Frequency Conversion Guide
Frequency measures how many cycles of a periodic event occur per unit time. The SI unit is hertz (Hz), where 1 Hz = 1 cycle per second. Angular frequency ω (rad/s) = 2πf provides the radian-based equivalent.
Key conversions: 1 Hz = 60 RPM, 1 RPM = 1/60 Hz, ω (rad/s) = 2π × f (Hz) = π/30 × N (RPM). A 2-pole motor at 60 Hz runs at 3,600 RPM synchronous speed; at 50 Hz it runs at 3,000 RPM.
Frequency conversion is essential in rotating machinery (motor speed selection), vibration analysis (natural frequency identification), signal processing (sampling rates per Nyquist theorem), power systems (50/60 Hz grid compatibility), and communications (RF band allocation).
Critical pitfalls: confusing Hz with rad/s (a 2π ≈ 6.28x error), forgetting the 2π factor when computing angular velocity from frequency, connecting 50 Hz equipment to 60 Hz power (20% overspeed can destroy bearings and exceed torque ratings), and mixing up frequency with period (T = 1/f).