Mechanisms based on the rule of moments
The shortest (perpendicular) distance from the line of action of a force to the rotation axis is the lever arm l of the force. The moment of force is M = F·l, unit 1 N·m; take the moment that turns clockwise as positive and the opposite as negative. A body with a rotation axis is in equilibrium if the algebraic sum of all moments is zero: M₁ + M₂ + … = 0 (Archimedes’ rule of moments). For a lever this reads F₁l₁ = F₂l₂. There are three kinds of lever: fulcrum between the forces (two-arm lever, scissors, balance), load between the fulcrum and the effort (wheelbarrow), and effort between the fulcrum and the load (spoon, shovel, human forearm). A fixed pulley gives no gain in force, only changes direction; a movable pulley halves the force. In a block and tackle with the load shared by n ropes, ideally F = P/n, but the rope to be pulled is n times longer (no gain in work). In real mechanisms friction makes the efficiency less than 100%.
In class: balance a 30 cm ruler on a pencil, place stacks of identical coins at both ends and find the number/distance of coins for balance (F₁l₁ = F₂l₂). Record the results in a table. Do it on a flat table so the pencil does not roll away.