GCSE · Physics · Edexcel · Spec 1PH0

Principle of moments

Can a 200 N push hold up a 1200 N load? On a lever, easily, because where you push matters as much as how hard you push.

A 1200 N load sits 0.2 m from the pivot. How hard must you push on the other side to balance it?

Turning effects

Balanced forces can still make something spin

View: In line. Showing 1 layer: In line

View

Two equal forces pull opposite ways along the same line. No resultant force and no turning: the block is in equilibrium.

Switch views. Look at where each force acts, not just how big it is.

Which distance?

Working out a moment on a tilted lever

A lever 1.0 m long is tilted up at an angle. A 50 N force pushes straight down on its end. That end is 1.0 m from the pivot measured along the lever, 0.8 m above the pivot, and 0.6 m across from the pivot horizontally.

Which is closest to how you would work out the moment of the 50 N force about the pivot?

Use the length along the lever: 50 N × 1.0 m = 50 N m.Use the height of the end above the pivot: 50 N × 0.8 m = 40 N m.The moment is just the force, so it's 50 N whatever the distance.Use the distance straight across from the pivot to the force's line: 50 N × 0.6 m = 30 N m.

How sure are you?

I'm sureI think soI'm guessing

Use the length along the lever: 50 N × 1.0 m = 50 N m.

This is a common misconception

The lever's length isn't what matters here. The force pushes straight down, so draw its line of action as a vertical line through the end. The distance you need is the shortest one from the pivot to that line, which meets it at a right angle. That's the 0.6 m across, not the 1.0 m along the lever. Moment = 50 N × 0.6 m = 30 N m. Tilting the lever shortens that distance, so the same push turns it less.

Use the height of the end above the pivot: 50 N × 0.8 m = 40 N m.

This is a common misconception

Good instinct to look for a right angle, but it's the wrong one. The distance has to be at right angles to the FORCE. This force acts vertically, so the distance that meets its line of action at 90° is horizontal: 0.6 m. The height would only matter for a force pushing sideways. Moment = 50 N × 0.6 m = 30 N m.

The moment is just the force, so it's 50 N whatever the distance.

This is a common misconception

A moment isn't a force. It's the turning effect a force produces, and that depends on how far from the pivot it acts. That's why a moment has its own unit, the newton metre (N m). Here it's 50 N × 0.6 m = 30 N m.

Use the distance straight across from the pivot to the force's line: 50 N × 0.6 m = 30 N m.

This matches the evidence

Yes. The distance in moment = force × distance is the perpendicular distance from the pivot to the line of action of the force. For a vertical force, that's the horizontal gap: 0.6 m. So the moment is 30 N m.

Moment = force × perpendicular distance from the pivot to the force's line of action. Measure at right angles to the force, not along the lever, and give the answer in N m.

The principle of moments, step by step

Problem

A lever is balanced. A 200 N effort pushes down 1.2 m from the pivot. The load is 0.2 m from the pivot on the other side. What is the load force?

Same rule, two jobs

Force multiplier (crowbar)vsDistance multiplier (lower arm)

The principle of moments trades force against distance. Which way round you set up the lever decides what you gain.

Focus

Where the effort acts

Force multiplier (crowbar)

Far from the pivot, at the end of the handle

Distance multiplier (lower arm)

Close to the pivot: the muscle pulls near the elbow

The insight

The side with the bigger distance needs the smaller force to make the same moment.

Where the load is

Force multiplier (crowbar)

Close to the pivot, at the tip

Distance multiplier (lower arm)

Far from the pivot, in the hand

Forces

Force multiplier (crowbar)

A small effort gives a much larger force on the load

Distance multiplier (lower arm)

The force on the load is smaller than the effort

How far the load moves

Force multiplier (crowbar)

Only a small distance

Distance multiplier (lower arm)

Through a large distance

Your turn

Finish the method

A lever is balanced. A 900 N load sits 0.3 m from the pivot. You push down on the other side, 1.5 m from the pivot. What effort force do you need?

Find the moment you can calculate: the load's moment = 900 N × 0.3 m = 270 N m.
missing step

Which line is step 2?

