A router bit makes 45,000 rev/min. What is the linear velocity in miles per hour of the outside edge of a bit that cuts a 1 inch wide path? I know how to work these problems out but I keep getting 267.75 mph but the answer is 133.9 mph. Any kind of help would be appreciated. Thanks!
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Without actually solving the problem it seems to be that your answer is double the correct one. Are you taking into account that the 1 inch path represents the diameter and not the radius of the bit?
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45000 rpm = 45000(2π)/min = 90000π/min
90000π/min • 1/2 in • 1 ft/12 in • 1 mi/5280 ft • 60 min/1 hr = 133.8746869... ≈ 133.9 mph
90000π/min • 1/2 in • 1 ft/12 in • 1 mi/5280 ft • 60 min/1 hr = 133.8746869... ≈ 133.9 mph