Paper 1: Mathematical and Scientific Content — Gear Ratios, Mechanical Advantage, Energy and Forces

AQA GCSE D&T Paper 1 requires a minimum of 15% mathematical content and 10% scientific content. This lesson covers the key calculations and scientific principles you need to know, with worked examples and exam-style practice. Specification reference: AQA 8552, Sections 3.1.4 and 3.1.5.

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Gear Ratios

What Is a Gear Ratio?

A gear ratio describes the relationship between two meshing gears. It tells you how many times the driven gear rotates for each rotation of the driver gear.

Formula:

Gear ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear

Worked Example 1

A driver gear has 20 teeth and a driven gear has 60 teeth.

Gear ratio = 60 ÷ 20 = 3:1

This means the driven gear rotates once for every three rotations of the driver gear. The driven gear turns more slowly but with more torque (turning force).

Worked Example 2

A driver gear has 40 teeth and a driven gear has 10 teeth.

Gear ratio = 10 ÷ 40 = 1:4 (or 0.25:1)

The driven gear rotates four times for every one rotation of the driver gear. This is a speed increase but with less torque.

Output Speed Calculation

Output speed (RPM) = Input speed (RPM) ÷ Gear ratio

Example: Input speed = 300 RPM, gear ratio = 3:1. Output speed = 300 ÷ 3 = 100 RPM.

Gear Trains

When multiple pairs of gears are used, the overall gear ratio is the product of the individual ratios.

Example: Stage 1 has a ratio of 3:1, Stage 2 has a ratio of 2:1. Overall ratio = 3 × 2 = 6:1. If the input speed is 600 RPM, the output speed = 600 ÷ 6 = 100 RPM.

Gear Type	Effect
Spur gears	Transfer motion between parallel shafts
Bevel gears	Transfer motion through 90°
Worm and worm wheel	Large speed reduction; cannot be reversed (self-locking)
Rack and pinion	Convert rotary motion to linear motion (e.g. steering)

AQA Exam Tip: Always show your working in gear ratio questions. If you make an arithmetic error, you can still earn marks for the correct method. Write the formula first, then substitute the values.

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Mechanical Advantage

What Is Mechanical Advantage?

Mechanical advantage (MA) measures how much a machine multiplies the input force. A lever, pulley or gear system can provide a mechanical advantage, allowing a small effort to move a large load.

Formula:

Mechanical Advantage = Load ÷ Effort

Worked Example

A lever is used to lift a rock weighing 600 N. The effort applied is 150 N.

MA = 600 ÷ 150 = 4

This means the lever multiplies the effort by a factor of 4.

Levers

Class	Fulcrum Position	Example
Class 1	Between effort and load	Seesaw, crowbar, scissors
Class 2	Load between effort and fulcrum	Wheelbarrow, nutcracker, bottle opener
Class 3	Effort between load and fulcrum	Tweezers, fishing rod, human forearm

Pulleys

System	Mechanical Advantage	Description
Single fixed pulley	MA = 1	Changes direction of force only
Single movable pulley	MA = 2	Halves the effort needed
Block and tackle (4 ropes)	MA = 4	Quarters the effort needed

Key trade-off: Increasing mechanical advantage means the effort moves through a greater distance to move the load a shorter distance. You gain force but lose distance (and speed).

AQA Exam Tip: In lever and pulley questions, draw a diagram and label the load, effort and fulcrum (or ropes). This helps you visualise the system and reduces errors.

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Velocity Ratio

The velocity ratio (VR) of a machine is calculated differently depending on the system: