A Frequency to Angular Velocity Calculator is a physics tool that converts the frequency of a rotating or oscillating object into its angular velocity. Frequency, measured in Hertz (Hz), tells you how many complete cycles or revolutions an object makes per second. Angular velocity, measured in radians per second (rad/s), describes the rate at which the object rotates through an angle. This conversion is fundamental in many areas of physics and engineering, especially when analyzing circular motion, waves, or alternating current circuits. The calculator uses a simple, direct formula to switch between these two related ways of describing rotational motion, making it a crucial tool for students and professionals.
formula of Frequency To Angular Velocity Calculator
The formula to convert linear frequency to angular velocity is based on the relationship that one full revolution (one cycle) is equivalent to 2π radians.
Angular Velocity (ω) = 2 * π * Frequency (f)
Where:
- ω (Omega): The angular velocity, measured in radians per second (rad/s).
- π (Pi): The mathematical constant, which is approximately equal to 3.14159.
- f: The linear or ordinary frequency, measured in Hertz (Hz), which means cycles per second.
Frequency to Angular Velocity Conversion Table
This table provides a quick reference for the angular velocity equivalents of several common frequencies.
| Frequency (f) in Hz | Calculation | Angular Velocity (ω) in rad/s (approx.) |
| 1 Hz | 2 * π * 1 | 6.28 rad/s |
| 10 Hz | 2 * π * 10 | 62.83 rad/s |
| 50 Hz | 2 * π * 50 | 314.16 rad/s |
| 60 Hz | 2 * π * 60 | 376.99 rad/s |
| 100 Hz | 2 * π * 100 | 628.32 rad/s |
| 1 kHz (1,000 Hz) | 2 * π * 1000 | 6,283.19 rad/s |
Example of Frequency To Angular Velocity Calculator
An engineer is designing a motor that needs to rotate at 3,000 revolutions per minute (RPM). The engineer needs to know the equivalent angular velocity in radians per second for their design calculations.
Step 1: Convert the frequency from RPM to Hz.
The formula requires frequency in Hertz (cycles per second).
Frequency (f) = 3,000 RPM / 60 seconds/minute
Frequency (f) = 50 Hz
Step 2: Apply the formula to find the angular velocity.
Angular Velocity (ω) = 2 * π * f
Angular Velocity (ω) = 100π ≈ 314.16 rad/s
Therefore, a motor rotating at 3,000 RPM has an angular velocity of approximately 314.16 radians per second.
Most Common FAQs
Frequency (f) is a measure of the number of complete cycles or revolutions that occur in one second. Angular velocity (ω) is a measure of the rate of change of angular displacement, or how quickly an object is rotating through an angle. They describe the same rotational motion but use different units. Frequency is more intuitive for counting cycles, while angular velocity is more convenient for use in the mathematical equations of circular motion and wave mechanics.
A radian is the standard unit of angular measure used in mathematics and physics. It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the circle's radius. One full circle (360°) contains 2π radians.
In electrical engineering, the electricity supplied to homes is an alternating current (AC) that oscillates at a specific frequency (typically 50 Hz or 60 Hz). When analyzing AC circuits, engineers find it much more convenient to work with angular velocity (ω) in their equations, as it simplifies the mathematics involved in dealing with sinusoidal waveforms.