Gear train game: direction of rotation, speed and rpm
A physics and technology game for understanding how the toothed wheels in a bike, a clock or a hand whisk work. A randomly generated chain of gears appears, each drawn with its real number of teeth and a size in proportion. The first is the driver and you can see it turning, with its direction and revolutions per minute. You say what the last one does: which way it turns, whether it is faster or slower and, at higher levels, exactly how many rpm. On hard there is a compound gear, two gears on one shaft, which is how big reductions are achieved. When you answer, every gear starts turning at its real speed.
Physics · Primary, Secondary, Sixth Form
Every time two gears mesh, the rotation reverses; and speed times teeth is conserved. That solves any chain, and the game makes you apply the rules instead of memorising cases: trains are generated at random and are never the same.
Almost everyone thinks each gear in the middle changes the speed. It does not: they only change the direction, and the final speed depends only on the first and last gear. Discovering it while playing, and watching it turn, sticks far better than reading it.
On medium you work out the rpm with n₁·z₁ = n₂·z₂, the gear ratio formula from lower secondary technology. The numbers are chosen to come out exact, so the effort goes into reasoning, not the calculator.
"A four-gear train appears: the first, with 12 teeth, turns at 60 rpm clockwise; then come gears of 40, 15 and finally 36 teeth. Many start multiplying gear by gear. The first and last are enough: 60 × 12 = n × 36, so the last turns at 20 rpm. And with three meshes, an odd number, it turns the opposite way to the first: anticlockwise."
Prefer to learn without screens? Try this analogue version:
Find something with gears at home: a hand whisk, a winged corkscrew, an old clock or a bike.
Count the teeth on two meshing gears and mark one tooth on each with a pen.
Turn the big one a full revolution and count how many times the small one turns.
Check that revolutions × teeth gives the same number for both gears.
If you like Gears, these activities work similar skills:
Revise levers and their three classes, pulleys, the crank and connecting rod, the cam and the rack and pinion, with an explanation for every answer.
With the bike upside down, turn the pedals once with the big chainring and small sprocket, then the other way round. Counting the wheel turns is the gear ratio live.
Cut out cardboard gears with different numbers of teeth, pin them to a corkboard and build your own train.
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