How do gears and pulleys change speed and torque, and how is the ratio calculated?
Gear trains and pulley and belt systems for transmitting rotary motion, the calculation of gear ratio and velocity ratio, how gearing changes output speed and torque, compound gear trains, the trade-off between speed and force, and the related ideas of mechanical advantage and efficiency.
A focused answer to the Edexcel 9DT0 content on gears and pulleys, covering gear trains and belt drives, calculating gear ratio and velocity ratio, how gearing trades speed for torque, compound gears, and mechanical advantage and efficiency.
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What this dot point is asking
Edexcel wants you to understand gear trains and pulley and belt systems, calculate gear ratio and velocity ratio, explain how gearing trades speed for torque (including compound gears), and apply the related ideas of mechanical advantage and efficiency.
The answer
Gear trains and the gear ratio
A ratio of (driven has 3 times the teeth) means the output turns one third as fast but with about three times the torque.
How gearing trades speed for torque
Compound gear trains
A compound gear train mounts two gears on the same shaft so their ratios multiply, achieving a large speed reduction (or increase) in a compact space. The overall ratio is the product of the individual stage ratios, for example two stages give overall.
Pulleys, belts and velocity ratio
A pulley and belt system transmits motion between shafts using a belt. The velocity ratio is , and the output speed is the input speed divided by the velocity ratio. Belt drives are quiet and absorb shock but can slip (so the ratio is not exact and drive can be lost under heavy load) and the belt stretches and wears; toothed gears give a positive, slip-free drive.
Mechanical advantage and efficiency
Examples in context
A hand whisk gears up so a slow handle spins fast beaters (speed, ratio less than 1), while a cordless drill gears down so the motor's high speed becomes high torque at the chuck for driving screws (force, ratio greater than 1). Bicycles change gear ratio to match terrain, low gears for climbing (torque), high gears for speed. Clocks and winches use compound gear trains for large reductions in a small case. Belt drives appear in pillar drills and washing machines, quiet but able to slip as a crude overload protection. Calculating the ratio and output speed, and explaining the speed-torque trade-off, are the central skills here.
Try this
Q1. A driver gear of teeth drives a -tooth gear. State the gear ratio. [1 mark]
- Cue. , that is .
Q2. A motor at rpm drives a gear reduction. Find the output speed and say what happens to torque. [2 marks]
- Cue. Output speed rpm; the torque increases by about four times (speed traded for force).
Q3. Give one limitation of a belt-and-pulley drive compared with meshing gears. [1 mark]
- Cue. The belt can slip (so the ratio is not exact and drive can be lost under load) and it stretches and wears, whereas gears give a positive, slip-free drive.
Exam-style practice questions
Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Edexcel 20204 marksA driver gear has 20 teeth and meshes with a driven gear of 60 teeth. Calculate the gear ratio and state what happens to the output speed and torque.Show worked answer →
Award marks for the ratio and for the effect on speed and torque.
Gear ratio , usually written .
Because the driven gear is larger (more teeth), the output turns slower than the input, at one third of the speed, and the torque is increased by the same factor (about three times, before losses). So this gearing trades speed for force.
Markers reward the ratio of driven to driver teeth (3:1), the slower output speed (one third) and the increased torque, showing understanding that more teeth on the driven gear reduces speed and increases torque.
Edexcel 20226 marksA pulley system on a drill has a 40 mm driver pulley on the motor and a 120 mm driven pulley on the chuck. The motor runs at 2400 rpm. Calculate the chuck speed and explain the design reason for the ratio, including one limitation of belt drives.Show worked answer →
Extended-response item marked on levels (correct calculation, design reasoning and a limitation).
Velocity ratio , so the chuck turns three times slower than the motor.
Chuck speed rpm.
Design reason: reducing the speed three times increases the torque at the chuck, so the drill can turn larger bits through tougher material; a slower, higher-torque output is more useful than raw motor speed.
Limitation of belt drives: the belt can slip (so the ratio is not exact and drive can be lost under high load), and belts stretch and wear, unlike toothed gears which give a positive, slip-free drive.
A strong answer shows the velocity-ratio calculation, the 800 rpm result, the speed-for-torque reasoning, and a genuine belt-drive limitation (slip or stretch).
Related dot points
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Sources & how we know this
- Pearson Edexcel A-Level Design and Technology: Product Design (9DT0) specification — Pearson Edexcel (2017)