The lever is balanced, so the effort's moment about the pivot must also be 270 N m.The lever is balanced, so the effort must also be 900 N.The lever is balanced, so the effort's moment must be zero.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

How a small force far from a pivot can balance a big one close to it.

What you need to know

A force can produce a turning effect called a moment. A moment is not a force; it is measured in newton metres (N m).
Moment = force × distance (M = F d), where d is the perpendicular distance from the pivot to the line of action of the force.
Two equal forces acting in opposite directions but not in line make an object turn, even though there is no resultant force on it.
An object is in equilibrium only when there is no resultant force AND no resultant moment on it.
A force on a lever turns it about the pivot, either clockwise or anticlockwise.
Principle of moments: when a lever is balanced, the moment on one side of the pivot equals the moment on the other, so there is no resultant moment.
To find an unknown load or effort: calculate the known moment, set the other side's moment equal to it, then use force = moment ÷ distance.
Levers are force multipliers (effort far from the pivot, load close, e.g. a crowbar) or distance multipliers (effort close, load far, e.g. the lower arm with the elbow as pivot).

The big picture

A force can make something turn, and that turning effect is called a moment. Moment = force × distance, where the distance is the perpendicular distance from the pivot to the force's line of action, and moments are measured in newton metres (N m). An object is in equilibrium only when there is no resultant force and no resultant moment. For a balanced lever, the moment on one side of the pivot equals the moment on the other (the principle of moments), so you can find an unknown load or effort with force = moment ÷ distance. Levers can multiply force or multiply distance, but never both.

Key points

1Whether a lever turns depends on moments, not on which force is bigger.

2The further a force acts from the pivot, the smaller the force needed for the same moment.

3On a tilted lever, measure at right angles to the force, not along the lever.

4No resultant force is not enough for equilibrium: there must be no resultant moment too.

5A force multiplier moves the load only a little; a distance multiplier gives a load force smaller than the effort.

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Worked example

Problem

A crowbar is used to lift the lid off a crate. A 150 N effort pushes down on the handle 0.9 m from the pivot. The lid is 0.05 m from the pivot on the other side. What force does the crowbar exert on the lid?

⚠ Watch out

Comparing forces instead of moments. A bigger force does not automatically win: you have to multiply each force by its perpendicular distance from the pivot, and the lever balances when those moments are equal.

🧠

Memory hook

Far and small balances near and big. Force times distance decides who wins, not force alone.

✓

Check yourself

A 300 N load is 0.4 m from a pivot. How far from the pivot must a 100 N effort push to balance it? What happens if that effort then moves closer?

Flashcards

(12)

What is the turning effect of a force called?

A moment.

What unit is a moment measured in, and is a moment a force?

Newton metres (N m). No, a moment is not a force; it is the turning effect of a force.

Write the equation for the moment of a force.

Moment = force × distance (M = F d), with M in N m, F in N and d in m.

Which distance goes into M = F d?

The perpendicular distance from the pivot to the line of action of the force, not the distance measured along a tilted lever.

What happens when two equal forces act in opposite directions but not in line?

The object turns, even though there is no resultant force on it.

What are the two conditions for an object to be in equilibrium?

No resultant force on it, and no resultant moment on it.

What are the two directions a force can turn a lever about its pivot?

Clockwise or anticlockwise.

State the principle of moments for a balanced lever.

The moment on one side of the pivot equals the moment on the other side, so there is no resultant moment.

You know the moment needed on one side of a balanced lever. How do you get the force?

Divide that moment by the force's own distance from the pivot.

A balanced lever's effort is moved closer to the pivot. What must happen to the effort force to keep it balanced?

It must get bigger, because the smaller distance has to be made up by a larger force to keep the same moment.

How is a lever set up to act as a force multiplier?

Effort far from the pivot, load close to it (e.g. a crowbar). A small effort gives a much larger force on the load, but the load moves only a small distance.

How is a lever set up to act as a distance multiplier?

Effort close to the pivot, load far from it (e.g. the lower arm, with the elbow as pivot). The load moves a long way, but the force on it is smaller than the effort.

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A 1200 N load sits 0.2 m from the pivot. How hard must you push on the other side to balance it?

Working out a moment on a tilted lever

Finish the method

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