The slippage JimDawson refers to is not to be confused with mechanical slippage. In electrical terms it's conventionally called "Slip." Slip is unique to induction motors. Inside the motor's stator (the outside part) there are pairs of coils (electromagnets, called "Poles") that alternate polarity every time the incoming AC changes polarity. For 60Hz, the poles change from (North-South) to (South-North) 60 times per second. When you take these poles and arrange them in a circle, you create a rotating magnetic field. It's this rotating outer magnetic field that the magnetic field of the rotor is "chasing" and that's why it spins.
An induction motor has no magnets of it's own in the rotor. The rotor develops a magnetic field when the magnetic lines of flux from the rotating outer magnetic field cut through the rotor. So the stator creates a rotating magnetic field which
induces (hence
induction motor) a magnetic field in the rotor, which in turn opposes the original magnetic field of the stator, which results in the stator "chasing" the rotating magnetic field of the stator.
If we look at the math:
we see that for a 4 pole motor at 60hz, the rotating magnetic field of the stator is spinning at 1800rpm.
So why does the rotor not spin at 1800 rpm also?
Because if it did, then no magnetic lines of flux from the stator would cut through the rotor, no current would be induced in the rotor, and the rotor would have no magnetic field of its own.
In order for there to develop any magnetic field in the rotor, the rotor must spin some RPM less than the stator.
This 1800 RPM is called "Synchronous Speed."
Since the rotor does not spin at synchronous speed, it is classified as an "Asynchronous Motor."
There are such things as synchronous AC motors. They employ permanent magnets in the rotor.
Since Permanent Magnet AC motors do not rely on induction, they are not Induction Motors.
NOTE the difference between synchronous speed and rotor speed is called "Slip."
Slip is variable. An unloaded motor will have very little slip. With no load, your "1725" RPM motor may spin much closer to 1800RPM.
1725RPM is given as the rated RPM because that's the speed it will spin when loaded to it's rated load. if you overload the motor, it will spin even slower than 1725rpm.
1725RPM should never be assumed to be the actual speed of the motor, only a close guess. There is only once instance where the speed will be exactly 1725 RPM, and that is at rated load. If you need to make an induction motor go an exact speed, then you need a VFD with encoder feedback to force it to that speed, and even then, it will always be +/- some amount. That is why induction motors are not typically used in servo applications.