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When a rotating disk drives linear motion—think of a car wheel or a gear train—knowing how to translate its revolutions per minute (RPM) into feet per minute (FPM) is essential for design and analysis.
Consider a point P on the edge of a spinning disk. Each full rotation moves P a distance equal to the disk’s circumference. If the disk has radius r, its circumference is 2πr. Thus, for a shaft that rolls without slipping, the forward distance covered per minute is n × 2πr, where n is the rotational speed in RPM.
In most cases we measure the diameter d instead of the radius. Since r = d/2, the formula simplifies to s = n × πd, where s is the linear speed in feet per minute.
Suppose a vehicle equipped with 27‑inch tires is traveling at 60 mph. How fast are its wheels turning?
First, convert 60 mph to feet per minute: 60 mph = 1 mile/min ≈ 5,280 ft/min. The tire diameter in feet is 27 in ÷ 12 = 2.25 ft. Applying the formula gives:
n = s ÷ (πd) = 5,280 ÷ (3.14 × 2.25) ≈ 746 RPM.
For the shaft to advance, the friction between the disk and its contact surface must be sufficient to prevent slipping. This friction depends on the coefficient of friction and the normal force pressing the surfaces together. When a vehicle climbs an incline or traverses ice, the normal force—and thus available friction—decreases, potentially causing wheel slip.
In practice, engineers account for slip by applying a correction factor that incorporates the coefficient of friction and the incline angle. This ensures that the theoretical linear speed matches real-world performance.
