Big gear, small gear: which one turns faster, and why?

What you'll discover

• When two gears mesh, the one with fewer teeth turns faster than the one with more teeth.
• The ratio of the numbers of teeth tells you exactly how much faster or slower each gear turns.
• Gaining speed costs turning force, and meshing gears always spin in opposite directions.

The science in plain words

Gears are wheels with teeth that interlock, so when one turns it drives the other. Because the teeth mesh one by one, both gears move the same number of teeth past the contact point in any given time. That simple fact explains how they behave.

Suppose a big gear with 40 teeth drives a small gear with 10 teeth. One full turn of the big gear pushes 40 teeth past the meeting point, which is four full turns of the small gear. The small gear spins four times as fast. The relationship between the teeth counts is called the gear ratio, here 4 to 1. If the small gear drives the big one instead, the big gear turns four times more slowly.

There is a trade-off. Gears cannot create energy, so when a gear train increases speed it reduces turning force, or torque, and when it slows things down it increases torque. That is why a bicycle's low gear makes climbing hills easier but you pedal fast for little speed, while a high gear gives speed on the flat but is hard to push. Meshing gears also turn in opposite directions, so engineers add a small idler gear between two gears when they need both to turn the same way.

Where it fits

• India, NCERT: Gears and gear ratios go beyond the NCERT syllabus for classes 6 to 10; the lab builds on Class 8 Exploring Forces.
• United States: Grades 6 to 8

Common questions

Which gear turns faster, big or small?

The smaller gear turns faster. When gears mesh, the same number of teeth pass the contact point on each, so a gear with fewer teeth has to complete more turns to keep up. A gear with a quarter of the teeth turns four times as fast.

What is a gear ratio?

A gear ratio compares the number of teeth on two meshing gears, and so how many turns one makes for each turn of the other. A 3 to 1 ratio means the driving gear turns three times for each turn of the larger driven gear, giving more turning force but less speed.

Why do bicycles have gears?

Gears let the rider match pedalling to the road. A low gear makes each push easier for climbing hills, though the bike moves slowly. A high gear makes each turn of the pedals cover more ground on flat roads, but needs more force to push.

Related labs

• Pulleys and a Newton Meter: Lift a brass weight with one wheel, then with more. How hard do you have to pull?
• Ruler See-saw: Hang brass weights on a ruler. Can a light weight far out balance a heavy one close in?
• Hydraulics: Push a little piston gently. Can the oil lift a heavy crate?

See all physics labs or every Taz science lab.

Try it yourself

The Gear Mechanisms lab is one of the interactive 3D science labs inside Taz. Change one thing, predict what will happen, then run it and watch. Labs open after you sign in.

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