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Rotational equilibrium confusion

  1. Oct 11, 2007 #1
    1. The problem statement, all variables and given/known data
    A uniform bar has 4 forces acting on it as shown in the diagram. Is the object in rotational equilibrium? Explain.

    2. Relevant equations
    Rotational equilibrium happens when there is no net moment.
    Summation of anti clockwise moments = summation of clockwise moments
    Moment about a pivot if given by the product of the force by the perpendicular distance from its line of action to the pivot.

    3. The attempt at a solution
    Yes, it is in rotational equilibrium. Taking center of mass as pivot, summation of anti clockwise moments = summation of clockwise moments. Therefore the bar is in rotational equilibrium. We take center of mass as center of the bar as pivot, since it is a uniform bar. Mass is not* needed because it acts through the pivot and will cause no turning effect about the point.

    However, my school insists that to tackle these kind of questions, the pivot should be taken at the extreme corner of the uniform bar and not the center of mass. Therefore the answer is that the bar is not in rotational equilibrium; the bar will start to rotate. If that is the case, then the same uniform bar in the following diagram should start to rotate irrevocably:


    Imagine the bar is in a wind tunnel which effectively* eliminates its weight, and it is floating, applying 2 equal forces at each extreme ends should result in rotational equilibrium but not translational equilibrium. However, my school insists that despite the case we should take the pivot at the corner of the bar and calculate the moment about that point, causing the said bar to start spinning. This defies logic! If you hang a ruler by both ends with identical strings of identical length, the ruler will start spinning wildly?! Help! I do not wish to sit for my GCE A' levels with this confusion. Thanks in advance :)
    Last edited: Oct 11, 2007
  2. jcsd
  3. Oct 11, 2007 #2


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    Homework Helper

    The problem here is with definitions... what is rotational equilibrium? when the sum of the moments about a point is 0... but which point? I think the definition requires that the sum of moments be 0 about every point. I think this can only occur when Fnet is 0...

    Since there is at least one point here about which sum of moments is not 0, the system is not in rotational equilibrium.
  4. Oct 11, 2007 #3


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    There is a difference between rotation about a fixed axis and 'free' rotation when there is no pivot point or points. In this latter case the tendency of an object to rotate is always about the center of mass. There is no rotation in your example because there is no unbalanced torque about the center of mass.
  5. Oct 11, 2007 #4


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    Staff: Mentor

    There is no net moment about the center of mass or midpoint of the 4-m horiontal bar. However, if one looks at any point on the horizontal bar other than the midpoint, there would be a net moment.
  6. Oct 12, 2007 #5
    So, if the above question appeared again, should I answer by taking pivot as the center of mass or should I follow my school's method and take pivot as the extreme end of the bar? Both methods will yield different answers, and it would be Cambridge that would be marking my GCE A level paper, not my school. Thanks.
  7. Oct 12, 2007 #6


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    Staff: Mentor

    Consider all possibilities.
  8. Oct 13, 2007 #7
    I'm sorry I don't quite understand what you mean... The previous time it appeared in my paper was when it was a multiple choice question, so I can't use words to explain my choice and convince the marker that he or she should accept my answer...
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