Angular Frequency Calculator
Calculate ω, f, T, and RPM
Calculate angular frequency, frequency, period, and RPM with detailed step-by-step solutions.
Input Parameters
Cycles per second (Hz)
Key Formulas:
ω = 2πf
f = 1/T
T = 1/f
RPM = f × 60
What is Angular Frequency?
Angular frequency (ω) is the rate of change of angular position, measured in radians per second.
Formula:
ω = 2πf
where f is frequency in Hz
Relationships:
• ω = 2πf = 2π/T
• f = ω/(2π) = 1/T
• T = 2π/ω = 1/f
Features
- Calculate from frequency
- Calculate from period
- Calculate from RPM
- Angular frequency (ω)
- Frequency (f)
- Period (T)
- RPM conversion
- Step-by-step solutions
- Copy results
Units
Angular Frequency (ω):
Radians per second (rad/s)
Frequency (f):
Hertz (Hz) = cycles per second
Period (T):
Seconds (s)
RPM:
Revolutions per minute
Common Values
AC Power (US):
60 Hz = 377 rad/s
AC Power (EU):
50 Hz = 314 rad/s
Earth Rotation:
7.27 × 10⁻⁵ rad/s
Typical Motor:
3000 rpm = 314 rad/s
Use Cases
- Physics and engineering
- Electrical engineering (AC circuits)
- Mechanical engineering (rotating systems)
- Signal processing
- Oscillations and waves
- Motor speed calculations
- Vibration analysis
- Telecommunications
Applications
Real-World Applications:
Electrical:
AC power systems, generators, transformers
Mechanical:
Motors, turbines, rotating machinery
Physics:
Simple harmonic motion, pendulums, springs
Communications:
Radio waves, carrier frequencies, modulation
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