When you look at two ends of a shaft, they must both be spinning at the same speed because they are connected.
If you connect two shafts together with gears, then their speeds will be coupled – one will always spin at some multiple of the other. Let’s say double. By changing the gearing ratio, it may change from double to triple or quadruple.
So, if the wheels are spinning at, say, 1000 RPM, and the gears are 1:1, then the engine must be spinning at 1000 RPM. If we shift gears, the shafts are now connected to a 1:2 ratio. The engine must now be spinning at double the speed of the wheels, and any discrepancy is rectified by friction in the clutch.
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