Question about angular frequency

In summary: 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).
  • #1
Nomad91
4
0
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.
 
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  • #2
but we use degrees when we write the phase differences in the equations
Maybe that is just easier to recognize (45° is easier to imagine than 0.79 if you are not used to the second one). You can use any angular measure everywhere, as long as you use it consistently and transform values given in other measures, if necessary.
 
  • #3
mfb said:
Maybe that is just easier to recognize (45° is easier to imagine than 0.79 if you are not used to the second one). You can use any angular measure everywhere, as long as you use it consistently and transform values given in other measures, if necessary.

Sorry, I might not have been clear with what I was asking. Let me rephrase it:

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
Nomad91 said:
Sorry, I might not have been clear with what I was asking. Let me rephrase it:

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).

You would have to convert the 10 degrees to radians to get a value for that expression. But when you add expressions with the same angular frequency but different phase shifts, superposition applies, so you only need to add the phase angles. You don't need to convert them since they are in the same units already; its only when you want to find the total value of the expression that you have to convert.

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?).
 
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  • #5
DragonPetter said:
You would have to convert the 10 degrees to radians to get a value for that expression. But when you add expressions with the same angular frequency but different phase shifts, superposition applies, so you only need to add the phase angles. You don't need to convert them since they are in the same units already; its only when you want to find the total value of the expression that you have to convert.

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?).

Thanks!
 
  • #6
Nomad91 said:
Thanks!

Yes, but I should clarify that the phase angles don't necessarily just "add", but you can add the individual sine expressions with superposition, and you then have to do some trig if the sine expressions are of different magnitudes. But the point is that in all of the calculations for the final phase, you can remain in units of degrees.
 
  • #7
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.
 

1. What is angular frequency?

Angular frequency is a measure of how quickly an object or system rotates or oscillates per unit of time. It is typically represented by the Greek letter omega (ω) and is measured in radians per second.

2. How is angular frequency related to linear frequency?

Angular frequency and linear frequency are related by the formula ω = 2πf, where ω is the angular frequency and f is the linear frequency. This means that the angular frequency is equal to 2π times the linear frequency.

3. What are some real-world examples of angular frequency?

Angular frequency can be observed in many natural phenomena, such as the rotation of a planet around its axis, the pendulum motion of a grandfather clock, or the oscillation of a guitar string. It is also used in engineering and technology, such as in the rotation of motors or turbines.

4. How is angular frequency different from angular velocity?

Angular frequency and angular velocity are related concepts, but they are not the same. Angular frequency is a measure of how quickly an object rotates or oscillates per unit of time, while angular velocity is a vector quantity that measures the rate of change of angular displacement. In simpler terms, angular frequency is a scalar quantity, while angular velocity is a vector quantity.

5. How can angular frequency be calculated or measured?

Angular frequency can be calculated using the formula ω = 2πf, where f is the linear frequency. It can also be measured using various instruments, such as a tachometer for rotational motion or an accelerometer for oscillatory motion.

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