If a gear with 1,000 teeth turns at 50 r/min, what would be the corresponding speed of a 40-teeth gear?

To determine the speed of the 40-tooth gear when the 1,000-tooth gear is turning at 50 revolutions per minute (r/min), we need to understand the relationship between the two gears. Gears operate on the principle that the product of the speed (in r/min) and the number of teeth must remain constant for meshed gears due to the conservation of energy and motion.

When the 1,000-tooth gear is turning, it has a specific rotational speed. The 40-tooth gear will turn faster in response due to its smaller number of teeth. The formula used to relate the speeds and the number of teeth of both gears is:

[

\text{Speed of Gear A} \times \text{Number of Teeth in Gear A} = \text{Speed of Gear B} \times \text{Number of Teeth in Gear B}

]

In this scenario:

• Gear A is the 1,000-tooth gear turning at 50 r/min.

• Gear B is the 40-tooth gear whose speed we want to determine.

Plugging in the values, we have:

[

50 , \text{r/min} \times 1,000 = \