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The crankshaft in your car engine also does not turn at the same speed as your car’s wheels. This is achieved through the gears in your transmission: if you have one gear of radius *r* being turned at *f* revolutions per minute, and it’s meshed with another gear of radius *r*/2, then that second gear will be turning at 2*f*.
The reason comes down to the difference in circumferences. Both gears have to turn by the same number of gear teeth at any time or else the gears aren’t meshed, they’re slipping, but the larger gear has a larger circumference and therefore more teeth than the smaller one, so covering the same number of teeth takes more rotations of the smaller gear.
Now, when you gain speed in a gear ratio, you also lose torque, but clearly that’s not a problem in the sawmill situation.