"rad' [radian] is the math unit of trig functions.
So many radians/sec is the angular velocity.
"Hz" refers to signals ... so many periods/s

Good luck converting Mathcad indexed 0 to Smath index 1,
Often => simple ... most of the times a nightmare.

I understand that in rotating machinery, rad/s is needed
for deep maths, establish your own conversion user unit.

What's the point to plug units in calculations ... only in result YES.
Engineering maths existed before computing machinery. So, if you want
to use units, they are "userunits" after calculations are done, just
in same order they appeared in the computation life.
If you compute sin(30) => result is in rad by default of the maths
that approximate sin(x). If you want ° ... paste ° from unit in the
empty place holder of the result.

I read ~ 125 000 Mathsoft Collaboratory. How many engineering
projects were posted with units ? NONE, though the "Units War"
lasted for ever, never ended.
All my Smath projects [Process Control & Instrumentation] are
done in Engineering Unit style, i.e: in results from Engineering formulas.

The only bug with respect to angular velocity units is that quantities of dimension 1/time are shown with Hz as default unit.

See bug report 2395 for details.

Edited by moderator 21 January 2018 14:07:46(UTC)  | Reason: Not specified

You mix angular velocity (angle per time) with frequency (events like full revolutions per time). Your formula gives full revolutions per time, which isn't consistent with the symbol omega (which at least in Germany indicates an angular velocity).
If you want to switch from frequency to angular velocity you shouldn't use the same symbol and yes, you need your factor 2 pi.

My recommendation: always stick to angular velocity, divide your speed by the radius instead by the perimeter length of the wheel and use the unit rev whenever revolutions are to be indicated.

Edited by user 02 January 2018 15:36:23(UTC)  | Reason: Not specified

As for the rad/rev problem: This seems to pop up in the forum constantly. Part of the confusion is created by SMath Studio, see here: here. Of course, SMath can't replace basic knowledge in math and physics but it also must not act in contradiction to such knowledge. I blame SMath for
- using Hz as default unit for whatever is of dimension 1/time. This is plain wrong in many but just a few cases (that is, if the 1 in the numerator stands for cycles or events).
- listing units of angular velocity in the group "frequency" in the units selection dialog

As for getting started with SMath Studio, I'd be ready to improve the tutorial, which you find under Help> Examples. Switch there from local storage to online gallery. Browse to the example "Getting started with SMath Studio". This tutorial is tailored to my pre-configured portable distribution (see my signature).

I am about to generate other Tutorials, one which works with the pristine desktop installation under Win or Linux (no requirement of additional plugins) and one for the online version (SMath Studio in the cloud).

Fellas,
I've put together these calcs that anaise the vibrations in a transmission support fram that I have a

Cardin Shaft FD1 -Trans 180125.sm (862kb) downloaded 22 time(s).

Smath does not have the option to insert math region in text region.
You can still publish nicely, otherwise.
In the attached [2], the "Formated label" is incorrect vs Smath 6179.
The word EXPLAIN should replace the image RGBY square, as title



Cardin Shaft FD1 -Trans 180125[2].sm (884kb) downloaded 22 time(s).