Angular velocity
ω = 2 * π * f
Frequency
f = ω / (2 * π)
ω = Angular velocity (rad/s)
f = Frequency (Hz)
π = 3.1415926535
A tool for converting between frequency (Hz) and angular velocity (rad/s), commonly used in electrical engineering, motor design, and physics.
This calculator helps convert between frequency (number of cycles per second) and angular velocity (rate of change of angle), essential for analyzing rotating systems and periodic motion.
Hz → rad/s: ω = 2π × f
rad/s → Hz: f = ω / (2π)
Where:
- f: Frequency in Hertz (Hz)
- ω: Angular velocity in radians per second (rad/s)
- π ≈ 3.14159
| Parameter | Description |
|---|---|
| Frequency | The number of complete cycles per second, unit: Hertz (Hz). For example, AC power at 50 Hz means 50 cycles per second. |
| Angular Velocity | The rate of change of angle over time, unit: radians per second (rad/s). Used to describe rotational speed. |
Household AC frequency = 50 Hz
Then angular velocity:
ω = 2π × 50 ≈ 314.16 rad/s
Motor angular velocity = 188.5 rad/s
Then frequency:
f = 188.5 / (2π) ≈ 30 Hz
Corresponding RPM: 30 × 60 = 1800 RPM
1. Motor and generator design
2. AC power system analysis
3. Mechanical transmission systems
4. Signal processing and Fourier transforms
5. Academic learning and exams
Frequency represents the number of complete cycles per second, measured in Hertz (Hz); angular velocity represents the number of radians traversed per second, measured in rad/s. One complete cycle corresponds to 2π radians, so the conversion relationship is ω = 2π × f. For example, 50 Hz AC power has an angular velocity of 2π × 50 ≈ 314.16 rad/s.
RPM stands for revolutions per minute, while rad/s stands for radians per second. Converting between them requires handling both "minutes to seconds" and "revolutions to radians": ω = (2π / 60) × RPM, and the reverse is RPM = (60 / 2π) × ω. For example, 188.5 rad/s corresponds to approximately 1800 RPM.
AC voltage and current are typically expressed as sinusoidal functions, such as u(t) = Uₘ sin(ωt + φ). In calculus operations (such as differentiation and integration), using ω allows direct differentiation with respect to the angle, making the mathematical expression more concise. Frequency f is more suitable for describing macroscopic characteristics (such as 50 Hz or 60 Hz power grids). Both have their advantages in different scenarios.
It is commonly used for motor and generator design (frequency to rotational speed conversion), AC power system analysis (50/60 Hz angular velocity calculation), mechanical transmission system modeling, angular frequency calculation in signal processing and Fourier transforms, and academic learning and exams in physics and engineering.
Login
