Consider a shaft which connects a turbine to a generator. Initially, none of the parts are moving. Now the turbine starts to rotate and the torques act on the shaft from both the turbine and generator side. I'm interested in knowing, what happens to the torques acting on the shaft from both ends and the angular speed of rotation of the shaft, from the start of the turbine until some angular speed $\omega$ is reached.
It makes sense to me that as the turbine starts rotating it applies a torque on the shaft from the turbine side, and because of some net unbalanced torque the speed of the shaft starts to increase. It is my guess that the shaft starts to rotate at some constant angular speed when an equal and opposite torque is developed from the generator side. I do not understand how the generator applies this torque? why the torque from the generator side increases along with the torque from the turbine side?