## Moment theory.

Moment theory
Balance in an object concerns the size, the force exercised on the object and place where the forces are applied.

Imagine a see-saw.
When the fulcrum is in the middle of the see-saw and two children of equal weight sit on it the see-saw is balanced. Only the removal of the children will bring the see-saw into motion. Put a heavier child on one side of the see-saw and the see-saw will become unbalanced. The heavier child will fall to the ground and the lighter child will go into the air.
Put the two children of equal weight back onto the see-saw but put one child further forward than the other. The child sitting farthest from the fulcrum will fall to the ground and the other will go into the air.
There is therefore a relationship between the balance of the bodies and the forces being exercised and the area where the forces are being applied.
This connection is recorded in the so called moment theory.
A moment is the product of force and arm.
The theory is as follows:
“Whenever an object is balanced, then the sum of the forces that are necessary to rotate that object in one direction, around a fulcrum are equal to the forces that are necessary to rotate that object in the opposite direction”.
In order to avoid any confusion it has been agreed upon that the forces travelling to the right (clockwise) are the positive (+) forces and the forces travelling to the left (anti-clockwise) are the negative (-) forces.
If the sum of the forces of the working moments is equal to 0 then the object is in balance.
This is mostly expressed as:
ΣM = 0
Σ is the Greek letter sigma, which means the sum of all the forces, negative and positive.

The forces are attacking the beam in such a way that the beam is in balance.
Anyone who can understand this simple example works understands the theory behind the Weight and Balance of an aircraft.
Compare the downward forces on the beam with that of the weight of an aircraft, the fuel, the crew, the passengers etc. and the upward force produced by the aircraft wings.

Below a second example.