Originally Posted by: overlord 
Nothing is wrong with rpm definition in smath, with respect to SI units.
According to SI and National Institute of Standards and Technology (NIST);
rpm is defined as revolution per minute, or rad/s, or (1047197xE-1 Hz).
Overlord, you've misread the NIST conversion table. As listed on page 54 and again on page 67 at
https://physics.nist.gov/cuu/pdf/sp811.pdf:
The table says:
Quote:To convert from:
rpm
Torad/s
Multiply by
1.047198E−01
Note that the NIST table
does not convert rpm to Hz, it converts
rpm to rad/s. I've laid out the calculations to prove it below:
1 rev = 360° = 1 cycle
π rad = 180° ==> 360° = 2π rad
So:
1 rev/s = 360°/s = 2π rad/s = 1 cycle/s = 1 Hz
Therefore:
1 rpm = 1 rev/min * (1 min)/(60 s) = 1/60 rev/s
1/60 rev/s = 1/60 cycle/s = 1/60 Hz
Or, using angular frequency, the NIST value is calculated:
1 rpm = 1/60 rev/s = 2π/60 rad/s = 0.1047 rad/s (matches the NIST table).
The easy way to tell if the calculation is right is by using the relation between
frequency (
f [Hz]) and
angular frequency (
ω [rad/s]):
ω=2πf
f=ω/(2π)
In other words, the angular frequency (in rad/s) is 2 pi times greater than the frequency (in Hz).
SMath erronously reports:
1 rev/s = 6.2832 Hz
1 rad/s = 1 Hz
1 rpm = 0.1047 Hz
1 radpm = 1 Hz
If I tried to use this kind of bad math in my engineering courses, I would have failed every one of my physics & mechanics courses!
The correct conversions should therefore be:1 rev/s = 1 Hz
1 rad/s = 1/(2π) Hz = 0.1592 Hz
1 rpm = 1/60 Hz = 0.01667 Hz
1 radpm = 1/(120π) Hz = 0.002653 Hz
The SI Brochure (9ed) specifically warns against making this kind of error (Page #140 (page 26 of the PDF))
Quote:It is especially important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor of 2π. Ignoring this fact may cause an error of 2π. Note that in some countries, frequency values are conventionally expressed using “cycle/s” or “cps” instead of the SI unit Hz, although "cycle" and "cps" are not units in the SI. Note also that it is common, although not recommended, to use the term frequency for quantities expressed in rad/s. Because of this, it is recommended that quantities called “frequency”, “angular frequency”, and “angular velocity” always be given explicit units of Hz or rad/s and not s−1.
IMPORTANT NOTE: That last line: "... explicit units of Hz or rad/s..." is NOT equating Hz and rad/s (i.e. 1 Hz = 1 rad/s). It is saying that a person needs to SPECIFY whether they are using frequency (Hz) OR angular frequency (rad/s), especially since both of these "frequencies" can be represented with units 1/s, since radians are dimensionless:
1 [rad] = (Circumferential path segment that is the same length as the radius)/(Radius) = [m]/[m] = [unitless]
QED.
Edited by user 30 November 2021 04:40:19(UTC)
| Reason: Not specified
