Not all forces make things move along — some make them turn. The turning effect of a force is called a moment, and understanding moments lets you explain levers, see-saws, balances and the stability of structures. This topic is part of statics, the study of objects in balance (equilibrium).
The moment of a force
The moment of a force is its turning effect about a pivot:
moment = force × perpendicular distance from the pivot (units: newton metre, N·m)
The bigger the force, or the further it acts from the pivot, the greater the turning effect. This is why a long spanner loosens a tight nut more easily than a short one — the larger distance gives a larger moment for the same effort.
The principle of moments
An object is in rotational equilibrium (balanced, not turning) when:
total clockwise moments = total anticlockwise moments
This is the principle of moments. It lets you solve see-saw and beam problems. For example, if a 200 N child sits 1.5 m from the pivot of a see-saw, to balance, a 300 N child must sit at a distance d where 300 × d = 200 × 1.5, giving d = 1.0 m from the pivot.
For an object to be in complete equilibrium, two conditions must hold:
- the resultant force is zero (no net push), and
- the resultant moment is zero (no net turn — principle of moments).
Centre of gravity
The centre of gravity of an object is the single point through which its whole weight appears to act. For a uniform regular object it is at the geometric centre. You can find the centre of gravity of an irregular flat shape by hanging it from two different points and using a plumb line: the centre of gravity lies where the lines cross.
Stability
An object's stability depends on its centre of gravity and its base:
- A low centre of gravity and a wide base make an object more stable (e.g. a racing car, a bus carrying passengers low down).
- A high centre of gravity and a narrow base make it unstable and easy to topple.
An object topples when its centre of gravity passes outside its base — when the line of action of its weight falls beyond the edge it is resting on.
Simple machines
A machine lets us do work more conveniently, often by applying a small effort to overcome a large load.
- A lever uses moments: effort × effort distance = load × load distance. A crowbar and a see-saw are levers.
- A pulley changes the direction of a force and (with several wheels) lets a small effort raise a heavy load.
- An inclined plane (ramp) lets a load be raised using a smaller force over a longer distance.
Two useful quantities describe machines:
mechanical advantage = load ÷ effort velocity ratio = distance moved by effort ÷ distance moved by load efficiency = (useful work output ÷ work input) × 100%
No machine is 100% efficient, because some energy is always wasted overcoming friction (as heat).
A worked beam problem
Beam questions can involve more than two forces. Suppose a uniform 2 m plank rests on a pivot at its centre. A 40 N weight hangs 0.8 m to the left of the pivot and a 30 N weight hangs 0.5 m to the left of the pivot; you must find a single weight placed 1.0 m to the right that balances the beam.
- Total anticlockwise moment (the two left-hand weights): (40 × 0.8) + (30 × 0.5) = 32 + 15 = 47 N·m.
- For balance, the clockwise moment must also be 47 N·m.
- So W × 1.0 = 47, giving W = 47 N.
Because the plank is uniform and the pivot is at its centre, the plank's own weight acts through the pivot and has zero moment, so it can be ignored — a point examiners like to test. If the pivot were not at the centre, you would have to include the plank's weight acting at its centre of gravity.
Types of lever
Levers are classified by where the load, effort and pivot lie, and CSEC may ask you to give examples:
- First-class — pivot between effort and load (a see-saw, a pair of scissors, a crowbar).
- Second-class — load between pivot and effort (a wheelbarrow, a bottle opener).
- Third-class — effort between pivot and load (tweezers, the human forearm).
In the body the forearm is a third-class lever: the elbow is the pivot, the biceps provides the effort close to the pivot, and the load is in the hand. This gives a large, fast movement of the hand for a small contraction of the muscle — though the muscle must pull with a large force, which is why our limbs are built for speed rather than for lifting with least effort. Linking moments to the human body is a good way to connect physics with everyday life.
Common exam mistakes
- Using the wrong distance — it must be the perpendicular distance from the pivot to the line of the force.
- Forgetting that both force and moment must balance for full equilibrium.
- Thinking a tall, narrow object is stable; a high centre of gravity and small base make it unstable.
- Confusing mechanical advantage (a ratio of forces) with efficiency (a percentage).
Key terms to remember
- Moment — the turning effect of a force = force × perpendicular distance from the pivot (N·m).
- Pivot (fulcrum) — the fixed point about which an object turns.
- Principle of moments — at balance, total clockwise moments = total anticlockwise moments.
- Equilibrium — a state of balance: zero resultant force and zero resultant moment.
- Centre of gravity — the single point through which an object's whole weight acts.
- Stability — resistance to toppling; greatest with a low centre of gravity and a wide base.
- Mechanical advantage — load ÷ effort.
- Efficiency — (useful work output ÷ work input) × 100%; always less than 100%.
Quick recap
- A moment = force × perpendicular distance from the pivot (N·m); it is the turning effect.
- Principle of moments: at balance, clockwise moments = anticlockwise moments.
- The centre of gravity is where all the weight acts; low centre of gravity + wide base = greater stability.
- Levers, pulleys and ramps are simple machines; efficiency is always less than 100% because of friction.