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

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

• A. 12.2 r/min
• B. 1,562.5 r/min
• C. 609.8 r/min
• D. 640 r/min

Answer: (B)

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

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