Two gears, one big and one small — which spins faster, and can gears ever give you free speed?
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After you watchTwo 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.
Try this next
- What if you put a third gear in between the two? Imagine adding a middle gear, then predict before you decide: does it change the final speed, or just which way the last gear turns? Watch what the in-between gear really does.
- What if both gears had exactly the same number of teeth? Set the driven gear to match the driver tooth-for-tooth and guess first: does it spin faster, slower, or the same? Then watch the weight it can lift to check the trade.
Now you — bend it
- What if The driver gear is locked at 18 teeth. Shrink the driven gear to its smallest, 6 teeth, then read the speed and force meters and multiply them together.Speed should jump to 18/6 = 3× while force drops to 1/3 ≈ 0.33×. Predict their product before you check — does 3 × 0.33 land back near 1, the same total you started with?
- What if Slide the driven gear all the way to 36 teeth — double the driver — and watch the lift test instead of the meters.Now the driven gear turns at half speed but pushes twice as hard. Predict whether a 36-tooth gear can lift a load that the 6-tooth gear stalled on, and roughly how much slower it crawls up.
- What if Real gears lose a sliver of power to friction at every meshing tooth. Imagine chaining ten of these gear pairs in a row, each one wasting 3% of the power it passes on.Each stage keeps 0.97 of the power. Predict whether ten stages still deliver over 90%, around 70%, or under half — then reason: 0.97 multiplied by itself ten times.
Can you prove it?Whatever factor the driven gear's speed goes UP, its pushing-force goes DOWN by that exact same factor, so speed × force never changes. — Set the driven gear to 9 teeth: speed reads 18/9 = 2×, force reads 0.5×, product = 1. Now set it to 6 teeth: speed = 18/6 = 3×, force = 0.33×, product = 1. Try 36 teeth: speed = 0.5×, force = 2×, product = 1. Three different gears, same product every time — that constant product is the power you can't add to with gears alone.
Design your own test:Pick a tooth count and, before you move the slider, predict the exact speed factor (18 ÷ your teeth) and force factor (its reciprocal). Then check both meters — were your two numbers right, and did they multiply to 1?
Explain it to a 6-year-old: A little gear spins fast but pushes softly, and a big gear spins slowly but pushes hard — gears can swap fast-for-strong, but they can never give you both at once.
The whole story
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.
Talk about it
- If gears never give you free power, why do we bother putting them on bikes and cars? Guess before you answer.
- Which would you rather have climbing a steep hill — a gear that's fast or one that's strong? Why can't you have both?
- Where in our house do you think something is quietly trading speed for strength right now?
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.
Keep going
What else makes you wonder?
- If gears can't make free power, where does the extra force in a car or a crane actually come from?
- A clock has lots of gears chained together — what trade is each one making?
- Does a bike chain count as a gear, even though the two wheels it connects don't touch?