The principle of moments states that for a balanced object, the total clockwise moment about any pivot equals the total anticlockwise moment. A moment is calculated by multiplying the force by its perpendicular distance from the pivot. This rule applies to any lever, beam, or seesaw in equilibrium.
What is a moment of a force?
A moment is the turning effect of a force about a pivot (also called a fulcrum). It measures how much a force tends to rotate an object rather than push it in a straight line.
$$\text{Moment} = \text{Force} \times \text{Perpendicular distance from pivot}$$
Units: the moment is measured in newton-metres (N·m). Force is in newtons (N) and distance is in metres (m).
The critical word is perpendicular: the distance must be measured at 90° to the line of action of the force. If you push at an angle and use the straight-line distance to the pivot instead of the perpendicular component, your calculation will be wrong.
What does the principle of moments state?
For an object that is in rotational equilibrium (not turning), the principle of moments states:
Sum of clockwise moments = Sum of anticlockwise moments
Both sums are taken about the same pivot point. If the clockwise moments outweigh the anticlockwise moments, the object rotates clockwise; if the reverse is true, it rotates anticlockwise; only when they are equal does the object stay balanced.
This is a consequence of Newton's first law applied to rotation: a balanced object has zero net turning effect, just as a stationary object has zero net force.
How do you calculate moments — worked example?
Worked example:
A 60 N child sits 2.0 m to the left of the pivot on a seesaw. A 40 N child sits on the right. How far from the pivot must the 40 N child sit for the seesaw to balance?
- Clockwise moment (right side): F × d = 40 × d
- Anticlockwise moment (left side): 60 × 2.0 = 120 N·m
- Apply the principle of moments: 40 × d = 120
- Rearrange: d = 120 ÷ 40
- Calculate: d = 3.0 m
The lighter child must sit further from the pivot to produce the same moment as the heavier child sitting closer. This is the fundamental mechanic of a lever: a small force at a large distance can balance — or overcome — a large force at a small distance.
What does it mean for an object to be in equilibrium?
An object is in equilibrium when two conditions are both met:
- The resultant force on the object is zero (no net linear acceleration — the object is not speeding up, slowing down, or changing direction).
- The resultant moment about any point is zero (no net rotational acceleration — the object is not starting to rotate).
Both conditions must hold simultaneously. A bridge, a see-saw, and a crane jib balancing its counterweight are all examples of objects in rotational equilibrium. Exam questions often give you several forces and ask you to find an unknown force or distance by applying condition 2.
How do you find an unknown force using the principle of moments?
Worked example:
A uniform beam of length 4.0 m is pivoted at its centre. A 200 N weight hangs 1.5 m to the left of the pivot. A second weight W hangs 1.0 m to the right. Calculate W.
- Anticlockwise moment: 200 × 1.5 = 300 N·m
- Clockwise moment: W × 1.0
- Principle of moments: W × 1.0 = 300
- W = 300 ÷ 1.0 = 300 N
Note on uniform beams: a uniform beam has its weight acting at its midpoint (centre of mass). If the beam is pivoted at its centre, its weight creates no moment (zero distance from pivot). If the pivot is off-centre, the beam's own weight must be included as an additional moment.
How are moments applied in real life?
| Application | How the principle of moments is used |
|---|---|
| Seesaw / see-saw | Heavier child sits closer to pivot; lighter child sits further away |
| Wheelbarrow | Handles are far from the wheel pivot → a small upward force lifts a heavy load |
| Crowbar | Long handle gives a large moment from a small force to shift heavy objects |
| Crane | Counterweight on the short side balances a large load on the long arm |
| Scissors / pliers | Force applied far from pivot; blades close to pivot amplify the cutting force |
The common thread: move the force further from the pivot to increase the moment without increasing the force — this is called mechanical advantage.
Frequently asked questions
What is the principle of moments in GCSE physics?
The principle of moments states that for an object in rotational equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments. A moment equals force multiplied by perpendicular distance from the pivot, measured in newton-metres (N·m). If the two sides are unequal, the object will rotate towards the side with the larger total moment.
How do you calculate a moment?
Multiply the force (in newtons) by the perpendicular distance from the line of action of the force to the pivot (in metres). The result is the moment in newton-metres (N·m). The word "perpendicular" is essential — if the force acts at an angle, use the component of distance that is at 90° to the force. Forgetting to use the perpendicular distance is the most common error in exam calculations.
What is the difference between a moment and a torque?
In GCSE physics, the terms moment and turning effect are used interchangeably. At A-level and beyond, torque (τ) is the more precise term, defined as the cross product of force and displacement vectors. At GCSE, you only need to know that moment = force × perpendicular distance, measured in N·m.
Why must both linear equilibrium and rotational equilibrium hold?
An object can have zero net force but still rotate — for example, two equal and opposite forces applied at different points on a rod create zero net force but do rotate it (this is called a couple). True static equilibrium requires both the resultant force and the resultant moment to be zero, so that the object neither accelerates in a straight line nor starts spinning.
For Socratic GCSE physics with Professor Newton — predict which side of a beam will tip before applying the principle of moments, then check whether your intuition about distance and force agrees with the arithmetic — visit aitutors.me.