How to Calculate Synchronous Speed and Slip of AC Induction Motors

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Synchronous Speed
When Alternating current (AC) is applied to the stator of a three phase motor, a rotating magnetic field is setup. This rotating magnetic field moves with a speed called synchronous speed. The Synchronous speed can be calculated as follows: 120 times the frequency (F), divided by the number of poles (P):
The synchronous speed decreases as the number of poles increases. The table below shows the synchronous speed associated with various numbers of poles at supply frequencies of 50Hz and 60Hz:


No. of Poles Synchronous Speed @ 50Hz Synchronous Speed @ 60Hz
2 3000 3600
4 1500 1800
6 1000 1200
8 750 900
12 500 600

Rated Speed
The speed of operation of an AC motor when fully loaded at rated voltage is called the rated speed. It is usually given in RPM (Revolutions per minute) on an electric motor nameplate. The rated speed is the speed of the rotor.

Slip
The speed of the rotor magnetic field in an induction motor lags slightly behind the synchronous speed of the changing stator magnetic field. This difference in speed between rotor and stator fields is called slip and is measured in %.The slip  of an AC motor is a key factor and is necessary to produce torque. The greater the load (torque), the greater slip. The formula for calculating motor slip is given by:


Note that rotor speed is the same as the rated speed of the AC motor as given on the motor nameplate