Frequency describes the time it takes for the motion of an object to repeat itself. Its units are in hertz, which is defined as one oscillation per second.
A radian is a unit used to indicate the angle an object is at, or how far it has rotated. One radian is 360 degrees divided by 2Pi, and it is dimensionless. Therefore, radians cannot be converted to hertz. However, a radian per second, which is the angular speed or frequency, may be, because it specifies the rate of change of the angular position of the object as it moves.
- Skill level:
Things you need
- Angular Frequency to Frequency Conversion Problem
- Introductory Physics textbook
Obtain a problem where the angular frequency or speed needs to be converted to hertz. The angular frequency is denoted by the Greek letter omega.
Study the conversion formula. One revolution or complete turn is 2PI radians or rad. If the object is moving, then the equation states that a revolution per second is proportional to a radian per second. This is the relationship between angular frequency and the frequency f, and so omega = 2Pi*f, where Pi is approximated at 3.14.
Practice Step 2 by converting 15 radians per second to hertz. The equation is 15 rad/s = 2Pif. Therefore f = (15 rad/s)/2 3.14 rad = 2.4/s = 2.4 Hz.
Use the equation in Step 2 to practice converting hertz to angular frequency. An object rotates five times per second, and so its frequency is 5 hertz. Then omega = 2Pi*5 rev/s = 31.4 radians per second.
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