What is best way to stop a rotor at a specific location without abruptly stopping it from an obstruction?

I am reading about many braking methods employed in motors and rotors but none outline the criteria for their general applications. My project involves stopping rotors at specific locations, for example, precisely every circular arc of C/x, where C is the circumference of the circle about which the rotor rotates, and x is a predefined variable of user preference. The carry weight is relatively light (approximately 100 pounds, perhaps less, not including the rotor) and the rotor needs to rotate and stop as quickly as possible. Needless to say, minimal friction is desired, so obstruction is out of question unless the lifespan of the motor/rotor can last for a long time. However since we are moving about a circular arc, obstructions might be necessary since each rotation would have the actual location farther away from expected location. I am using a microcontroller/PLC for the project. Given the situation, what is the best method to go about doing this?

I like idea of inductive brakes applied in the reversal of a different rotor in the project, but the /utmost/ important quality is the reversing rotor and non-reversing rotor stopping precisely at the same location on each rotation.

Any insight on some possibilities or suggested methods is immensely appreciated. Thank you.