Synchronous speed, slip and rotor frequency of an induction motor

Synchronous speed N_s = 120f/P.

Worked answer.

Step 1: Synchronous speed. The stator field rotates at
N_s = 120f / P = (120 × 50) / 4 = 1500 rpm.

Step 2: Slip. Slip is the speed of the rotor relative to the field, as a fraction of synchronous speed:
s = (N_s − N_r) / N_s = (1500 − 1440) / 1500 = 60 / 1500 = 0.04 (4%).

Step 3: Rotor frequency. The rotor conductors are cut by the field at the slip speed, so the induced rotor frequency is
f_r = s × f = 0.04 × 50 = 2 Hz.

Check. The relative speed between the field and the rotor is 60 rpm. For a 4-pole machine, f = PN/120 = (4 × 60)/120 = 2 Hz, which matches Step 3.

Why the rotor can never reach synchronous speed. If the rotor turned at N_s, there would be no relative motion between the rotor conductors and the field, no induced EMF, no rotor current and therefore no torque. The motor would slow down. That is why an induction motor always runs with some slip, typically 2% to 6% at full load for general-purpose machines.

Common mistake. Writing slip as (N_r − N_s)/N_s gives a negative answer. A negative slip actually means the machine is being driven above synchronous speed and is working as an induction generator.

Likely follow-up. "At standstill, what is the rotor frequency?" At starting, s = 1, so f_r = f = 50 Hz. This is also why the rotor reactance is highest at starting and falls as the motor speeds up.