulum that is restricted to oscillate in only the radial direction. find the Lagrangian of the system.

    M= mass of pendulum
    L= Length of Pendulum
    ∅= angle the pendulum makes with the vertical
    ω=angular velocity of hoop
    R= radius of hoop

    2. Relevant equations

    L= T-U
    T= Kinetic energy
    U=Potential Energy


    3. The attempt at a solution
    T(hoop)=(1/2) I(hoop)*ω^2
    But I is dependent upon the mass of the hoop and since the mass of the hoop is 0 so is I(hoop)->T(hoop)=0

    T(pendulum)=(1/2)M[L*(d∅/dt)]^2+(1/2)I(pendulum)*ω^2
    T=1/2M[(L*d∅/dt)^2+(R+Lsin∅)^2*ω^2
    U=-MgLcos∅

    L=(1/2M[(L*d∅/dt)^2+(R+Lsin∅)^2*ω^2)+MgLcos∅

    Is this right?
     
  2. jcsd
  3. Dec 4, 2012 #2

    haruspex

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    Looks right to me.
     
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