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Calculation of Angular Frequency

  1. Dec 19, 2011 #1
    Hi everyone,

    I need to calculate the Angular frequency based on the input angular speed.
    I'm thinking the formula would be

    Angular Speed, ω = 2∏f
    => Angular Frequency, f = ω/2∏ = ω/360°

    so, does the formula "f = ω/360°" will give me correct solution.

    Kindly guide me please.
  2. jcsd
  3. Dec 19, 2011 #2
    No....do not use degrees...you need to leave 2.pi in radians...in other words, you just performed some kind of bad conversion...is 2.pi = 360? is it? No, it is not. 2x3.14=6.28!
  4. Dec 19, 2011 #3
    But, my input angular speed is in Deg/sec....
    so, you say, i convert that deg/sec to radian/sec and then use the formual f = ω/2∏ ??
  5. Dec 19, 2011 #4
    oh...that's weird.

    Then, yes, convert deg/s to rad/s, first and then...
  6. Dec 19, 2011 #5
    I'm little confused :(

    Is in't the same thing ?

    Lets say,

    1. Angular Velocity = 10deg/sec
    2. Convert it to radians/sec --> 10*(∏/180)
    3. Now, calculate the angular frequency, f = ((10*∏)/180)/2∏
    4. If we see in the above equation, ∏ in the neumarator and ∏ in the denominator will be cancelled. So, I left with the equation, f = 10/2*180 = 10/360.

    So, angular freq, f = ω/360 (Hertz) ..
    where ω - Angular velocity in deg/sec

    Am I thinking correctly?
  7. Dec 19, 2011 #6
    You are kind of correct..you just need to be more careful and keep things absolutely clear.

    In your first posting, you never specified in which units ω was...typically, it is understood that it is in rad/s...what's more, you even included your starting equation as ω=2∏f...in this equation, ω is necessarily in rad/s!!! Then, suddenly, you replaced 2∏ with 360...what was I to think of this?

    You see what I am coming from?

    More often than not, it is best to keep things in radians or radians per second...you'll see.
  8. Dec 19, 2011 #7

    Doc Al

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    Staff: Mentor

    Close enough.

    Generally, ω is called the angular frequency and is measured in radians/second. f is just the frequency.

    So, in standard units ω = 2πf. (Since one cycle = 2π radians.) But if you wanted the angular frequency in degrees/second instead, then ω = 360f. (Since one cycle = 360 degrees.)

    I'm curious as to what context would give you an angular frequency in degrees/sec? I'd be very careful, since standard formulas for simple harmonic motion assume that ω is in radians/sec.
  9. Dec 19, 2011 #8


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    Science Advisor
    Gold Member

    This is particularly true when you start using Trig functions in Calculus. If you try to work in degrees, life becomes a nightmare.

    It is worth while remembering that the three fingered Grigs of the planet Tryd will be dealing in exactly the same Radians that we deal in on Earth. However, their 'degrees' could be any fraction of a complete turn, depending on their particular culture - 1/360th, 1/350th, 1/297th or whatever.
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