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How do gears and pulleys change the speed and direction of rotation, and how do you calculate a gear ratio?

Describe how gears, pulleys and belts transmit motion, and calculate gear ratios to find changes in speed

A clear answer to the N(A)-Level D&T outcome on gears and pulleys. How gear trains and belt-and-pulley systems change speed and direction, the idler gear, and calculating a gear ratio from the number of teeth.

Generated by Claude Opus 4.88 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
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What this dot point is asking

SEAB wants you to describe how gears, pulleys and belts pass on rotation and change its speed and direction, and to calculate a gear ratio from the number of teeth. Like levers, this topic has a clear calculation, so showing the formula and working is where the marks are.

The answer

Gears: passing on rotation

A gear is a toothed wheel. When two gears mesh, one turns the other. The gear you drive is the driver; the gear it turns is the driven gear. Meshed gears turn in opposite directions. Gears let you change the speed and the turning force between an input and an output.

The gear ratio

The gear ratio compares the teeth:

gear ratio=number of teeth on the driven gearnumber of teeth on the driver gear\text{gear ratio} = \frac{\text{number of teeth on the driven gear}}{\text{number of teeth on the driver gear}}

  • A ratio greater than 1 (a large driven gear) means the driven gear turns slower but with more turning force.
  • A ratio less than 1 (a small driven gear) means the driven gear turns faster but with less force.

The output speed is the input speed divided by the gear ratio.

The idler gear

An idler gear sits between the driver and driven gears and meshes with both. It is used to make the driven gear turn the same way as the driver, or to bridge a gap between gears that are far apart. Importantly, an idler gear does not change the overall gear ratio between the driver and the driven gear.

Pulleys and belts

A belt and pulley system passes rotation between wheels using a belt instead of teeth. The speed change works the same way: a small pulley driving a large pulley slows the output and increases force. Belts can slip, which can be a safety feature, and they let you place the two shafts further apart than meshed gears allow. Pulleys with a belt usually turn the same direction (unless the belt is crossed).

Examples in context

Example 1. A hand-cranked toy. A small driver gear turns a large driven gear so a fast, easy crank produces a slow, strong output, letting the toy lift a small weight that a direct crank could not.

Example 2. A belt drive in a model. Two pulleys joined by a belt link motors and wheels that are set apart on the chassis; using a smaller drive pulley speeds up the wheels, and the belt can slip safely if the wheels jam.

Try this

Q1. Write the formula for the gear ratio. [1 mark]

  • Cue. Gear ratio = teeth on the driven gear divided by teeth on the driver gear.

Q2. A 10-tooth driver meshes with a 40-tooth driven gear. Calculate the ratio and say whether the output is faster or slower. [3 marks]

  • Cue. Ratio = 40 divided by 10 = 4 (4 to 1); the output is slower (and has more turning force).

Q3. Explain what an idler gear does to the direction and to the ratio. [2 marks]

  • Cue. It reverses the direction of the driven gear (so it matches the driver) but does not change the overall gear ratio.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original5 marksA driver gear has 20 teeth and meshes with a driven gear of 60 teeth. (a) Calculate the gear ratio. (b) If the driver gear turns at 90 revolutions per minute, how fast does the driven gear turn? (c) State whether the driven gear turns faster or slower than the driver.
Show worked answer →

(a) Gear ratio = teeth on driven gear divided by teeth on driver gear = 60 divided by 20 = 3, written as 3 to 1.

(b) The driven gear turns slower. Its speed = driver speed divided by the ratio = 90 divided by 3 = 30 revolutions per minute.

(c) The driven gear turns slower than the driver (a ratio greater than 1 reduces speed but increases turning force).

What markers reward: the gear ratio as driven teeth over driver teeth (3 to 1), the correct driven speed of 30 rev/min, and the statement that the larger driven gear turns slower. Showing the working earns the method marks even if the final number slips.

Original4 marksExplain what an idler gear is and one reason a designer would include one in a gear train.
Show worked answer →

An idler gear is a gear placed between the driver and the driven gear. It meshes with both. A designer includes it to change the direction of rotation of the driven gear so it turns the same way as the driver, or simply to bridge a gap between two gears that are far apart. The idler gear does not change the overall gear ratio between the driver and driven gears.

What markers reward: an idler gear sits between driver and driven, its purpose to reverse the direction (or bridge a distance), and the key fact that it does not change the overall gear ratio.

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