If a pinion gear with 14 teeth is driving a spur gear with 42 teeth at 140 rpm, what is the speed of the pinion gear?

To determine the speed of the pinion gear, we can use the relationship between the number of teeth on the gears and their rotational speeds. The formula for calculating the speeds of two gears that are meshed together is given by:

(Np / Ng) = (Rg / Rp)

Where:

• Np is the number of teeth on the pinion gear,

• Ng is the number of teeth on the spur gear,

• Rg is the speed of the spur gear,

• Rp is the speed of the pinion gear.

In this case, the pinion gear has 14 teeth, and the spur gear has 42 teeth. The speed of the spur gear is given as 140 rpm. We first calculate the speed of the pinion gear using the ratios of the teeth and the speed of the spur gear as follows:

Substituting the known values into the formula:

(14 / 42) = (140 / Rp)

This can be simplified to:

(1 / 3) = (140 / Rp)

Now, cross-multiplying gives:

Rp = 140 * 3

After calculating that, we find:

Rp = 420 rpm

This tells us that the speed of the pinion gear is