Levers and Moments

The secret of turning forces

Imagine trying to open a heavy door by pushing right next to the hinges. It barely budges. Now push at the far edge, by the handle, and it swings open easily — even though you are using the same hand. The door has not changed and your strength has not changed. What changed is where you pushed. This is the secret of the lever, and the physics behind it is called the moment of a force.

A lever is one of the oldest and most useful machines ever invented. Crowbars, scissors, wheelbarrows, spanners, bottle openers, and even your own arm are all levers. Understanding moments explains how a small push in the right place can move a very large load.

What is a moment?

A moment is the turning effect of a force around a pivot. The pivot (sometimes called the fulcrum) is the fixed point that the lever turns about — like the hinge of a door or the middle bar of a seesaw.

The size of the moment depends on two things:

1. How big the force is. A harder push gives a bigger turning effect.
2. How far from the pivot the force is applied. A force acting further out has a bigger turning effect.

We put these together in a simple equation:

Moment = force × distance from the pivot

The force is measured in newtons (N), the distance in metres (m), so the moment is measured in newton-metres (N·m). One important rule: the distance must be measured at a right angle to the direction of the force. Pushing straight toward the pivot produces no turn at all.

Working out moments

Worked example 1. You push down on the end of a crowbar with a force of 30 N, and your hand is 1.2 m from the pivot. What is the moment?

Moment = force × distance = 30 N × 1.2 m = 36 N·m

Worked example 2. A child sits on a seesaw 1.5 m from the pivot and produces a moment of 450 N·m. What is the child's weight (the downward force)?

Force = moment ÷ distance = 450 N·m ÷ 1.5 m = 300 N

Notice how the distance does the heavy lifting. If you could only manage a small force but moved further from the pivot, you could still create a large moment — which is exactly why long levers are so powerful.

The principle of moments: how levers balance

A lever balances when it is not turning either way. For that to happen, the turning effects on each side must cancel out. This is the principle of moments:

A lever is balanced when the total clockwise moment equals the total anticlockwise moment about the pivot.

Picture a seesaw. A big child sits on the left, a small child on the right. They can still balance perfectly if the smaller child sits further from the pivot. The smaller force times the bigger distance gives the same moment as the bigger force times the smaller distance.

Worked example 3. On a seesaw, a 400 N child sits 1.0 m to the left of the pivot. Where must a 250 N child sit on the right to balance it?

Set the moments equal:

400 N × 1.0 m = 250 N × d 400 N·m = 250 N × d d = 400 ÷ 250 = 1.6 m

So the lighter child must sit 1.6 m from the pivot — further out — to balance the heavier child. This balancing act is closely related to where an object's weight acts, which you can explore in centre of mass and balance.

The three classes of lever

Levers come in three types, depending on where the pivot, the effort (the force you apply), and the load (the force you are trying to move) sit.

Class	Order along the lever	Examples
1st class	Pivot in the middle	Seesaw, scissors, crowbar
2nd class	Load in the middle	Wheelbarrow, nutcracker, bottle opener
3rd class	Effort in the middle	Tweezers, fishing rod, your forearm

In a first- or second-class lever, putting the effort far from the pivot lets a small effort lift a big load — the lever multiplies your force. In a third-class lever the effort is closer to the pivot than the load, so it does not multiply force, but it lets you move the load a long way quickly (handy for casting a fishing line or flicking a fly off with tweezers).

Why levers feel like magic

Levers seem to give you something for nothing — a tiny push moving a huge weight. But there is a trade-off. To lift a heavy load a small distance, your end of the lever has to move a large distance. You do not get free energy; you swap a small force over a long distance for a large force over a short distance. This is true of all simple machines, which you can read more about in simple machines.

This is also why tools are shaped the way they are. A long spanner undoes a stiff bolt because the extra length increases the distance in moment = force × distance. A wheelbarrow lets you carry a heavy load with one easy lift because the load sits close to the wheel (the pivot) while your hands are far away.

Try it yourself! 🧪

Build a balancing ruler — safe and simple.

You will need a ruler, a pencil, and some identical coins (all the same value, so they weigh the same).

1. Lay the pencil flat on a table. Balance the ruler across it so it teeters at the middle — that point is your pivot.
2. Place one coin on the ruler, a few centimetres to the right of the pivot. The ruler tips down on that side.
3. Now place one coin on the left at the same distance. The ruler balances! Equal forces at equal distances give equal moments.
4. Here is the clever part: put two coins on the right, then find where one coin must go on the left to balance them. You should find the single coin has to sit about twice as far from the pivot. One coin at double the distance makes the same moment as two coins at the normal distance — exactly what the principle of moments predicts.

Try different combinations and predict the balance point before you test it. You are doing real physics: moment = force × distance, in action on your kitchen table.