1)What is linear wrt omega in layman's terms?
2)What do you mean by the change in kinetic energy?
If you mean at a constant rotor velocity in an ideal motor, the change magnetic force would be directly proportional to the change in kinetic energy.
Sorry for late reply...
I need to read this thread a bunch more times...
1) Doesn't, back emf occur as a scalar times the angular velocity of the unloaded motor ?
This force needs to be overcome and requires more torque. To make the forces balance, net force the motor provides is at least equal to the back emf plus force to turn a constant load.
2)I was thinking that if the load is too much for a given motor, we use gears to get more torque and in exchange loose angular velocity, and KE_rot = 1/2mw^2 .
@Dretron, I can't easily go back get the quote sorry, but I liked what you wrote about when the motor and load are at a steady state rpm, then the need for torque is only to overcome the back emf and the friction, which is presumed to be less force than to get it rotating from rest.
I think this whole thread needs to move to physics.stackexchange.com
because we need to see the equations and work out the frames of reference for the forces. It's pretty hard to do that with words. I know that the ideal cases can be analytic but that most of the time the torque equations for real loads are computed numerically.
wbg