If a pinion gear has 14 teeth and drives a spur gear with 42 teeth at 140 RPM, what is the speed of the pinion gear?

To find the speed of the pinion gear when it drives a spur gear, you can use the gear ratio formula which relates the number of teeth on the gears to their speeds. The gear ratio can be calculated by dividing the number of teeth on the driven gear (spur gear) by the number of teeth on the driving gear (pinion gear).

In this case, the spur gear has 42 teeth, and the pinion gear has 14 teeth. Thus, the gear ratio is:

[ \text{Gear Ratio} = \frac{\text{Teeth on Spur Gear}}{\text{Teeth on Pinion Gear}} = \frac{42}{14} = 3 ]

This means that for every one rotation of the pinion gear, the spur gear rotates one-third of a rotation. Conversely, for every rotation of the spur gear, the pinion gear must rotate three times to compensate for the difference in teeth.

If the spur gear is rotating at 140 RPM, the speed of the pinion gear can be calculated by multiplying the speed of the spur gear by the gear ratio:

[ \text{Speed of Pinion Gear} = \text{Speed of Spur Gear} \times \text{Gear Ratio