If an 8" pulley turns at 120 RPM, what is the diameter of the driven pulley turning at 150 RPM?

To determine the diameter of the driven pulley when one pulley is known, we can use the relationship between the rotational speeds and diameters of two pulleys connected by a power transmission system. This relationship is based on the principle of conservation of energy and can be expressed in the following formula:

[

\frac{D_1}{D_2} = \frac{N_2}{N_1}

]

Where:

• (D_1) is the diameter of the first pulley (the driver),

• (D_2) is the diameter of the second pulley (the driven),

• (N_1) is the RPM of the first pulley (the driver),

• (N_2) is the RPM of the second pulley (the driven).

In this case, we have:

• (D_1 = 8) inches,

• (N_1 = 120) RPM (the driver),

• (N_2 = 150) RPM (the driven).

Plugging in the values into the formula, we can rearrange it to solve for the diameter of the driven pulley:

[

D_2 = D_1 \times \frac{N_1}{N