You already know that gears can change the speed of rotating axles. They also do another thing, change the strength, or torque, of the rotating axle. The gear ratio is the ratio of the number of teeth of the gear on the output axle to the number of teeth of the gear on the input axle. Here is a 40 tooth output gear meshed with an 8 tooth input gear. The gear ratio of this gear pair is 5 to 1.
Recall that the 40 tooth output gear rotates 5 times as slow as the 8 tooth input gear. However, the torque of the output axle has increased 5 times. Why is this so? The answer, again, lies with the diameter of the gears. Both gears exert the same amount of force in opposite directions at the point where the gear teeth mesh.
Since f40 = -f8, we can substitute the equations for the torque of each axle, which is dependent on the radius of the gear. This gives us t40 / r40 = -t8 / r8. Rewriting the equation gives t40 = -t8 x (r40 / r8). The ratio of r40 to r8 is 5 to 1, so the torque on the axle with the 40 tooth gear is 5 times as great as the torque on the axle with the 8 tooth gear.
See also: Gears, Gears and Speed, Torque