Moments, Levers and Gears

This lesson covers the turning effect of forces — known as moments — and how levers and gears act as force multipliers. This is part of the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to be able to calculate moments, apply the principle of moments, and explain how levers and gears work.

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What Is a Moment?

A moment is the turning effect of a force about a pivot (also called a fulcrum). When you push a door handle, turn a spanner, or use a see-saw, you are applying a moment.

The moment of a force is calculated using:

Moment = Force × Perpendicular Distance from the Pivot

M = F × d

Quantity	Symbol	Unit
Moment	M	Newton-metres (Nm)
Force	F	Newtons (N)
Perpendicular distance from pivot	d	Metres (m)

Key Points

• The distance must be the perpendicular (at right angles) distance from the line of action of the force to the pivot.
• A larger force creates a larger moment.
• A greater distance from the pivot creates a larger moment.
• The unit of moment is Nm (newton-metres) — do not confuse this with energy (also measured in Nm or J).

Exam Tip: A very common mistake is using a distance that is not perpendicular to the force. Always check that the distance is measured at 90° to the line of action of the force. If the force is applied at an angle, you must use the perpendicular component.

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Worked Examples: Calculating Moments

Worked Example 1

A force of 20 N is applied at a perpendicular distance of 0.3 m from a pivot. Calculate the moment.

M = F × d = 20 × 0.3 = 6 Nm

Worked Example 2

A spanner is 0.25 m long. A mechanic applies a force of 40 N at the end. What moment is produced?

M = F × d = 40 × 0.25 = 10 Nm

Worked Example 3

A moment of 15 Nm is required to turn a bolt. If the spanner is 0.5 m long, what force must be applied?

F = M ÷ d = 15 ÷ 0.5 = 30 N

Worked Example 4

A moment of 12 Nm is produced by a 60 N force. At what distance from the pivot is the force applied?

d = M ÷ F = 12 ÷ 60 = 0.2 m

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The Principle of Moments

When an object is in rotational equilibrium (balanced and not rotating), the following rule applies:

The sum of the clockwise moments about any point = the sum of the anticlockwise moments about the same point.

This is known as the principle of moments.

flowchart LR
    A["Anticlockwise<br/>Moments"] -- "=" --- B["Clockwise<br/>Moments"]
    A --> C["F₁ × d₁"]
    B --> D["F₂ × d₂"]

    style A fill:#2980b9,color:#fff
    style B fill:#c0392b,color:#fff
    style C fill:#3498db,color:#fff
    style D fill:#e74c3c,color:#fff

Worked Example 5: Balanced See-Saw

A child of weight 400 N sits 2 m from the pivot of a see-saw. Where must a child of weight 500 N sit on the other side for the see-saw to balance?

Anticlockwise moment = Clockwise moment

400 × 2 = 500 × d

800 = 500 × d

d = 800 ÷ 500 = 1.6 m from the pivot

Worked Example 6: Two Forces on One Side

A uniform beam is pivoted at its centre. On the left side, a 30 N weight hangs 0.4 m from the pivot. On the right side, a 10 N weight hangs 0.6 m from the pivot and an unknown weight W hangs 0.2 m from the pivot.

Anticlockwise moment = 30 × 0.4 = 12 Nm

Clockwise moments = (10 × 0.6) + (W × 0.2) = 6 + 0.2W

For balance: 12 = 6 + 0.2W

0.2W = 6

W = 6 ÷ 0.2 = 30 N

Exam Tip: The principle of moments can be applied about any point, not just the obvious pivot. Choosing a clever pivot point (where an unknown force acts) can simplify your calculation because that force creates zero moment about that point.

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Levers

A lever is a simple machine that uses a rigid bar (or beam) and a pivot to multiply force.

How Levers Work

• A small effort (input force) applied at a large distance from the pivot produces a large load (output force) at a small distance from the pivot.
• By the principle of moments: Effort × distance from pivot = Load × distance from pivot.
• If the effort is further from the pivot than the load, the lever multiplies the force.

Types of Lever

Class	Arrangement	Example
Class 1	Pivot between effort and load	See-saw, crowbar, scissors
Class 2	Load between pivot and effort	Wheelbarrow, nutcracker, bottle opener
Class 3	Effort between pivot and load	Tweezers, fishing rod, tongs

Worked Example 7: Crowbar

A crowbar is used to lift a rock. The pivot is 0.1 m from the rock (load) and 1.0 m from where you push (effort). If the rock weighs 500 N, what effort is needed?

Effort × 1.0 = 500 × 0.1

Effort = 50 ÷ 1.0 = 50 N

The crowbar multiplies the force by a factor of 10.

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Gears

Gears are toothed wheels that interlock to transmit rotational forces (turning effects).

Key Principles of Gears

• When two gears mesh together, they turn in opposite directions.
• A larger gear (more teeth) turns more slowly than a smaller gear (fewer teeth).
• A larger gear exerts a greater turning force (moment) than a smaller gear.
• The smaller gear turns faster but with less force.
• Gears can be used to change the speed, direction, or force of rotation.

How Gear Ratios Work

Driving Gear	Driven Gear	Effect
Small gear (fewer teeth)	Large gear (more teeth)	Speed decreases, force (moment) increases
Large gear (more teeth)	Small gear (fewer teeth)	Speed increases, force (moment) decreases

Why Gears Are Used