Trying to understand two masses connected by a shaft

[anon6912]

I have the following system I got from a book, which models the dynamics of two masses connected by a shaft.

The system is given below:

And the equations given in the book for this system is below:

The nominal speed is w0.
And the interest here is the deviations from the nominal for mass 1 (Δw1) and mass 2 (Δw2).

I understand all the equations except for the ones below:

How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?

 

[Dr.D]

I can't answer your question, but just judging by the notations involved, I'd guess that you got this from an EE textbook. The generally make a hash of rotor dynamics. By the time everything is expressed in "per unit," nothing makes sense anymore.

 

[haruspex]

How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?

Quite - it makes no sense dimensionally.