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Lagrangian Mouse on Wheel

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data
    A mouse of mass m runs around the inner circumference of a vertical wheel which is free to rotate about the centre. The wheel has mass M and moment of inertia I. Let θ be the angle that the radius vector makes to the mouse from the downward vertical at time t. Write down the lagrangian for the motion.


    2. Relevant equations
    L = T - V


    3. The attempt at a solution
    So I can write down the kinetic energy of the mouse quite easily, in polar coordinates it's at constant ρ so T_mouse = 1/2*m*a^2*θ^2
    Also the potential energy is V=mgacosθ.
    The bit i'm confused about is the rotational energy of the wheel

    Thanks!
     
  2. jcsd
  3. Apr 10, 2013 #2

    tiny-tim

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    hi starryskiesx! :smile:

    (try using the X2 button just above the Reply box :wink:)
    you mean 1/2*m*a22 :wink:
    1/2 Iω2 :smile:
     
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