An 8" diameter pulley revolving at 120 rpm drives a pulley which must rotate at 150 rpm. What diameter is the second pulley?

To determine the diameter of the second pulley that needs to achieve a certain speed, you can use the relationship between the diameters of the pulleys and their rotational speeds, known as the pulley speed ratio. This relationship can be expressed with the formula:

(Diameter of first pulley x RPM of first pulley) = (Diameter of second pulley x RPM of second pulley).

In this case, the first pulley has a diameter of 8 inches and is spinning at 120 RPM. We need to find the diameter of the second pulley that will spin at 150 RPM. By rearranging the formula to solve for the diameter of the second pulley, we get:

Diameter of second pulley = (Diameter of first pulley x RPM of first pulley) / RPM of second pulley.

Now, substituting in the known values:

Diameter of second pulley = (8 inches x 120 RPM) / 150 RPM.

Diameter of second pulley = (960 inch-RPM) / 150 RPM.

When you perform the division:

Diameter of second pulley = 6.4 inches.

Therefore, the diameter of the second pulley that would allow it to spin at 150 RPM when the first pulley is rotating at 120 RPM is 6.4 inches. This calculation