Which equation governs maximum peripheral tool velocity as a function of tool size?

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

Answer: (A)

Peripheral velocity is the distance a point on the tool’s edge travels per unit time. For a circular edge, each revolution carries the point a distance equal to the circumference, πD. If the tool completes N revolutions each unit time, the edge covers πD per revolution times N revolutions per unit time, giving V = π D N. This shows the speed scales directly with both diameter and rotation rate.

If you tried the other forms, you’d see mismatches with how distance around the edge accumulates: increasing the speed should increase peripheral velocity, not decrease it; a formula that has N in the denominator or D in the denominator would imply the opposite behavior or inconsistent units. Remember, depending on how you measure N (RPM vs. rev/s) you may need a unit conversion, but the relationship V = π D N correctly captures the dependence of peripheral velocity on tool size and rotational speed.