Electric motors come in standard speed ratings determined by the power supply frequency and number of magnetic poles. Understanding these speeds — and how to convert between RPM and rad/s — is fundamental for motor selection and mechanical design.
AC Motor Synchronous Speeds
Synchronous speed = 120 × frequency ÷ number of poles. At 60 Hz (North America):
- 2-pole: 3,600 RPM (377 rad/s)
- 4-pole: 1,800 RPM (188 rad/s) — most common industrial motor
- 6-pole: 1,200 RPM (126 rad/s)
- 8-pole: 900 RPM (94 rad/s)
Induction motors run 2–5% slower than synchronous speed due to "slip." A 4-pole motor at 60 Hz runs at about 1,750 RPM under load.
RPM vs rad/s in Engineering
Power calculations use rad/s: P = τ × ω (power = torque × angular velocity). To convert: ω = RPM × 2π/60.
Example: A 4-pole motor at 1,750 RPM producing 50 N·m torque: ω = 1,750 × 0.1047 = 183.3 rad/s. Power = 50 × 183.3 = 9,165 W ≈ 12.3 hp.
This is why motor nameplates show both RPM and kW — you need both speed and torque to calculate power.
Variable Speed Drives
Variable frequency drives (VFDs) change the supply frequency to control motor speed. A motor rated for 1,800 RPM at 60 Hz runs at 900 RPM at 30 Hz. This is the primary method for energy-efficient flow control in pumps and fans.
Reducing a fan speed by 20% (via VFD) reduces power consumption by about 49% — because fan power varies with the cube of speed. This is why VFDs save enormous energy in HVAC systems.
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