Angular Frequency to Frequency Converter
Convert angular frequency (ω) to regular frequency (f) with detailed calculations
Mathematical Relationship
f = ω / (2π)
T = 1 / f = 2π / ω
Where:
- f = frequency in Hertz (Hz)
- ω = angular frequency in radians per second (rad/s)
- T = period in seconds (s)
- π = 3.14159… (pi)
Angular Frequency vs Regular Frequency
Angular Frequency (ω)
Measures how fast an object rotates or oscillates in terms of angle per unit time. Expressed in radians per second (rad/s). One complete rotation equals 2π radians.
Regular Frequency (f)
Measures the number of complete cycles or rotations per unit time. Expressed in Hertz (Hz), where 1 Hz = 1 cycle per second.
Period (T)
The time required for one complete cycle or rotation. Inversely related to frequency: T = 1/f. Measured in seconds.
Applications
Used in physics, engineering, signal processing, mechanical systems, electrical circuits, and wave analysis.
Common Examples
AC Power Systems: 60 Hz electrical frequency = 377 rad/s angular frequency
Engine RPM: 3000 RPM = 314.16 rad/s = 50 Hz
Radio Waves: FM radio at 100 MHz = 628,318,531 rad/s
Pendulum: 1 Hz oscillation = 6.28 rad/s angular frequency