What is the relationship between the number of teeth on gears and their rotational speed?

The correct understanding of the relationship between the number of teeth on gears and their rotational speed is that the speed is inversely proportional to the number of teeth. This means that as the number of teeth on a gear increases, the rotational speed decreases, and vice versa.

This principle is rooted in the basic mechanics of gear systems. When two gears are meshed together, the gear with fewer teeth must rotate more times to match one complete turn of the gear with more teeth. For example, if a smaller gear with fewer teeth is driving a larger gear with more teeth, the smaller gear will complete a greater number of rotations in the same time period than the larger gear. This results in a higher speed of rotation for the smaller gear and a lower speed for the larger gear.

Conversely, if you increase the number of teeth on a gear, it requires more rotations to cover the same distance as a gear with fewer teeth, thus reducing its speed. Understanding this relationship is crucial in designing and analyzing any system that involves gears, especially in mechanical engineering, robotics, and even everyday machinery where gear ratios play a significant role in performance.