Pulleys, gears, and handwheels
Pro-Tip. Count the ropes holding the load. Fewer gear teeth spin faster and turn the other way. A bigger handwheel is an easier turn.
A single fixed pulley only changes direction. You pull down, the load goes up, and the advantage is 1. The load does not get lighter. On a diagram, count the rope parts that hold the load. Two supporting parts means about half the weight and about two feet of rope for each foot the load rises. Four supporting parts means about one fourth of the weight, and about four feet of rope. Do not count the free end you pull down off a fixed block.
Meshed gears pass the same number of teeth each minute. Teeth × RPM on one gear equals teeth × RPM on the other. The gear with fewer teeth spins faster. They also turn in opposite directions. A big gear drawn larger is not the faster one.
A handwheel on a shaft is a wheel and axle. Advantage = wheel radius ÷ shaft radius. Your hand travels a bigger circle, so the force can be smaller. The wheel and the shaft turn at the same RPM.
Worked example
A 48-tooth gear at 20 RPM drives a 16-tooth gear.
60 RPM. 48 × 20 = 16 × RPM, so the small gear turns three times as fast.