Hello
Please look at this post
http://en.smath.info/for...ition-file.aspx#post8896

You are right. I'm really confused.
This seems a common confusion as explained in this article
http://en.wikipedia.org/wiki/Radian_per_second
which says right after the table :

I would like to hear other forum member's opinions about this question.
For now, you always can redefine Hz:=2π rad/sec

Thanks Martin for your explanation though I still have to read the reference on your handbook to fully understand this matter.
I've made some tests on the attached sheet, the cells remarked in yellow are thought to be incorrect whereas the cells in green should be expected as correct.

I agree with kilele´s suggestion...

Thanks!!

Eppur si muove..
No, seriously I think I get your point.
Hz and rad/s measure different magnitudes, therefore Hugo's question was posed in the wrong way.

Radians is usually thought of as a unitless ratio and an angle. Really it is not. Physically it is a self-aligning, normalized unit of distance. The one unit meter is a standard unit of distance for all the world and its one and only perfect prototype is sitting in a vault in france. All units of distance referring to meters is calculated against this prototype length by taking a raw measured distance and (theoretically) dividing it by the prototype length (i.e., breaking the raw length into a bunch of distinct meter prototype long segments and a fractional remainder and then counting up all the segments) to yield a distance in meters. Is this ratio of raw length over meter prototype length unitless? No. Rather, the ratio is defined as a unit.

Radians is not a standard length with a perfect prototype like the meter, but it is a unit of distance like the meter. It is a scalable unit of distance. It is used as a measure of length for measures of arc distance where the prototype length is the length of the circle's radius (the circle being the one upon which the arc distance is being measured). This is not a unitless ratio as is taught. It is a distance made by segmenting the arc into sections, each one radius long and a fractional remainder and then counting up all the segments. This unit of length is called a radian. It is physical.

Angle is taught as a ratio called radians. This just confuses the issue. Degrees are truly angles as they are not tied to any length, but are a "linearized" ratio of rise over run (i.e., a linearization of the tangent ratio). Gradians are similar to degrees, but represent the angle as a linear percentage from perfectly parallel alignment to perpendicular. Radians may be treated as an angle and we are taught to see them that way, but they are truly a measure of length and therefore are not unitless as an angle truly is. It just looks that way because of the slick way the radian length was defined.

It seems to me that one factor in the solution to properly representing radians vs hertz is to have a pseudo unit (geometric unit?) called radius as a predefined entity. Assignment of a value with the radius unit would tell smath what radius length (in meters or other) is in force. Similarly, arc length and arc velocity could be defined. These geometric units (circular units?) would allow smath to keep proper track of what's going on and then be used to properly convert between hertz and radians with the 2PI factor properly enforced inside smath. I haven't thought this all the way through, but this is the germ of the idea.

Edited by user 03 April 2013 19:32:23(UTC)  | Reason: Not specified

And about the "linearized tangent ratio". I doubt that I understand you very well, but I don't see degrees (and other proportional angle units) as linearization of ratio of rise over run. They are better defined in terms of dividing whole turn by an integer (360). Linearization of ratio of rise over run is tangent itself.