Sprocket, where I come from, is the toothed gear most forward on a bike. It is turned by some sort of motor or by the rider via the cranks on a bicycle. The larger the front sprocket, the harder it is to turn and the higher the speed at a given rpm.
If you are talking about the rear wheel sprocket, it is turned by the chain and rotates the wheel. The smaller it is, the harder it is to turn and the faster the wheel will turn, given the same rpm at the front sprocket.
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