Question

the blade on a typical table saw rotates at 4000 revolutions per minute. calculate the linear velocity in miles per hour of one of the teeth at the edge of the 9 inch diameter blade. the linear velocity is miles per hour. (round to the nearest tenth as needed.)

Explanation:

Step1: Convert revolutions per minute to revolutions per hour

Since there are \(60\) minutes in an hour, if the blade rotates at \(n = 4000\) revolutions per minute (rpm), then the number of revolutions per hour \(N\) is \(N=4000\times60 = 240000\) revolutions per hour.

Step2: Find the circumference of the blade

The formula for the circumference of a circle is \(C=\pi d\), where \(d = 9\) inches. So \(C=\pi\times9=9\pi\) inches.

Step3: Calculate the total distance in inches per hour

The distance \(D\) traveled by a point on the edge of the blade in one hour (in inches) is the number of revolutions per hour times the circumference. So \(D = N\times C=240000\times9\pi\) inches.

Step4: Convert inches to miles

We know that \(1\) mile \(=5280\times12 = 63360\) inches.
Let \(v\) be the linear velocity in miles per hour. Then \(v=\frac{240000\times9\pi}{63360}\)

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Answer:

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