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Angular acceleration of a beam?

  1. Mar 23, 2013 #1
    This problem is making me want to tear my hair off.
    I am trying to calculate the time it takes for a beam to fall to the ground.


    It would be great if I could calculate the rate of change of angular acceleration, as the acceleration would depend on the angle.

    The equation for momentum or torque = moment of inertia * angular acceleration = cos(angle) * arm * m*g

    Here the arm would be equal to the distance from the point of rotation to the center of the mass of the beam.

    The other equation I find useful is: s = -1/2gt^2 + Vt + s

    Again, with changing acceleration, I am lost.
  2. jcsd
  3. Mar 23, 2013 #2


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    Science Advisor

    Consider an analysis based on energy. How fast must the bar be rotating as it passes through a given angle in order for total energy to be conserved?

    That should then allow you to derive angular velocity as a function of angle.

    That should lead you to a solution that does not involve solving a differential equation.
  4. Mar 23, 2013 #3
    Google something called the 'inverted pendulum' for some insight how to solve this.
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