Why pinion wheel is smaller than spur wheel?

The pinion wheel is smaller than the spur wheel to achieve a mechanical advantage in gear systems. The smaller size of the pinion allows it to rotate faster than the larger spur wheel, resulting in an increase in speed while reducing torque. This size differential is essential for applications requiring changes in speed and torque, enabling efficient power transmission in machinery. Additionally, using a smaller pinion helps minimize space and weight in gear assemblies.