What is a moment?

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.

The key thing you missed is that moment isn't a unit, so you don't say '1 moment...'

Moment is the same thing as torque, which you probably have an intuitive understanding of already. It's a measure of your ability to cause rotation with force.

You can visualize it by thinking of pushing a door from a point really close to the hinge of the door, or a point near the opposite edge. It's obviously easier to open it from the edge.

This brings us to our formula. Your ability to open the door is influenced by:

• the force you apply (directly proportional)
• the distance between your point of application of the force and the center axis around which the door rotates (directly proportional again)

Hence we find that the unit of torque (or moment, if you prefer) is $Nm$, because the formula is: $tau =Ftimes s$.

$mathrm{Nm}$ 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 $tau = Jalpha$, 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).