For the rotating fan that completes 1160 revolutions every minute, with a tip's radius of 19.0 cm, we have:
a) The tip will move a distance of 1.19 m in one revolution.
b) The tip's speed is 23.08 m/s.
c) The magnitude of the tip's acceleration is 2803.6 m/s².
d) The period of the motion is 0.052 s.
a) The distance to which the tip move in one revolution is given by the circumference of the circle:
[tex]d = 2 \pi r[/tex]
Where:
r: is the radius of the blade = 19.0 cm
[tex]d = 2 \pi r = 2\pi*0.19 m = 1.19 m[/tex]
Hence, the tip will move a distance of 1.19 m in one revolution.
b) The speed of the tip can be calculated with the following equation:
[tex] v = \omega r [/tex]
Where:
ω: is the angular speed = 1160 rev/min
Then, the tip's speed is:
[tex] v = \omega r = 1160 \frac{rev}{min}*\frac{2\pi rad}{1 rev}*\frac{1 min}{60 s}*0.19 m = 23.08 m/s [/tex]
c) The acceleration of the tip is given by:
[tex] a = \frac{v^{2}}{r} = \frac{(23.08 m/s)^{2}}{0.19 m} = 2803.6 m/s^{2} [/tex]
Therefore, the magnitude of the acceleration is 2803.6 m/s².
d) The period of the motion is:
[tex] T = \frac{1}{f} = \frac{2\pi}{\omega} [/tex]
Where:
f: is the frequency
[tex] T = \frac{2\pi}{\omega} = \frac{2\pi}{1160 \frac{rev}{min}*\frac{2\pi rad}{1 rev}*\frac{1 min}{60 s}} = 0.052 s [/tex]
Hence, the period of the motion is 0.052 s.
You can find more about the period and angular acceleration here: https://brainly.com/question/9708010?referrer=searchResults
I hope it helps you!
