What is the result of calculating the RPM using a cutting speed of 120 SFPM and a diameter of 3 inches?

To determine the RPM when given a cutting speed in surface feet per minute (SFPM) and the diameter of the workpiece, you use the formula:

[ \text{RPM} = \frac{\text{Cutting Speed (SFPM)} \times 12}{\pi \times \text{Diameter (in inches)}} ]

In this case, the cutting speed is 120 SFPM and the diameter of the workpiece is 3 inches.

First, converting the cutting speed into inches per minute, you have:

[ \text{Cutting Speed in Inches per Minute} = 120 \text{ SFPM} \times 12 \text{ inches} = 1440 \text{ inches per minute} ]

Next, applying the values to the RPM formula:

[ \text{RPM} = \frac{1440}{\pi \times 3} ]

Calculating this gives:

1. First find (\pi \times 3 \approx 9.42) (using (\pi \approx 3.14)).
2. Then compute ( \frac{1440}{9.42} \approx 152.6).

However, for cleaner calculations, using