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Tangent force on a rotating rod

  1. Jun 21, 2009 #1
    1. The problem statement, all variables and given/known data
    I've been working on this problem for several hours with no luck. Any help would be appreciated. (It's not homework)

    A thin rod of mass M and length L is hinged at the bottom, and almost balanced vertically. It starts to fall. Find the tangential component of the force that the part of the rod below r exerts on the part of the rod above r.

    (Theta is the angle between the rod and the vertical, r is the distance on the rod from the hinge)


    2. Relevant equations

    SOLN: F = Mg(L-r)(3r-L)/(4 L^2) * Sin(theta)

    d x F = I *(angular acceleration)


    3. The attempt at a solution

    I've already determined the angular acceleration to be

    3/2 g/L Sin(theta)

    using the Lagrangian.

    I've calculated the moment of inertia to be:

    1/3 M (L-r)/L [(L-r)^2 + 3*r^2]

    using the parallel axis theorem.

    I've tried for several hours to get the final equation for the force but I haven't been able to do so yet.... maybe there is a mistake in the moment of interia?
     
  2. jcsd
  3. Jun 21, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Good.

    Rather than go this route, focus on the center of mass of the piece in question. What is its acceleration? What must be the net force on it?
     
  4. Jun 22, 2009 #3
    Doc Al,

    Thanks for your help. I was able to get the solution this morning. I won't spoil the rest of the details for anyone who wants to try it.
     
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