Answered

IDNLearn.com makes it easy to get reliable answers from experts and enthusiasts alike. Discover comprehensive answers to your questions from our community of experienced professionals.

he fan blades on a jet engine make one thousand revolutions in a time of 54.9 ms. What is the angular frequency of the blades?

Sagot :

MDKPfromIDNidn

So, the angular frequency of the blades approximately 36.43π rad/s.

Introduction

Hi ! Here I will discuss about the angular frequency or what is also often called the angular velocity because it has the same unit dimensions. Angular frequency occurs, when an object vibrates (either moving harmoniously / oscillating or moving in a circle). Angular frequency can be roughly interpreted as the magnitude of the change in angle (in units of rad) per unit time. So, based on this understanding, the angular frequency can be calculated using the equation :

[tex] \boxed{\sf{\bold{\omega = \frac{\theta}{t}}}} [/tex]

With the following condition :

  • [tex] \sf{\omega} [/tex] = angular frequency (rad/s)
  • [tex] \sf{\theta} [/tex] = change of angle value (rad)
  • t = interval of the time (s)

Problem Solving

We know that :

  • [tex] \sf{\theta} [/tex] = change of angle value = 1,000 revolution = 1,000 × 2π rad = 2,000π rad/s >> Remember 1 rev = 2π rad/s.
  • t = interval of the time = 54.9 s.

What was asked :

  • [tex] \sf{\omega} [/tex] = angular frequency = ... rad/s

Step by step :

[tex] \sf{\omega = \frac{\theta}{t}} [/tex]

[tex] \sf{\omega = \frac{2,000 \pi}{54.9}} [/tex]

[tex] \boxed{\sf{\omega \approx 36.43 \pi \: rad/s}} [/tex]

Conclusion :

So, the angular frequency of the blades approximately 36.43π rad/s.

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.