If a workpiece has a diameter of 2 inches and runs at 100 rpm, what is the cutting speed in feet per minute?

To find the cutting speed in feet per minute, you first need to understand the relationship between the diameter of the workpiece, its rotation speed, and the cutting speed.

The cutting speed (also known as surface speed) can be calculated using the formula:

[ \text{Cutting Speed} (V) = \pi \times D \times N ]

where:

• ( V ) is the cutting speed in inches per minute,
• ( D ) is the diameter in inches, and
• ( N ) is the rotational speed in revolutions per minute (rpm).

In this case, the diameter ( D ) of the workpiece is 2 inches, and the rotational speed ( N ) is 100 rpm.

Substituting these values into the formula gives:

[ V = \pi \times 2 \text{ inches} \times 100 \text{ rpm} ]

Calculating this step-by-step:

1. Multiply the diameter by the rotation speed: [ 2 \times 100 = 200 ]

2. Now, multiply this by ( \pi ): [ V \approx 3.14159 \times 200 \approx 628