Two pulleys have diameters of 10" and 12". If they are connected by a belt and if the large pulley rotates at 180 rpm, what is the rpm of the small pulley?

To determine the rpm of the small pulley when it is connected by a belt to the larger pulley, it’s important to understand the relationship between the diameters of the pulleys and their rotational speeds.

The formula used to relate the rotational speeds and diameters of the pulleys is based on the principle of continuity of the belt, which states that the linear speed of the belt must be the same on both pulleys. This relationship can be expressed as:

[

\text{Speed of Large Pulley} \times \text{Diameter of Large Pulley} = \text{Speed of Small Pulley} \times \text{Diameter of Small Pulley}

]

Given that the diameter of the large pulley is 12 inches and it rotates at 180 RPM, while the diameter of the small pulley is 10 inches, this can be set up as:

[

180 , \text{RPM} \times 12 , \text{inches} = \text{Speed of Small Pulley} \times 10 , \text{inches}

]

Solving for the Speed of the Small Pulley gives:

[

\text{Speed of Small Pulley} = \frac{180