3.2MechanicsCore

Moments and Equilibrium

A small child can lift an adult off the ground on a see-saw, without being anywhere near as strong — simply by sitting further from the pivot. The turning effect of a force depends on more than just its size, and understanding exactly what else it depends on is the key to this entire topic.

40 min Video by Launchpad Learning Module 3.2 Forces in action

Moments — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define the moment of a force about a point
State and apply the principle of moments
Explain what is meant by a couple
Solve problems involving objects in rotational and translational equilibrium

The moment of a force

The $moment$ of a force about a point is a measure of its turning effect, equal to the force multiplied by the perpendicular distance from the pivot to the line of action of the force. A larger force, or a force applied further from the pivot, produces a larger moment — exactly why a longer spanner makes loosening a tight bolt easier.

Moment = F \times d

Moment (N m) = force (N) × perpendicular distance from the pivot (m).

1Use

Moment = F \times d

= 40 \times 0.25

Answer

10

N m

Tip — The distance used must always be the PERPENDICULAR distance from the pivot to the force’s line of action — if the force is applied at an angle, you may need to resolve it, or use the perpendicular component of the distance instead.

The principle of moments

The $principle of moments$ states that for an object in rotational equilibrium (not turning), the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that same point. This is exactly the physics behind a balanced see-saw, or any beam supported at a pivot.

1Anticlockwise moment (left side):

30 \times 0.80 = 24

N m.

2For equilibrium, clockwise moment (right side) must equal this:

48 \times d = 24

3Rearranging:

d = \frac{24}{48}

Answer

d = 0.50

m from the pivot.

Tip — Choosing the pivot itself as the point to take moments about is often the smartest move — any unknown force acting exactly AT the pivot then has zero moment and simply drops out of the equation.

Couples

A $couple$ is a pair of equal and opposite forces, not acting along the same line, whose combined effect is a pure turning effect with no resultant (translational) force at all — like the two hands used to turn a steering wheel. The total moment of a couple is the size of one force multiplied by the perpendicular distance between the two lines of action.

Full equilibrium

An object is in complete equilibrium only when BOTH conditions hold simultaneously: the resultant force in every direction is zero (translational equilibrium), and the principle of moments is satisfied about every point (rotational equilibrium). Problems involving beams, ladders and levers typically require both conditions to find every unknown force.

Equation recap

Moment = F \times d

Moment of a force about a point.

Σ (clockwise moments) = Σ (anticlockwise moments)

Principle of moments (rotational equilibrium).

Common mistakes to avoid

Using the direct distance to a force rather than the perpendicular distance to its line of action.

Moment = F × PERPENDICULAR distance — if the force acts at an angle, you may need to resolve it or find the perpendicular component of the distance.

Assuming rotational equilibrium alone (principle of moments satisfied) means an object is in full equilibrium.

Full equilibrium also requires zero resultant FORCE in every direction — a satisfied moments equation alone doesn’t guarantee the object isn’t accelerating sideways.

Forgetting that a force acting exactly at the chosen pivot has zero moment about it.

Choosing the pivot as your reference point conveniently eliminates any unknown force acting there — a useful problem-solving trick.

Key takeaways

Moment of a force = force × perpendicular distance from the pivot to its line of action.
Principle of moments: for rotational equilibrium, sum of clockwise moments = sum of anticlockwise moments about any point.
A couple is a pair of equal, opposite, non-collinear forces producing a pure turning effect with no net force.
Full equilibrium requires both zero resultant force AND the principle of moments satisfied.

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Moments and Equilibrium

40 min Video by Launchpad Learning Module 3.2 Forces in action