NapkinCalc

AC Motors

Synchronous speed

ELI5: the rotating field spins at n_sync = 120·f / p, where p is the number of magnetic poles. More poles → a slower field. At 60 Hz: 2 poles → 3600 rpm, 4 → 1800, 6 → 1200.

fline=60f_{line} = 60 line frequency (Hz)
ppoles=4p_{poles} = 4 number of poles
nsync=120⋅flineppolesn_{sync} = \frac{120 \cdot f_{line}}{p_{poles}} = 18001800 synchronous speed (rpm)

Real-world hook: this fixed speed is why AC motors make great clocks and record turntables, and why a ceiling fan with more poles spins lazily while a 2-pole pump motor screams at 3600 rpm.

Try it yourself: the synchronous speed of a 6-pole motor on 60 Hz power? (n = 120·f/p.)

nsyncyou=120⋅606nsync_{you} = \frac{120 \cdot 60}{6} = 12001200 ✏️ Your turn: compute 120 × 60 / 6 (rpm).
✓ pass abs(nsyncyou−120⋅606)<0.000001\mathrm{abs}\left(nsync_{you} - \frac{120 \cdot 60}{6}\right) < 0.000001 green when your synchronous speed is correct