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Block on a Cylinder, using Lagrange's Equation

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data
    A hard rubber cylinder of radius r is held fixed with its axis horizontal, and a wooden cube of mass m and side 2b is balanced on top of the cylinder, with its center vertically above the cylinder's axis and four of its sides parallel to the axis.

    Assuming that b < r, use the Lagrangian approach to find the angular frequency of small oscillations about the top.

    2. Relevant equations
    T (kinetic energy) = (1/2)(mv^2 + I[tex]\dot{\theta}[/tex][tex]^{2}[/tex])
    I (moment of inertia about the center of mass) = (2mb^2)/3
    U (potential energy)= mg[(r + b)cos[tex]\theta[/tex] + r[tex]\theta[/tex]sin[tex]\theta[/tex]]

    3. The attempt at a solution

    Now, what would be nice would be to write the coordinates of the center of mass. I can differentiate that and get v, which I plug into T and then I have L = T - U and I can do the problem.

    But how can I write down the coordinates of the CM? I never was very good at center of mass problems.

    Thanks ahead of time.
  2. jcsd
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