What is the speed of the driven gear in rpm if a driving gear with 60 teeth turns at 750 rpm and drives a gear with 90 teeth?

To determine the speed of the driven gear, we can use the gear ratio formula, which states that the speed of the driven gear is inversely proportional to the number of teeth on the gears involved. The relationship can be expressed as follows:

[

\text{Speed of Driving Gear} \times \text{Number of Teeth on Driving Gear} = \text{Speed of Driven Gear} \times \text{Number of Teeth on Driven Gear}

]

In this case, we know the driving gear has 60 teeth and is turning at 750 rpm, while the driven gear has 90 teeth. We can rearrange the formula to find the speed of the driven gear:

[

\text{Speed of Driven Gear} = \left( \frac{\text{Speed of Driving Gear} \times \text{Number of Teeth on Driving Gear}}{\text{Number of Teeth on Driven Gear}} \right)

]

Substituting in the known values:

[

\text{Speed of Driven Gear} = \left( \frac{750 \text{ rpm} \times 60 \text{ teeth}}{90 \text{ teeth}} \right)

]

Calculating this gives:

[

\