Assuming a pinion gear has 14 teeth and drives a ring gear with 42 teeth, what is the speed of the ring gear if the pinion turns at 420 rpm?

To determine the speed of the ring gear when the pinion turns at 420 rpm, we can use the gear ratio, which is derived from the number of teeth on the pinion and the ring gear.

The gear ratio can be calculated by dividing the number of teeth on the ring gear by the number of teeth on the pinion. Here, the ring gear has 42 teeth, and the pinion has 14 teeth. Therefore, the gear ratio is:

Gear Ratio = Teeth on Ring Gear / Teeth on Pinion = 42 / 14 = 3.

This means that for every one rotation of the pinion gear, the ring gear will make one-third of a rotation.

To find the speed of the ring gear, we take the speed of the pinion and divide it by the gear ratio:

Speed of Ring Gear = Speed of Pinion / Gear Ratio = 420 rpm / 3 = 140 rpm.

This calculation indicates that when the pinion gear is rotating at 420 rpm, the ring gear will rotate at 140 rpm. This rationale supports the choice indicating that the speed of the ring gear is 140 rpm.