If a 20-tooth sprocket turns at a speed of 10 rpm, how fast will a 10-tooth sprocket turn when driven by the same chain?

To determine the speed of the 10-tooth sprocket when driven by the same chain as the 20-tooth sprocket, it is essential to understand the relationship between sprocket size and rotational speed. When two sprockets are connected via a chain, the rotation speed of each sprocket is inversely proportional to the number of teeth on the sprocket.

In this scenario, the 20-tooth sprocket is turning at 10 revolutions per minute (rpm). The relationship can be articulated as follows:

• The larger the sprocket, the slower it turns because it has more teeth to move the same chain.

• Conversely, a smaller sprocket with fewer teeth will turn faster since it has less distance to travel for each revolution.

Using the formula relating the speed (rpm) and the number of teeth:

[

\text{Speed of 20-tooth sprocket} \times \text{Teeth of 20-tooth sprocket} = \text{Speed of 10-tooth sprocket} \times \text{Teeth of 10-tooth sprocket}

]

Plugging in the numbers:

[

10 , \text{rpm} \times 20 = \text{Speed