Explain how the gear ratio relates to the number of teeth of the driving and driven gears.

The gear ratio is a measure that describes the mechanical advantage of a gear system. It is calculated by comparing the number of teeth on two gears that are meshed together.

Here's how it works:

1. Identify the driving gear and the driven gear. The driving gear is the one that is connected to the power source and initiates the motion, while the driven gear is the one that is moved by the driving gear.

2. Count the number of teeth on both the driving gear and the driven gear.

3. The gear ratio is then calculated by dividing the number of teeth on the driven gear (the one being turned) by the number of teeth on the driving gear (the one doing the turning).

For example, if the driving gear has 10 teeth and the driven gear has 30 teeth, the gear ratio would be 30/10 = 3:1. This means that for every one turn of the driving gear, the driven gear will make three turns.

In summary, the gear ratio is directly related to the number of teeth on the driving and driven gears. The more teeth the driven gear has in comparison to the driving gear, the higher the gear ratio and the greater the mechanical advantage, meaning the driven gear will turn faster than the driving gear. Conversely, if the driving gear has more teeth, the gear ratio will be less than one, and the driven gear will turn slower than the driving gear.