Question for you electric folks!
 

Do electric motors use less power when at lower rpm?

I ask this because most electric cars don't have multi gear transmissions. I feel like it would make sense that less rotations would use less power than if it was at 6,000 rpm. I guess it is a pretty straight forward answer but i couldn't find any info on it on the internet or on this forum. Any Info would be greatly appreciated as I am starting to do research on building an electric for my wife. Thanks!!!

The slip angle and RPM is what determines most the amount of power the motor will need.
Generally they will use more power at higher RPM just to over come windage.
You don't decide the operating RPM of the motor. The manufacturer does that.
For example DC motors need to turn at 5,000 to 6,000 rpm to develop enough power to drive with out drawing so many amps they burn up, which is exactly what will happen if you run the motor too slowly.

So for instance, would you very more range of you re geared a Tesla model s to be at lower rpm on the freeway?

Sure unless the motor burns up.

So the engine will burn up at lower rpm so how can the tesla maintain multiple speeds? How will it burn up if the rpm are lower at hwy but it doesn't burn up in stop and go traffic or while maintaining slower speeds?

Teslas are fixed gear. My question is touching on "why didn't tesla put gears in?"

Electric motors have a much broader range of good efficiency than infernal combustion engines, so there is less need for a transmission. Also, transmissions have losses from the gears, extra bearings, and mechanisms to shift the gears.

Less power is required at lower speeds, so less heat is generated. If you asked the same RPM at higher speeds, that's when you'd have issues. Like all engineering, it's a compromise. If you did enough stop go acceleration tests, without letting the motor cool, you'd likely damage it. But again it's been designed for that an likely the electronics will start limiting torque if the motor gets too hot (batteries might be the limiting factor).

By limiting current so that the motor runs in the danger zone at safe current levels.
I believe these vehicles have been idiot proofed to avoid all most all accidental over heating.

Electric motors are similar to ICEs in that they too have efficiency curves where there is a peak efficiency zone in which efficiency drops off on either side- too slow and too fast.