Angular Frequency?

Discussion in 'Math' started by ELECTRONERD, Oct 2, 2009.

  1. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    Hey Everyone,

    I've seen this "Angular Frequency" expressed as "ω", and I was wondering what it meant. I know that frequency can be expressed as a sine wave and then a circle in degrees so would this angular frequency calculate a certain angle of a true frequency? What is the purpose of angular frequency and how do you use it? I've also seen a lot of other "angular" type things such as "angular velocity."

    Thanks!
     
  2. RimfireJim

    Member

    Apr 7, 2008
    22
    1
  3. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    Thanks for the links, they say that angular frequency is a measure of how fast an object is rotating. Is it used for other things as well?

    According to the equation:

    [​IMG]

    They say that angular frequency is simply a multiple of ordinary frequency.

    They also have ω = dθ/dt. Is the "θ" symbol a constant? Also, do each of the "d's" mean that it is a differential equation (just a wild guess). What is the significance of a differential equation?

    Thanks!
     
  4. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    ELECTRONERD,

    The links tell you where and why it is used.

    Yes, you can see that from the equation. What is the question?

    No, θ is constantly changing as the rotation progresses.

    Yes, "d" means derivative.

    Significant with respect to what? What is the significance of the straight line equation y=mx+b ?

    Ratch
     
  5. Tesla23

    Active Member

    May 10, 2009
    318
    67
    There's nothing special about angular frequency, it simply helps avoid writing down factors of 2\pi all over the place. So don't think that there is something special to be understood about it, it is just that lots of equations have the term 2\pi f so folks came up with the shorthand ω and gave it a name.
     
  6. notxjack

    New Member

    Sep 7, 2009
    20
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    The 'multiple of an ordinary frequency' is a result of unit conversion.

    f has units of cycles per second. One cycle is 2pi radians.
     
  7. count_volta

    Active Member

    Feb 4, 2009
    435
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    Austin, without trigonometry this is a little hard to understand. But let me try.

    You have a circle. Called unit circle in trig. The circle has 360 degrees. Another way to express degrees is in radians. Radians are multiples of ∏. You really only need to remember 4 of these radians. Here they are.

    π/2 = 90°

    π = 180°

    3π/2 = 270°

    2π = 360°

    Now imagine the circle like a clock. But you only have one hand. Say the big hand.

    You start at 3:00 which cooresponds to 0 degrees or 0 radians. Now you move anticlockwise. 12:00 is 90°. 9:00 is 180°. 6:00 is 270°. And now you move back to 3:00 or 0 degrees. You have made 1 revolution.

    Now ω in rad/s is how many of these revolutions you are making a second.

    This is exactly what happens in an electrical generator, which is why you get an AC sine wave. A disc with coils of wire attached moves in a circle around a permanent magnet. How fast its moving can be measured in hertz or rad/s.

    You have to think of a sine wave and a circle as the same thing expressed in different forms. When you get to college you will also learn that a sine wave or a circle can be expressed using imaginary numbers or sqrt(-1). So pay close attention to them when you guys learn about them.

    Check this out. This is a phasor. (not star trek one ;))

    [​IMG]

    A phasor is one way to express a sine wave in terms of imaginary numbers. Phasors have a speed. The speed of that arrow. And the speed is in rad/s which is angular frequency. It shows exactly what I was explaining above.


    I think I made it pretty clear and easy right? ;)
     
    Last edited: Oct 18, 2009
  8. count_volta

    Active Member

    Feb 4, 2009
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    When you see something like dx/dt or ds/dt or etc it means derivative. It means the variable X or S or etc is changing as time moves forward. A derivative is a rate of change. Remember we talked about velocity being a derivative. Its change in position as time changes. How fast is the position changing while time changes. Thats what a derivative is.

    A differential equation is an equation which contains derivatives. Derivatives are the main topic of calculus.

    Any circuit which has capacitor and inductors has derivatives in it. Any AC circuit has derivatives in it. (Well not entirely true, an AC circuit with an AC power source and resistors has no derivatives, but this circuit also doesn't do anything interesting)
     
    Last edited: Oct 17, 2009
  9. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    Frequency is given as cycles per unit time. When it's associated with a rotation, it usually means rotations per unit time. It's commonly given in rotations per second.

    Angular frequency ω is just the conversion of rotations per second to radians per second. In other words, it's simply a change of units. It helps make some formulas a bit simpler (analogous to why you do calculus with angles in radians -- if they were in degrees, you'd have an annoying constant to carry around with you). That's it -- nothing more fundamental than that.
     
