Which equation represents spindle speed N in terms of surface speed V and drill diameter D?

• A. N = 12V/(pi D)
• B. N = pi D /(12V)
• C. N = V/(pi D)
• D. N = 12D/(pi V)

Answer: (A)

The key idea is that the surface speed at the cutting edge is determined by how far that edge travels in one minute, which depends on both the diameter and the rotation rate. The edge travels a circumference of πD inches each revolution, so at N revolutions per minute it covers N·πD inches per minute. If we’re using V in feet per minute as the surface speed, convert those inches to feet by dividing by 12, giving V = (πDN)/12. Solving for the spindle speed yields N = 12V/(πD). This matches the form when V is in feet per minute and D is in inches, with N in RPM. If different units were used, the constant 12 would change or the formula would look different (e.g., using V in meters per minute with D in meters would give N = V/(πD) without the 12).