the blade of a circular saw rotates at a rate of 2000 revolutions per minute. what is the linear velocity in…

the blade of a circular saw rotates at a rate of 2000 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a $7\\frac{1}{4}$ inch diameter blade? the linear velocity is approximately $\\square$ miles per hour. (round to the nearest tenth as needed.)

the blade of a circular saw rotates at a rate of 2000 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a $7\\frac{1}{4}$ inch diameter blade? the linear velocity is approximately $\\square$ miles per hour. (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Calculate the radius

The diameter (d = 7\frac{1}{4}=\frac{29}{4}) inches. The radius (r=\frac{d}{2}=\frac{29}{8}) inches.

Step2: Convert revolutions per minute to revolutions per hour

Since there are (60) minutes in an hour, the number of revolutions per hour (n = 2000\times60=120000) revolutions per hour.

Step3: Calculate the circumference of the circle

The circumference of a circle (C = 2\pi r). Substituting (r = \frac{29}{8}) inches, we get (C=2\pi\times\frac{29}{8}=\frac{29\pi}{4}) inches per revolution.

Step4: Calculate the linear distance in inches per hour

The linear distance (D) (in inches per hour) is the number of revolutions per hour times the circumference. So (D=n\times C=120000\times\frac{29\pi}{4}=870000\pi) inches per hour.

Step5: Convert inches per hour to miles per hour

We know that (1) mile ( = 5280\times12 = 63360) inches. Let (v) be the linear velocity in miles per hour. Then (v=\frac{D}{63360}). Substituting (D = 870000\pi) inches, we have (v=\frac{870000\pi}{63360}). [v=\frac{870000\times3.14159}{63360}] [v=\frac{2733183.3}{63360}\approx43.1]

Answer:

(43.1)