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Homework Help: Name of equilibrium when ∑Fx and Fy = 0 but there's still a moment (statics)

  1. Sep 8, 2012 #1
    1. The problem statement, all variables and given/known data
    "For there to be static equilibrium of a rigid body the sum of the forces and moments must equal zero."
    From high school i've understood that a body in equilibrium doesn't accelerate but remains at rest or ofc in constant motion.
    Is the idea of static equilibrium of rigid bodies the same? For the body to remain in its "state of motion" all the forces and moments must balance?

    3. The attempt at a solution
    I have only solved 2D static problems. In this case for forces to balance the sum of Fx and Yx must equal zero for there to be static equilibrium.

    My question is, does the moment need to be balanced too because we need to consider the 3rd dimension as well (z)?
    If we have a body in plane x, and two balanced forces (whos lines of action don't intersect the point about which we take the moment) are applied in plane y, there will be a rotation about plane z. If there is a rotation then the must be a centripetal acceleration and so therefore forces are unbalanced. Thus, the're cannot be a moment if we want all forces to sum 0.
    However, the point about which we calculate the moment will actually remain in the same (x,y) coordinates so there is still some sense of equilibrium as well when there's a moment.

    So, when there's "static equilibrium" everything sums to zero. What the type of equilibrium when there's a moment about a point and Fx and Fy balance?
  2. jcsd
  3. Sep 8, 2012 #2


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    When the forces all sum to zero but the moments do not, the body is in translational equilibrium, but not in rotational equilibrium. So it's center of mass will not accelerate (if it was initially at rest, the center of mass will not move), but there will be rotation about it.
    Last edited: Sep 8, 2012
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