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Homework Help: Kinematics of Inverted Physical Pendulum

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data

    A stick of mass M, length L, stands upright on a table, pivoted to the table.

    What is the angular velocity as it hits the table?


    2. Relevant equations

    ang. accel = (3g/2L)cos theta

    w = (3g/2L) integral cos theta dt


    3. The attempt at a solution

    theta (t) = ????

    Solution involves elliptic integrals?? Not familiar with numeric methods.

    Any approximation of the velocity at the table would be good for now.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 1, 2010 #2
    Why don't you conserve mechanical energy?
     
  4. Apr 1, 2010 #3
    Yeah this seems right. All you need to use is the parallel axis theorem, find the initial potential energy and solve for omega noting that the stick gains both rotational and translational kinetic energy.
     
  5. Apr 1, 2010 #4
    Translational?
     
  6. Apr 1, 2010 #5
    linear kinetic energy 1/2mv2 instead of 1/2Iw2

    Actually thinking about it, it's not rolling so there probably wouldn't be translational kinetic energy gained.
     
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