What is the relationship between the PWM duty cycle input and the angular displacement and RPM of a DC motor?
If the PWM frequency is high enough in relation to motor inductance, the behavior is the same as a DC voltage proportional to the duty cycle and the supply voltage.
Ideally this results in a torque proportional to the difference between that voltage and the back-EMF. Non-ideally there is some friction and windage loss.
The back-EMF, in turn is proportional to the RPM.