If a motor pulley with a diameter of 90 mm is rotating at 1,800 rpm, what is the final speed of a fan pulley with a diameter of 300 mm?

To determine the final speed of the fan pulley, it's important to understand the relationship between the diameter of the pulleys and their rotational speeds based on the principle of conservation of energy in mechanical systems. Specifically, the linear speed (tangential velocity) at the edge of the pulleys must remain constant for both connected pulleys.

The formula that expresses this relationship is:

[

N_1 \times D_1 = N_2 \times D_2

]

Where:

• (N_1) is the speed of the motor pulley (in rpm),

• (D_1) is the diameter of the motor pulley,

• (N_2) is the speed of the fan pulley,

• (D_2) is the diameter of the fan pulley.

Plugging in the values:

• The motor pulley has a diameter of 90 mm and is rotating at 1,800 rpm.

• The fan pulley has a diameter of 300 mm.

Using the formula:

[

1800 , \text{rpm} \times 90 , \text{mm} = N_2 \times 300 , \text{mm}

]

Solving for (N_2