You are doing the same mistake again and again.
You write:
Originally Posted by: Javier I completely agree:
1 rpm = 1 rev/min = 1/60 rev/sec = (2*pi/60) rad/sec
As soon as you write that, you proclaim that rpm is measure of angular velocity. Please take a note of this fact!
Then, you write:
Originally Posted by: Javier but, that is not how sMath Studio treats it. Because according to sMath Studio: 1 rpm = (2*pi/60) Hz!!! (not rad/sec)
And now it becomes evident that you confuse the two distinct, incomparable physical qualities: frequency and angular velocity. And you do it on the basis that their units are the same [s^-1].
I'll try to explain this.
There are different qualities in physics, that are related, though incomparable. First, let's consider mass and energy. Take the simple relation: e=mc^2. Given that, you may tell that mass of 1 kg relates to (in a sense, is the same as) 89875.5179 TJ. But it's incorrect to write calculations, based on previous "analisys", like that, like this:
x*kg+y*J=?This kind of error is evident, and is easily caught by SMath, if you use its units feature. But if you don't, or if a software doesn't support the units concept, then this kind of problem may happen in some areas.
Let's look at another, more difficult example. In humid air properties, there exist "Mixture specific heat per unit humid air" (Cha) and "Mixture specific heat per unit dry air" (C). Both have units [J/kg/K], but the first is actually [J/kg humid air/K], and the second is [J/kg dry air/K]. If a human does not pay due attention to that, one may write something like
C_1+Cha_2=? and get an erroneous result, where a software won't help catch the logical error. The same applies to specific volumes of gas (specific volume at normal conditions vs specific volume at given condition), etc.
Here we have another case of related, though very different qualities. You CANNOT measure angular velocities in Hz! Never. Hz measures frequencies. And you cannot measure frequencies in rad/s. Although they both have dimensions [T^-1].
A frequency is measure of how often some recurring event happens. Angular velocity measures how fast an angle measured from a point to another point changes WRT some chosen direction. Well,
if the angular velocity is measured for a rotational movement of an object,
then we also may measure its frequency - how often a point of the object will return to a chosen position. So, in this specific case, the two qualities of the rotating object relate to one another. But they are not the same!
rpm in SMath is a measure of angular velocity. Its base unit is 1 rad/s, because in SMath, 1 rad = 1. It's not 1 Hz. It's unfortunate that SMath doesn't keep that "rad" in the unit, but it just follows the SI concept to the letter.
Originally Posted by: Javier now the question is how do we get from there to Hertz?
In my opinion it should be: 1 rpm = 1 rev/min = 1/60 rev/sec = (2*pi/60) rad/sec = 1/60 Hz (not (2*pi/60) Hz)
Here is the answer:
AngVel := n*rpm
Freq := AngVel / 'revIt means, to get frequency of a rotational movement, you take its angular velocity and divide by full rotation angle. That's it.