Two gears, one big and one small — which spins faster, and can gears ever give you free speed?
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Two gears, one big and one small — which spins faster, and can gears ever give you free speed?
The short answer
When two gears are locked together, the smaller one always spins faster than the bigger one, because where their teeth meet the same number of teeth must pass on both gears. But faster never means stronger: gears trade speed for pushing-force and back again. Whatever factor the speed goes up, the turning-force goes down by the same factor, so gears swap speed and strength but never give you free power.
How it works
Two meshed gears share their teeth at the spot where they touch, so the same number of teeth has to march past that point on each gear. A gear with fewer teeth has to spin around more times to feed through the same teeth, so it turns faster; a gear with more teeth turns slower. The speed depends on the ratio of teeth: a gear with a third as many teeth spins three times as fast. Pushing-force (torque) does the opposite. If a gear spins three times faster, it can only push a third as hard, so its spin-speed multiplied by its pushing-force stays the same. That is why gears trade one for the other instead of creating extra power.
What people get wrong
Many people think gears multiply power — that you get more spin and more push out than you put in, like a free upgrade. They don't. A gear can give you more speed OR more force, never both at once. Speeding a gear up by a factor weakens its push by the very same factor, so the speed-times-force total never grows. Match the gears one-to-one (the same number of teeth) and nothing changes at all.
The catch
A small driven gear gives you whirling speed but only a little pushing-force, so it stalls under a real load. A big driven gear gives you lots of pushing-force to climb a hill or lift a weight, but it turns slowly, so you move at a crawl. Either way you trade speed for strength; the gears never hand you both. This is exactly why a bike has gears: a low gear is slow but strong for hills, a high gear is fast but weak for flat ground.
Questions kids ask
Why does the smaller gear spin faster?
Where two gears meet, their teeth pass each other one for one, so the same number of teeth must go by on both. A smaller gear has fewer teeth, so it has to spin around more times to feed the same teeth through — that makes it turn faster than the bigger gear.
If a gear spins faster, why can't it also push harder?
Because the energy you put in doesn't grow. Spin-speed and pushing-force multiply together to give power, and gears can't make extra power. So if a gear spins three times faster, it can only push a third as hard — the speed went up and the force came down by the same amount.
Do gears ever just give you free speed or free strength?
No. A gear gives you more speed only by trading away strength, and more strength only by trading away speed. The two multiplied together stay the same, so you always pay for one with the other.
Why does a bike have so many gears then?
Each gear is a different trade. A low gear turns the wheel slowly but with lots of force, which is great for climbing a steep hill. A high gear turns the wheel fast but with less force, which is great for going quick on flat ground. You pick the trade that fits the road.
For grown-ups
Meshing gears share the same tooth speed at the contact point, so their angular speeds are inversely proportional to their tooth counts — that ratio (N₂/N₁) is the gear ratio. Ignoring friction, an ideal gear train conserves power: torque rises by the same factor that speed falls (τ₁ω₁ = τ₂ω₂), so torque scales with the ratio while output power equals input power. A gear train is a rotational lever, and the speed-for-torque trade is just conservation of energy — the same rule behind every lever and pulley. Real gears lose a little to friction, so the output power is always slightly less than the input, never more.