Two gearwheels, whose teeth mesh together so that as one turns, the other has to turn as well. The smaller gear has 9 teeth, so if it is turning at 1000 rpm, its teeth are moving at 9000 teeth per minute. The larger wheel is twice the size, and has 18 teeth, so although its teeth must also be moving at 9000 teeth per minute, that means only 500 rpm. Note, too, that if the smaller wheel is turning clockwise, the larger wheel must be turning anticlockwise.

Now imagine that you're using a spanner a foot long to turn the smaller wheel. If you apply an effort of 10 lb to the end of the spanner, you're applying a torque of 10 lb/ft (10 lb at a radius of 1 ft). The gear-wheel is much smaller - let's say it has an effective radius of 1 in. That means its teeth must be pushing on the teeth of the other wheel with a force equivalent to 120 lb (120 lb at a radius of 1/12 ft = 120 x 1/12 = 10 lb/ft). The larger wheel has an effective radius of 2 in, so a force of 1201b to its teeth corresponds to a torque of 20 lb/ft (120 x 2/12 = 20 lb/ft).

In other words, by using a 9-tooth wheel to drive an 18-tooth wheel, we've halved the speed doubled the torque, and reversed the direction of rotation.

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