And what’s with all the confusing terminology…
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What does hard mean? It means how much force you need to make the pedals spin, right? So the pedal is your input. The “cogwheels” on the front (chainrings) are directly connected to the pedals, so one turn of the pedals equals to exactly one turn of the chainrings. The more diameter (and circumference) a chainring has, the more teeth it has, because teeth need to be always at the same distance from each other to make the chain fit. That means that one complete turn of the pedals pulls more chain, the larger the chainring is. Pulling more length of chain for each turn of the pedals takes more effort, because you make the bike travel further with the same amount of turns of your legs.
On the rear it’s the other way around. Once you’ve decided on a chainring on the front, you have a range of rear cogwheels (sprockets) to chose from. Again, the larger the sprocket, the more teeth it has. The smallest sprocket has the least amount of teeth, so a speed of the chain (driven by the front chainring) results in more rear wheel turns when the smallest sprocket is selected. Again, more distance travelled with the same amount of pedal turns, which means each pedal turn needs to take more work to make it happen.
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