Calculate angular velocity from frequency or frequency from omega, and find RPM, period, wavelength, and wavenumber from wave speed.
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Omega To Frequency Formula
The following formula is used to convert angular velocity (omega) to frequency:
Variables:
- f is the frequency (Hz)
- (omega) is the angular velocity (rad/s)
To convert omega to frequency, divide the angular velocity by (2pi).
| Angular Velocity (rad/s) | Frequency (Hz) | Rotational Speed (rpm) |
|---|---|---|
| 3.142 | 0.5 | 30 |
| 6.283 | 1 | 60 |
| 12.566 | 2 | 120 |
| 31.416 | 5 | 300 |
| 62.832 | 10 | 600 |
| 94.248 | 15 | 900 |
| 125.664 | 20 | 1200 |
| 157.080 | 25 | 1500 |
| 188.496 | 30 | 1800 |
| 314.159 | 50 | 3000 |
| 376.991 | 60 | 3600 |
| 471.239 | 75 | 4500 |
| 628.319 | 100 | 6000 |
| 753.982 | 120 | 7200 |
| 1256.637 | 200 | 12000 |
| 1884.956 | 300 | 18000 |
| 3141.593 | 500 | 30000 |
| 3769.911 | 600 | 36000 |
| 6283.185 | 1000 | 60000 |
| 12566.371 | 2000 | 120000 |
| Formulas: ฯ = 2ฯf, f = ฯ รท (2ฯ). Also, rpm = 60f = (60 รท 2ฯ) ร ฯ โ 9.5493 ร ฯ. | ||
What is Angular Velocity?
Angular velocity, often represented by the Greek letter omega ((omega)), is a measure of the rate of rotation. It is defined as the angle rotated per unit of time and is usually measured in radians per second (rad/s). In the context of circular motion, angular velocity corresponds to the number of radians that a rotating object covers in one second.
What is Frequency?
Frequency is the number of occurrences of a repeating event per unit of time. In the context of wave motion, it is the number of waves that pass a fixed point in unit time and is measured in hertz (Hz), which is equivalent to one event per second. Frequency is directly related to the angular velocity of a wave.
How to Calculate Frequency from Omega?
The following steps outline how to calculate the frequency from angular velocity:
- First, determine the angular velocity ((omega)) in radians per second.
- Next, select Frequency from omega and use f = omega / (2 pi).
- Finally, calculate the frequency (f) in hertz (Hz).
- After inserting the variable and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variable as an example problem to test your knowledge.
angular velocity ((omega)) = 6.28 rad/s
Using the formula above, the frequency (f) is calculated as:
f = 6.28 / (2 pi) = 0.999493 Hz, approximately 1 Hz.
