The lesson: Principle of Moments
Equilibrium
In this section
- Calculate clockwise and anticlockwise moments.
- Apply the principle of moments.
- Solve balancing-beam problems.
When an object is balanced and not turning, the principle of moments applies: the total clockwise moment about any pivot equals the total anticlockwise moment. This is the condition for rotational equilibrium, and it is the tool for almost every beam or see-saw question.
Work through it methodically. Choose the pivot. For each force, work out its moment and label it clockwise or anticlockwise. Set the two totals equal, then solve. A 4 N load 0.3 m to the left of the pivot gives 1.2 N m anticlockwise; to balance it, an 8 N load on the right must sit at 1.2 ÷ 8 = 0.15 m.
Notice what this shows: equal forces do not balance unless they are equally far from the pivot, and a small force far out can balance a large force close in. That is the whole principle of a lever, and it is why a crowbar works.
Full equilibrium needs one more condition. As well as the moments balancing, the resultant force must be zero, or the object would accelerate in a straight line while not rotating. For a beam on a pivot, the upward force from the pivot equals the total downward force on the beam.
Key points
- In equilibrium: total clockwise moment = total anticlockwise moment.
- Full equilibrium also requires zero resultant force.
- A small force far from the pivot can balance a large force close to it.