(a) The distance the tip of the blade moves in one revolution is the circumference of the circle it traces out. The formula for the circumference of a circle is 2πr, where r is the radius. So, the distance is 2π(0.15 m) = 0.3π m.

(b) The speed of the tip is the distance it travels in a given time. We know it completes 1200 revolutions per minute, so the time for one revolution is 1/1200 minutes = 1/20 seconds. The speed is then the distance per time = (0.3π m) / (1/20 s) = 6π m/s.

(c) The magnitude of the acceleration is given by the formula a = v^2/r, where v is the speed and r is the radius. So, the acceleration is (6π m/s)^2 / (0.15 m) = 240π^2 m/s^2.

(d) The period of the motion is the time it takes for one complete revolution. We already found this to be 1/20 seconds.

Question

(a) The distance the tip of the blade moves in one revolution is the circumference of the circle it traces out. The formula for the circumference of a circle is 2πr, where r is the radius. So, the distance is 2π(0.15 m) = 0.3π m.

(b) The speed of the tip is the distance it travels in a given time. We know it completes 1200 revolutions per minute, so the time for one revolution is 1/1200 minutes = 1/20 seconds. The speed is then the distance per time = (0.3π m) / (1/20 s) = 6π m/s.

(c) The magnitude of the acceleration is given by the formula a = v^2/r, where v is the speed and r is the radius. So, the acceleration is (6π m/s)^2 / (0.15 m) = 240π^2 m/s^2.

(d) The period of the motion is the time it takes for one complete revolution. We already found this to be 1/20 seconds.

Knowee AI · Accepted Answer

(a) The distance the tip of the blade moves in one revolution is the circumference of the circle it traces out. The formula for the circumference of a circle is 2πr, where r is the radius. So, the distance is 2π(0.15 m) = 0.3π m.

(b) The speed of the tip is the distance it travels in a given time. We know it completes 1200 revolutions per minute, so the time for one revolution is 1/1200 minutes = 1/20 seconds. The speed is then the distance per time = (0.3π m) / (1/20 s) = 6π m/s.

(c) The magnitude of the acceleration is given by the formula a = v^2/r, where v is the speed and r is the radius. So, the acceleration is (6π m/s)^2 / (0.15 m) = 240π^2 m/s^2.

(d) The period of the motion is the time it takes for one complete revolution. We already found this to be 1/20 seconds.

A rotating fan completes 1200 revolutions every minute.Consider the tip of a blade, at a radius of 0.15 m. (a) Throughwhat distance does the tip move in one revolution? What are(b) the tip’s speed and (c) the magnitude of its acceleration?(d) What is the period of the motion?

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