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This is consistent with frequency defined as revolutions per second in a mechanical context or cycles per second in an electrical context and lets you write frequency dependent equations without requiring the 2 pi conversion factor.
Angular velocity units math. Angular velocity units such as rad s deg s and rpm can also be used to measure frequency for cyclical processes. The si unit of angular velocity is expressed as radians per second with the radian having a dimensionless value of unity thus the si units of angular velocity are listed as 1 s or s 1. For instance if a wheel rotates sixty times in one minute then it has an angular velocity of 120π radians per minute. Angular velocity is a measure of turning per time unit.
By convention positive angular velocity indicates counter clockwise rotation while negative is clockwise. Angular velocity is usually represented by the symbol omega ω sometimes ω. Angular velocity is represented in units of radians per time or degrees per time usually radians in physics with relatively straightforward conversions allowing the scientist or student to use radians per second or degrees per minute or whatever configuration is needed in a given rotational.
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