Do some modern VORs not spin? Today in Ground School we learned about radio navigation. I read here that the rotating part of the VOR rotates at 1,800 RPM (wow! Is it an electric motor that spins it?)

We know that modern Active Electronically Scanned Array radars are able to send signals in different directions without physical moving but instead steering the signal electronically (by selectively delaying some of the signals precisely). 

Do some modern VORs implement a similar technology and use this to rotate the signal 360 degrees instead of physically spinning?
There are no spinning parts in the VOR.

It typically uses 60 antennae in a phased antenna array to steer the beam in a rotating sweep.

The VOR transmits a constant omnidirectional signal.  The phase of the secondary sweeping directional beam is varied in time such that it is out of phase with the constant signal by the same number of degrees from North.  The receiver measures the phase difference between the constant and sweeping signals to determine its bearing from the transmitter.