Moment Equilibrium
Take a look at the figure below.
A student pushes up on a pencil with his forefingers, as shown at the left. Mouse-over each finger; note that with reference to the center of the pencil, the left finger force tends to rotate the pencil clockwise (considered negative), while the right finger force tends to rotate the pencil counter-clockwise (considered positive). For the FBD of the pencil (right) fingers have been replaced by two forces, F1 and F2.Moment equilibrium is said to exist when there are no unbalanced moments acting on a body; it is a necessary condition for the overall static equilibrium of a body (i.e. the body does not spin or rotate). This can be denoted by the following vector equation:
where r is a position vector from the point of interest to each respective force. For the case above, this degenerates into:-(F1d) + (F2d) = 0
or
F1 = F2 It should be noted that having the sum of all moments on a body equal to zero is a necessary but not sufficient condition for static equilibrium. The force equilibrium condition must also be met, as previously discussed in the module. (Note: The physical situation above demonstrates moment equilibrium but not force equilibrium).Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.