In a gear system, what happens if the driving gear has more teeth than the driven gear?

In a gear system, if the driving gear has more teeth than the driven gear, the driven gear will indeed rotate faster than the driving gear, but with less torque. The principle at play here is the relationship between the sizes and number of teeth of the gears involved.

When the driving gear is larger and has more teeth, it requires more rotations to turn the smaller driven gear with fewer teeth. Because the driven gear is smaller, it completes more rotations for each full turn made by the driving gear. This results in an increased speed of rotation for the driven gear while simultaneously decreasing the torque. Torque is effectively reduced because a smaller gear, while spinning faster, has to apply its force over a smaller radius, thus diminishing its ability to do substantial work compared to a larger gear.

This setup is commonly used in machines where a greater speed is needed from the output, such as in bicycles and some automotive systems, where enabling faster movement at the expense of torque is a design preference.