Gear Ratio Demonstrator

Pre-Algebra · Axiom Academy

LESSON Gear Ratios & Inverse Variation Two meshed gears trade speed for teeth: the small one spins fast, the big one spins slow — and their product stays locked. 1. Meshed Gears Trade Teeth for Turns Watch two interlocking gears. The big gear has 24 teeth ; the small one has 12 . Their teeth pass the contact point one for one, so when the big gear makes one turn, the small gear is forced through two . Fewer teeth means more turns — the gears spin in opposite directions, but in lockstep. Keep one gear fixed — a 12-tooth driver making 90 turns — and swap the gear it drives. As the driven gear grows from 12 to 24 to 36 teeth, its turn-count falls from 90 to 45 to 30. More teeth, fewer turns. But notice the number that never moves: stays pinned at 1080 . The driver's product sets the budget Every driven gear must match it A bigger driven gear has more teeth to move past the contact point, so it completes fewer turns. A smaller driven gear runs out of teeth sooner, so it whips around more times. Teeth up, turns down — by exactly the factor that keeps constant. When two quantities have a constant product, doubling one halves the other. The 12-tooth driver and the 24-tooth gear are in a 1:2 tooth ratio, so their speeds are in the inverse ratio 2:1 — the small gear spins twice for every turn of the big one.

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