🌪️ Angular Frequency Calculator
Calculate angular frequency
How to Use This Calculator
Enter Frequency
Input the frequency (f) in hertz (Hz). Frequency represents how many complete cycles occur per second. For example, if a pendulum completes 2 full swings per second, enter 2.
Calculate Angular Frequency
Click the "Calculate" button to compute the angular frequency. The calculator will automatically convert your frequency to angular frequency in radians per second (rad/s) and also display the period (time for one complete cycle).
Review Results
Review the calculated angular frequency displayed in rad/s. The calculator also shows the period, which is the reciprocal of frequency (T = 1/f). Use these values for your physics calculations or engineering applications.
Formula
ω = 2πf
Where:
• ω = Angular frequency (rad/s)
• f = Frequency (Hz)
• π ≈ 3.14159
The period (T) is related by: T = 1/f = 2π/ω
Example 1: Simple Pendulum
A pendulum oscillates with a frequency of 2 Hz. Calculate the angular frequency.
Given:
• Frequency (f) = 2 Hz
Solution:
ω = 2πf
ω = 2π × 2
ω = 4π
ω = 12.566 rad/s
Period: T = 1/f = 1/2 = 0.5 s
Example 2: AC Circuit
An AC circuit operates at 60 Hz (standard household frequency). What is the angular frequency?
Given:
• Frequency (f) = 60 Hz
Solution:
ω = 2πf
ω = 2π × 60
ω = 120π
ω = 377.0 rad/s
Period: T = 1/60 = 0.0167 s (16.7 ms)
Frequently Asked Questions
What is angular frequency?
Angular frequency (ω) is a measure of how fast an object rotates or oscillates, expressed in radians per second. It's related to regular frequency (f) by the formula ω = 2πf. Angular frequency is commonly used in physics to describe oscillatory motion, waves, and rotational systems.
What's the difference between frequency and angular frequency?
Frequency (f) measures how many complete cycles occur per second (Hz), while angular frequency (ω) measures the angular displacement per second (rad/s). Angular frequency is 2π times the frequency, representing the phase change rate in radians. For example, 1 Hz = 2π rad/s ≈ 6.28 rad/s.
Why is angular frequency used instead of regular frequency?
Angular frequency is convenient in physics because it directly relates to the mathematical description of oscillatory motion using sine and cosine functions. When working with phase angles, radians, and trigonometric functions, angular frequency simplifies calculations and makes the math more elegant.
How do I convert RPM to angular frequency?
First convert RPM to Hz: frequency (Hz) = RPM / 60. Then use the formula: ω = 2πf. For example, 1200 RPM = 20 Hz, so ω = 2π × 20 = 40π ≈ 125.66 rad/s.
What is the relationship between angular frequency and period?
The period (T) is the time for one complete cycle, and it's the reciprocal of frequency: T = 1/f. The relationship with angular frequency is: T = 2π/ω. Higher angular frequency means shorter period (faster oscillation).
Where is angular frequency used in real-world applications?
Angular frequency is used extensively in: AC circuit analysis (60 Hz or 50 Hz power systems), oscillating systems (pendulums, springs), wave physics (sound waves, electromagnetic waves), rotating machinery analysis, control systems engineering, and signal processing applications.
About Angular Frequency Calculator
The angular frequency calculator converts frequency to angular frequency using ω = 2πf. Angular frequency is a fundamental concept in physics, particularly in oscillatory motion, wave mechanics, and AC circuit analysis.
This calculator is essential for students studying harmonic motion, engineers designing oscillating systems, and anyone working with periodic phenomena. It provides both the angular frequency in radians per second and the period in seconds, giving you a complete picture of the oscillatory behavior.