If a gear has 1,000 teeth and revolves at 50 r/min, how fast does the driven gear with 32 teeth turn?

To determine the speed of the driven gear, we can use the gear ratio relationship, which is based on the number of teeth on each gear.

In a gear system, the speed relationship can be expressed by the following equation:

[

\text{speed of driver gear} \times \text{teeth on driver gear} = \text{speed of driven gear} \times \text{teeth on driven gear}

]

Here, the driver gear has 1,000 teeth and is revolving at 50 revolutions per minute (r/min). The driven gear has 32 teeth, and we need to find its speed.

First, we can rearrange the equation to solve for the speed of the driven gear:

[

\text{speed of driven gear} = \frac{\text{speed of driver gear} \times \text{teeth on driver gear}}{\text{teeth on driven gear}}

]

Substituting the known values:

[

\text{speed of driven gear} = \frac{50 , \text{r/min} \times 1000 , \text{teeth}}{32 , \text{teeth}}

]

Calculating this gives