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[FBD] Stick balancing

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the linear and angular accelerations given that FA is the applied force.
    v is the current linear velocity and w is the current angular velocity.
    r is the radius of the stick.
    h is length of the stick.
    d is angle from the vertical axis.

    2. Relevant equations
    a = dv/dt; linear acceleration
    u = dw/dt; angular acceleration
    Icenter = m h2/12; moment of inertia of stick

    3. The attempt at a solution
    Sum of horizontal forces:
    m ax = -FA
    ax = -FA/m

    Sum of vertical forces:
    may = -mg + FN = 0

    Sum of torque
    T = I u = 0.5 h FN sin(d) - 0.5 h FA cos(d)
    u = 0.5 h ( mg sin(d) - FA cos(d) ) / ( m h2/12 )
    u = ( 6 / m h )( mg sin(d) - FA cos(d) )

    Is this correct?

    Shouldn't the vertical acceleration be non-zero? Because if w and u are non-zero, and the finger maintains at the same height, then the center of mass of the stick must be moving. What is wrong with the above?

    - Thanks
    And thank you for replying to my other thread. There are so many threads I thought I shouldn't bump the one that was solved.
  2. jcsd
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