What is the speed of a spur gear with 42 teeth driven by a pinion gear with 14 teeth turning at 420 RPM?

To determine the speed of the spur gear, we first need to understand the relationship between the pinion gear (the driving gear) and the spur gear (the driven gear) through their teeth.

When the pinion gear with 14 teeth rotates, it causes the spur gear with 42 teeth to rotate as well. The relationship between the speeds of the pinion and spur gear can be calculated using the gear ratio, which is the inverse of the ratio of the number of teeth on the gears.

The gear ratio can be calculated as follows:

[

\text{Gear Ratio} = \frac{\text{Number of Teeth on Driven Gear}}{\text{Number of Teeth on Drive Gear}} = \frac{42}{14} = 3

]

This means that for every rotation of the pinion gear, the spur gear will rotate ( \frac{1}{3} ) of a turn. Consequently, the speed of the driven spur gear will be reduced in relation to the speed of the pinion gear.

Next, since the pinion gear is turning at 420 RPM, we can calculate the speed of the spur gear using the gear ratio. Specifically, the speed of the spur gear is found by dividing the speed