What is base speed of induction motor?

Induction motor with squirrel cage rotor has two different speeds. The synchronous speed refers to the stator rotating magnetic field, which depends on the number of poles and frequency. The other speed is the rotor's. The rotor speed will be always slower than the stator speed, we call it slip. Without the slip, the squirrel cage induction motor doesn't have torque. Even without load the motor has slip. It increases with the load, according to the current x torque curves you can check it out.

You have to look at the asynchronous (squirrel cage, IM=induction motor) as a beast where "panta rei" (all flows). Manufacturer of the motor has to however put "something" on the motor tag to describe it. He, then puts something like voltage, current (FLA), poles, speed, type, frequency, insulation, sometimes torque etc. But all of this mean? E.g. if the motor is 460V (on the tag) can you run it at 380V? Sure you can but the rest of the variable values of the motor are also going to change. Then what the manufacturer is saying is that you are going to get the FLA at standard toque with standard voltage and then you will get standard slip (let say 3%) that will allow you to run the motor at speed that is standard for the motor. The speed of the motor is rpm=(60*f)/(p/2). Then at f=60Hz and p=4 poles you will get 1800 rpm but this is synchro speed of the motor then you will never achieve if you do not run it via VFD. If you want the "real" speed of the motor you can find it by multiplying the synchro speed by (1-s) where the "s" is the slip, then in our case real rpm=1800(1-0.03)=1746 and this is rated or standard speed (name plate speed or nominal speed). Note however again this is at RATED load. If you increase the load above rated (e.g. you got a rusted conveyor...) the slip will increase to example 5% and you will get 1710 rpm only and FLA will change too. Note then in asynchro motors - panta rei... - it is like a living organism.