How is output speed calculated in relation to input speed?

The calculation of output speed in relation to input speed is determined by the gear ratio, specifically when dealing with gears in mechanical systems. The formula for output speed shows how the speed of the output is influenced by the input speed and the gear ratio.

When using gears, the gear ratio indicates the relationship between the input gear's teeth and the output gear's teeth. If the gear ratio is greater than one, it means the input gear has fewer teeth than the output gear. In this case, the output gear will turn more slowly than the input gear as it is required to engage more teeth. Therefore, the output speed is derived by dividing the input speed by the gear ratio.

For practical understanding, if the input speed is, for example, 100 revolutions per minute (RPM) and the gear ratio is 4:1 (meaning the output gear has four times as many teeth), the output speed can be calculated as 100 RPM divided by 4, resulting in an output speed of 25 RPM.

This relationship illustrates how by using the gear ratio, one can determine the output speed that corresponds to the input speed accurately.