Slip⚠ unverified

Understanding the Parameters

• $n_s$ — the field speed, $120f/p$, fixed by supply frequency and poles.
• $n$ — the rotor's actual speed, always a little below $n_s$ under load.
• $s$ — the normalised gap. Typical full‑load slip is a few percent; $s=1$ at start, $s=0$ would mean no induced current and hence no torque.

Derivation (Approaching a Proof)

An induction rotor carries no external excitation; its current is induced by the relative motion between the rotating stator field (at $n_s$) and the rotor (at $n$). The relevant quantity is that relative speed, $n_s - n$, normalised by the field speed:

$$s = \frac{n_s - n}{n_s} \quad\Longleftrightarrow\quad n = n_s(1 - s).$$

The frequency of the induced rotor currents is $s f$, and the rotor sees an effective resistance $R_2/s$ in the equivalent circuit — which is why torque depends strongly on slip (see Starting Torque, Maximum Torque). If the rotor ever reached $n_s$ ($s=0$), the induced current — and the torque — would vanish, so it always runs slightly slower.

History

Slip is central to the induction motor invented by Tesla and Ferraris (1880s) and analysed by Steinmetz via the equivalent circuit. It is the parameter through which an induction machine self‑adjusts: as load rises, the rotor slows, slip increases, rotor current and torque grow to meet the demand.

Related Concepts: Synchronous Speed, Starting Torque, Maximum Torque, Three-Phase Power

Notes: Registry calculator slip (unverified). Dimensionless; often expressed as a percent. Slip also equals the fraction of air‑gap power dissipated in the rotor resistance.