unit problem-rad/s to Hz,1/s

[ptc-5651887]

I'm new to MathCad,And I have some dificulties When I try to calculate natural frequency for a system.I find the unit can not convert rightly from rad/s to Hz,

As you can see in the attached worksheet,when I change the unit of the circular frequency from rad/s to Hz,the value 144.644 will not change.Does the system see them as the same unit?but I know that the circular frequecy is not same as frenquency.

Thanks!

Best Regards!

[Werner_E · Accepted solution]

Frequency and angular frequency sure differ by a factor 2*pi, but the unit for both is 1/seconds.

You may say that frequency is oscillationscycles per seconds while angular frequency is radians per seconds. Both oscillations/cycles and radians are unitless. Radians is a pseudounit and not a conversion factor. So while both are of unit 1/s, this is called Hertz for frequency only, never for angular frequency. So to state clearly that a frequency is angular frequency, you may add the rad and write rad/s, but you mustn't. Think of rad as being 1.

That said it should be clear that there cannot be an automatic conversion between the two by stating different units, as the units for both basically are the same. rad is not a factor *(2pi)!

You have to do it as you already did - divide by 1/(2*pi) if you want to see the natural spring frequency, don't do it if you want to see it as angular frequency. Both will be of units 1/s and be of different value. Its up to you if you like to change the units seen to Hz for the one and to rad/s for the other.

[ptc-5651887]

Thanks for your careful answer!

But I have another question,if I only make some derivation work,deriving B formula from A formula,then get a value, How can know it is a angular frequency or just a frequency value?I'm not a physics professor!

[Werner_E]

Regardless of whether you are a physics professor or not you need to know what you calculate and how. Sometimes a unit check may give you a hint if your calculations are still correct, but you usually can't tell from the units alone what the meaning of the result is.

If you make some calculations and at the end you arrive at an area of 1 m^2, how can you tell whether its the cross section of a pipline, the area of a table cloth or the base area of a building? The magnitude of the result and common sense (but not the units) probably will tell you its not the latter. To distinguish between the first two you will have to know a bit more about your calculations. What is the meaning of the input parameters? What is calculated by a*b or by r^2*pi, etc.?

In case of frequency the unit is number_of_whatever/time. number_of_whatever is just a count, its unitless. So in case of traffic frequency you may say that you observed a frequency of 200 per hour and it would be correct in terms of units. Obviously it doesn't make much sense if you don't reveal what you counted - cars, passengers, cyclists,.... If we assume that a car has an average of 3 passengers, 200 cars per hour would be equivalent to 600 passengers per hour. But giving that (important) additional information what was counted has nothing to do with the units - passengers and cars are unitless.

So by convention we use Hz to denote cycles per second and rad/s to denote radians per second. In terms of units both are 1/s which is what Mathcad would tell you. Its up to you to interprete the results.

In short - you have to know what the meaning of the end result should be and how to arrive at, Mathcad can only be of help here and there.

In case of the formula you use sqrt(k/m) = frequency, it cannot be told by the formula and its units alone that the result should be interpreted as angular frequency. Thats an additional information which has to be added in some other way (I sure know it; a comment in the book; ...). Its a very important information, of course, but it cannot dealt with with regular units (and so people are using kind of pseudounits like rad to add that information).

[PhilipOakley]

Blame it all on SI and their failure to separate the distinction between the mathematician's radian and the normal folk's 'revolution' or 'cycle', in that when they defined the "Hertz" they don't clarify what they they are counting 'per second'.

In the good old days of 'cycles per second' you immediately knew what was being counted/measured. In the brave new world you have to guess where to put the 2.pi

Mathcad does define a magic extra 'unit' of Hza which allows for the 2pi factor, but most folk forget that it's there and even then the readers of worksheets don't grok it.

[After you have got over Hz problem, you may want to think about the loss of dimensional checking between the geometric 3d length and SI's 1d 'LENGTH', and how one would detect the cancellation of two 'Lengths' which are actually at right angles. If you labeled Lx, Ly and Lz you'd know which had come and gone, but in SI you loose fidelity]