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From: "Jim Wilkins" <muratlanne@gmail.com>
Newsgroups: rec.crafts.metalworking
Subject: Re: rod-mill project - "mains" electric motor advice
Date: Tue, 22 Apr 2025 07:54:03 -0400
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"Richard Smith"  wrote in message news:m1r01kwsh9.fsf@void.com...

P=power (Watts)
tau = torque (Newton.metres)
omega = rotation-rate (radians/s)
Latter makes total sense - well it does for me :-)  Radian is where a
radius is wrapped around the circumference.  Very often gives vast
simplifications (compared to working in angular Degrees or Revs Per
Minute, etc.).

------------------------------------

I took night school classes to keep up with my day job. The analytic 
geometry teacher gave many practical hints that made working with sines and 
cosines simple, but in Degrees. For me learning advanced math from night 
school teachers who used it as a tool in their day jobs was much easier than 
from those in college who considered it an abstract art form. In night 
school I aced calculus classes I'd barely squeaked through in college. I was 
probably correct to take chemistry which I could pass instead of more 
mathematical electrical engineering. DC isn't bad, AC requires advanced 
calculus.

Phase modulation for digital radio employs similar trigonometry but in 
Radians, expressed as a multiple of pi, 2*pi being a full circle. I 
struggled to quickly mentally convert between 45 degrees and pi/4 etc, also 
between decibels and voltage, when listening to explanations of what an 
engineer wanted me to build or interpreting an instrument display.

https://en.wikipedia.org/wiki/Phase-shift_keying

That and especially the error correction schemes were among the most 
difficult subjects I ever encountered, since I had lost my way while 
studying Laplace Transforms in college. Segway motor drives used similar 
math, based on the "imaginary" square root of -1 defining an orthogonal axis 
for "imaginary" capacitive and inductive current and voltage. Complex 
numbers that initially seemed useless to me are a perfect fit.

https://www.egr.msu.edu/~wierzba/steinmetz.pdf
"His paper on complex numbers revolutionized the analysis of ac circuits, 
though it was said at the time that no one but
Steinmetz understood the method."

https://www.smithsonianmag.com/history/charles-proteus-steinmetz-the-wizard-of-schenectady-51912022/