What is a moment?

The concept of a moment (or force moment) is that of a force at a distance. It not only measures how strong the force is but also how far away it is applied (for rotational purposes).

Consider s see-saw with a bear and a skunk.

In order to quantify the idea of "balance" you need a description of the weight of each object as well as how far away does this weight apply relative to the fulcrum (red triangle).

You equate the moments

$$ \mbox{moment of bear} = \mbox{moment of skunk} $$ $$ x_B\, W_B = x_K\, W_K $$

_{where $x_B$ and $x_K$ are the distances (of the bear and the skunk respectively), and $W_B$ and $W_K$ the weights (of the bear and the skunk respectively).}

The units are $\mbox{[force]} \times \mbox{[distance]} $ for moments. In the SI sytem that is $\rm N\,m$ (Newton-meters) and in the customary units $\rm lbs\;ft$ (Foot-pounds).

$\mathrm{Nm}$ is not the moment (or torque), but the physical unit of torque in the SI unit system. The torque is defined as $\tau = F_\bot d$ that is the component of the force orthogonal to the line connecting the point of action and the pivot point multiplied by their distance.

For example, if you use a wrench that is one meter long and apply a force of $1\,\mathrm{N}$ at the end of the wrench you exert a torque of $1\,\mathrm{Nm}$ on the nut, the point is that, due to the law of levers, the same force is applied to overcome the friction between the nut and the threading if you had a wrench that is $0.1\,\mathrm{m}$ long and you would apply the force of $10\,\mathrm{N}$ (giving also a torque of $\tau = 0.1\,\mathrm{m} \cdot 10\,\mathrm{N} = 1\,\mathrm{Nm}$). In this sense, you drive the nut with the same force in both cases, and therefore the correct quantity to describe the action on the nut is the torque.

To extend, the torque is the analogue of force for circular motion. If you, for example, consider a flywheel then there is the equation $\tau = J\alpha$, that is formally analogue to $F = ma$, and describes that you have to apply a certain torque to achieve a certain angular acceleration $\alpha$. The factor $J$ is called the moment of inertia.

For a rigid body to remain at rest the sum of the forces has to be zero (otherwise the centre of mass will be accelerated and the body will not be static) and the sum of the torques hast to be zero (otherwise the rigid body will begin to rotate and therefore will not be static).

The moment is not a force itself but is rather a quantity that describes the forces tendency to cause rotation about a certain fixed pivot. Consider for example the simple lever. The longer you make the arm, the easier it is to move a certain amount of weight with the same force. This is because by making the arm longer you increased the moment of the force in the object.