One property of gears is they change the rotational speed of the axles that hold the gears. In this picture, there is a 40 tooth spur gear on the output axle meshed with an 8 tooth spur gear on the input axle. |

The Why is this so? The answer is because of the different diameters of the gears, and the relationship between rotational speed and linear speed. Both gears are moving at the same linear speed at the point where the teeth of the gears mesh but in opposite directions. |

The relationship between linear speed and rotational speed
is, Since v40 = -v8, we can substitute the above equation for v and get w40 x r40 = -(w8 x r8). Rewriting this equation gives w40 = -w8 x (r8 / r40). The ratio of r8 to r40 is 1 to 5, or w40 = -w8 x (1/5). The rotational speed of the 40 tooth gear is 1/5 of the 8 tooth gear, or 5 times slower. The negative sign means the rotational speed is in the opposite direction. |