I've run your sound file through some audio processing tools I have to hand.
Looking at the raw data from your recording, there are four strong harmonic pitches when you hear the odd whine. (there are a number of other lesser harmonics that appear, I suspect these are related to the motor sound itself)
A lower rising pitch, two which are relatively stable, and an odd fuzzy mid range pitch sound.
The one thats the odd sound is a single very fuzzy mid range pitch sound, it does not appear anywhere else in the sonogram even at a reduced volume, so I'm not convinced that its something dragging as a result, otherwise I'd expect to see a trace of it in the background.
However fault finding from examing the spectral plot of some audio is imprecise at best.
* Interestingly the weird sound is actually dropping in frequency as the motor rises in frequency (rpm increases), so it could be some form of resonance in the motor however (resonances change or dissapear as RPM frequency changes). Interesting to note that it drops in frequency at the same rate as the motor appears to rise in frequency, not sure if that relevant though.
Given how quickly (and I mean immediatly) the odd sound disspears in the trace after the acceleration is removed from the motor, I'd start by investigating around the motor itself.