# Moments and Moment Equilibrium

## Moments

In the Forces section, the equilibrium of forces was discussed. If forces are equal and opposite, then the net effect will be zero and no acceleration will occur. However, there are instances when this doesn’t always hold true.

Imagine a rig bar, with a pivot at the middle. If masses are placed on the bar equally spaced each side of the pivot and with equal mass, then the pivot will remain in balance. The force equilibrium is shown in the diagram below:

Now, if we move one of the masses to be twice as far from the pivot as it started, we can still draw the force equilibrium diagram (and the vertical reaction force will be the same), but we all know that the bar will start to rotate.

There is clearly something additional going on in the system other than simply the equilibrium of vertical forces, clearly the position of forces from the pivot has a bearing. This introduces us to the concept of “Moments”.

A moment is very simply defined as:

M = Fz

Where F is the applied force, z is the distance to the point of rotation, measured at right angles to the direction of force and M is the moment that results (click for useful info). A moment usually applies along an axis, with the axis of the moment being perpendicular to both the direction of the force and also to the orientation of the lever arm (click for useful info).

By breaking down the two previous examples we can see how the moments applied change:

Moments can also be used to understand the action of levers, such as a crowbar. By positioning a pivot close to a load and applying a small load to the lever far away from the pivot a much greater load will result at the other end (click for useful info).

If a force is out of balance, it gives rise to an acceleration. If a moment is out of balance then it gives rise to an angular acceleration, i.e. it rotates. For a structural system to be in complete balance, both the forces and moments must be in balance.

Again, Structural and Civil Engineers aim for a system to be in equilibrium, with no out of balance forces or moments. Just as you don’t want a building or structure to accelerate away (forces), you also don’t want it to fall over (moments).

Mechanical Engineers in particular often desire moments to be out of balance, using the out of balance moment to give rise to a rotation, or vice versa (click for useful info).