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Question about angular frequency 
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#1
Apr3012, 06:21 PM

P: 4

Hey!
I've been studying AC circuit theory for a while now and there's always been something that's been bothering me. When using the complex impedance method to determine phase differences between current and voltage (and vice versa) we calculate the angular frequency in radians/seconds (omega = 2*pi*f) but we use degrees when we write the phase differences in the equations. The problem is that I'd assume that we'd have to use radians since the angular frequency is measured (in this case) in radians/second but apparently that's not the case? Could anyone explain this to me? Thanks. 


#2
May112, 09:27 AM

Mentor
P: 11,589




#3
May112, 11:48 AM

P: 4

Why is it possible to use degrees when you specify phase difference when using radians/second for the angular frequency? For example: 5*sin(ωt  10°) Where ω = 2*∏*f < (obviously measured in radians/second). 


#4
May112, 12:46 PM

P: 834

Question about angular frequency
Like mfb said, the phase is usually kept in degrees so that it is more easily read and for most people it is more intuitive to work in units of degrees than radians (when you say two things are perpendicular, is it more natural and convenient to say they are 90 degrees different in orientation than to say they are 1.571 radians different in orientation?). 


#5
May112, 12:56 PM

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#6
May112, 01:07 PM

P: 834




#7
May112, 05:41 PM

Sci Advisor
PF Gold
P: 11,919

The reason why Radians are used in formulae containing trigonometric functions is that, when you differentiate the function with ω (angular frequency in radians per second) in it, you keep your ω's.* When you use f (cycles per second) or degrees, you keep getting spurious and annoying 2π's all over the place.
We are more familiar with degree measurement so we often present results in degrees (except when the result is a neat and familiar multiple or fraction of π). *When you first learn to differentiate trig functions this is pointed out to you (or should have been!) and you may be given exercises to show what odd results you can get when not doing the right thing. 


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