  10. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    This is Great! Thank you so much Count Volta for all your help! You made me understand everything now! ;)
     
  11. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
    1,146
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    Ahhh... That's a great explanation! Now I know the difference.

    So, with angular velocity, would it convert the velocity of rotations (I think...) per second to radians per second also? Instead of frequency like angular velocity? Then I automatically know that anything "angular" will convert something to radians.
     
  12. count_volta

    Active Member

    Feb 4, 2009
    435
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    Well when you see a frequency stated in rad/s and you want to go to Hz, just use f= ω/2π

    where ω is in rad/s and f is in Hz or cycles/s.

    It depends on what you are doing, but honestly in order to use rad/s you need to know imaginary numbers and phasors. Radians are used for calculus. Most other calculations are in Hz.

    What are you trying to use this for anyway Austin?
     
  13. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    Well, I'm not really using it for anything actually. I just wanted to understand it in case I came across something having to do with it. Right now, I'm trying to pack in all this electronic theory and math so I can design my own circuits. Especially math.
     
  14. count_volta

    Active Member

    Feb 4, 2009
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    Many circuits don't involve calculus but since you are into radio you will be interested in filter circuits and oscillators which require imaginary numbers, calculus, and signal processing.

    Its awesome that you are trying to jump ahead so fast but anything with inductors and capacitors will be hard to you without calculus, and all filters have those even if with an op amp.

    You can design logic circuits and transistor circuits that do cool things and all you really need is algebra i.e. (ohms law, kvl, kcl) So stick to those for now.

    P.S. Do you know how to use Cramer's rule to solve the equations that result from KVL and KCL?
     
  15. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    Yeah, that's exactly true. Well I guess you'll just have to do all my math, eh? :D

    Nah, I've really been trying to get ahead in math right now and haven't been doing much electronic theory. I've been doing extra math almost every night. Hopefully I'm getting somewhere. Usually kids don't do calculus in their high school year but I'm planning on it.

    Nope, I've never heard of those rules you mentioned. Perhaps you could teach me? I'll stick with the electronic theory you suggested.
     
  16. count_volta

    Active Member

    Feb 4, 2009
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    You really should learn KVL and KCL. Its two of the 5 basic tools that an EE has. Here are the 5 tools.

    Ohms law, Voltage division, Current division, KVL, KCL.

    The truth is, if you know these 5, you can do literally anything with circuits. I noticed that the more advanced you get, you still see these 5 laws but in different mathematical forms. Only the math is harder, but they are still the same laws.

    I assume you know Ohms law. Here are the other 4 tools. Read about them.

    http://www.allaboutcircuits.com/vol_1/chpt_6/index.html

    The first semester in college is dedicated entirely to these 5 laws. ;)
     
  17. ELECTRONERD

    Thread Starter Senior Member

    May 26, 2009
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    Great!

    I've already used Ohms Law a LOT, so that's covered. I think I'll need to focus more on KVL and KCL.
     
  18. wr8y

    Active Member

    Sep 16, 2008
    232
    1
    You DID do good. But including this really helped, 'least I THINK it did:


    [​IMG]

    A phasor is one way to express a sine wave in terms of imaginary numbers. Phasors have a speed. The speed of that arrow. And the speed is in rad/s which is angular frequency. It shows exactly what I was explaining above.

    VERY good, Volta! :)

    So, I made a series circuit with a resistor and capacitor and inductor and applied a 120 volt ac source to it. I measured the voltage across the resistor with my DVM, then the capacitor, then the inductor and got 160 volts total!

    Will I get a ticket for violating Kirchoff's voltage law? :cool:
     
  19. count_volta

    Active Member

    Feb 4, 2009
    435
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    Welcome to KVL traffic court. ;)

    It sounds like you violated the law of conservation of energy, BUT I don't think you did. Was the 120 Volts you applied to the circuit peak or RMS?

    If it was RMS then you know the peak voltage is actually 120V *sqrt(2) = 169.7V

    Multimeters always show RMS values, so it could makes sense.

    If the 120V was peak then you are getting a ticket from Mr. Kirchoff. ;)

    So which is it?
     
    Last edited: Oct 18, 2009
  20. wr8y

    Active Member

    Sep 16, 2008
    232
    1
    I applied 120 volts rms. And I measured rms voltages across each component. :cool:
     
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