EASA / CAR Part-66 · Module 2 · 2.2 Mechanics · Cat A
Objective: calculate a moment as force × distance from the pivot, and predict when a loaded beam balances — the principle behind spanners, control surfaces and aircraft weight and balance.
The two moments are equal, so the beam is in equilibrium.
A moment is the turning effect of a force: the force multiplied by its perpendicular distance from the pivot, measured in newton-metres. Distance counts every bit as much as force, which is why a long spanner shifts a nut a short one will not, and why a small weight far out balances a large weight close in.
A body is in equilibrium when two conditions hold together: the forces balance, and the moments balance. For this beam that means the clockwise moment equals the anticlockwise moment. The beam does not care how the numbers are made up — 200 N at 0.5 m and 50 N at 2.0 m both give 100 N·m, and either will balance the other.
This is the arithmetic behind aircraft weight and balance. Every item of load has a moment about the datum, and the centre of gravity is the total moment divided by the total weight. Loading the same mass further aft gives a larger moment and moves the CG aft, which is why a loadsheet records both the weight and the arm of every item, never just the weight.