Winkelfrequenz

WinkelFrequenz, in physics often called angular frequency, denotes the rate at which the angle of a rotating or oscillating system changes in time. It is measured in radians per second and is commonly symbolized by ω.

It provides a link to ordinary frequency f, which counts cycles per unit time. The two quantities relate by ω = 2π f, and conversely f = ω/(2π).

In mathematical models, the angle evolves as θ(t) = ω t + φ for uniform rotation or oscillation. For a simple pendulum in the small-angle approximation, θ(t) ≈ θ0 cos(√(g/L) t + φ), where the natural angular frequency is ω = √(g/L). In wave theory, processes are often described with time dependence e^{i ω t}, where ω is the angular frequency.

Applications span physics and engineering. In electrical engineering, ω sets the impedance of inductors and capacitors (Z = R + jωL, 1/(ωC)); in signal processing and Fourier analysis, angular frequency is central. In quantum mechanics, time evolution includes factors e^{-i ω t} with ω = E/ħ.

Terminology varies by language and field. In German, angular frequency is frequently called Kreisfrequenz or Winkelgeschwindigkeit; WinkelFrequenz is a descriptive but less standard term and may be used in some contexts.

Example: if a system has period T, f = 1/T and ω = 2π f. For T = 0.01 s, f = 100 Hz and ω ≈ 628 rad/s.