If a 38-tooth gear running at 360 rpm is driving another gear at 144 rpm, what is the number of teeth on the driven gear?

To determine the number of teeth on the driven gear, we can use the relationship between the speeds and teeth of the gears involved. The formula that relates the two gears can be expressed as:

[

\frac{T_1}{T_2} = \frac{N_2}{N_1}

]

Where ( T_1 ) and ( T_2 ) are the number of teeth on the driving and driven gear, respectively, and ( N_1 ) and ( N_2 ) are the speeds of the driving and driven gear, respectively.

In this scenario:

• The driving gear has 38 teeth ( ( T_1 = 38 ) ).

• The speed of the driving gear ( ( N_1 ) ) is 360 RPM.

• The speed of the driven gear ( ( N_2 ) ) is 144 RPM.

• We need to find ( T_2 ), the number of teeth on the driven gear.

Using the formula provided:

[

\frac{38}{T_2} = \frac{144}{360}

]

We can simplify the right side:

[

\frac{144}{360} = \frac{2}{