Which factor directly affects rpm in the given formula?

• A. Cutting speed (CS)
• B. Tool material
• C. Workpiece color
• D. Lubricant viscosity

Answer: (A)

RPM is the rotational speed needed to maintain a specific surface speed at the cutting edge, so the formula ties it directly to cutting speed and the size of the feature being cut. In the equation, rpm is proportional to the cutting speed and inversely proportional to the diameter of the workpiece (rpm = (CS × 1000) / (π × D) when CS is in meters per minute and D is in millimeters). This means raising the cutting speed pushes rpm up, while increasing the diameter pushes rpm down, since a larger circumference requires more revolutions to sweep the same linear distance.

The other factors—tool material, workpiece color, and lubricant viscosity—do not appear in this relationship, so they don’t directly set the rpm. They may affect heat, wear, or finish, but not the rotational speed needed to achieve the desired cutting speed. For a quick sense, if you keep cutting speed the same and double the diameter, the rpm roughly halves. If you increase cutting speed while keeping diameter the same, rpm increases accordingly.