Electrical Machines  Basic vocational knowledge (Institut für Berufliche Entwicklung, 144 p.) 
5. Asynchronous motors 
5.2. Operating principles 

Relationship between slip and rotor speed
Rotor speed n lags behind the synchronous speed n_{D} and one refers to rotor “slippage”. The relative difference n between both speeds, which expresses the relative movement between the stator rotating field and the rotor, is characterised as slip speed n_{s }in asynchronous machines.
slip speed
n_{s} = n_{rel} = n_{D}  n
The quotient resulting from the slip speed and the rotating field speed has been defined as the slip s
slip
_{}
Example:
An asynchronous motor has been connected to a mains voltage of f_{1} = 50 Hz frequency. How great is the slip s given a rated speed n = 960 rpm?
Solution:
The rotor rated speed of n = 960 rpm at f_{1} = 50 Hz should be aligned to the next synchronous speed n = 1000 rpm.
Thus, the slip can be calculated
_{}
The slip accepts at rated load of motors values ranging between one and eight per cent. Greater slip values usually arise in less powerful motors. If we incorporate the speed limit values of the asynchronous machine in motor operation into the equation, we derive the following values for the slip s:
_{}
_{}
A solution according to the rotor speed yields the following:
sn_{D} = n_{D}  n
n = n_{D}  sn_{D}
n = n_{D} (l  s)
Rotor voltage and rotor frequency
Value and frequency of rotor voltage in idling rotors.
The voltage generated by idling rotors is characterized as rotor idling voltage U_{2.0}
U_{2.0} = C_{1} · F · n_{D}
f_{2.0} = p · n_{D} = f_{1}
The values of the voltage U induced in the rotor and its frequency f_{2} depend on the relative speed n_{s} between the stator rotating field and the rotor, that is to say, the slip. These values are there called slip voltage resp. slip frequency.
Value and frequency of the rotor voltage given any slip speed n_{s}
U_{2} = C_{1 }· F · n_{s}
t_{2} = p · n_{s}
If one establishes the quotient U_{2}/U_{2.0}  resp. f_{2}/f_{1}, one derives
_{}
and thus
U_{2} = s U_{2.0}
_{}
resp. with
w = 2 · p · f
w_{2} = s · w_{1}
The voltage (U_{2}) induced in the rotor and its frequency f_{2} are proportional to the slip.