InSIunits, angular frequency is normally presented in the unit radian per second. The unit hertz (Hz) is dimensionally equivalent, but by convention it is only used for frequency f, never for angular frequency ω. This convention is used to help avoid the confusion[4] that arises when dealing with quantities such as frequency and angular quantities because the units of measure (such as cycle or radian) are considered to be one and hence may be omitted when expressing quantities in terms of SI units.[5][6]
In a rotating or orbiting object, there is a relation between distance from the axis, , tangential speed, , and the angular frequency of the rotation. During one period, , a body in circular motion travels a distance . This distance is also equal to the circumference of the path traced out by the body, . Setting these two quantities equal, and recalling the link between period and angular frequency we obtain: Circular motion on the unit circle is given by
where:
An object attached to a spring can oscillate. If the spring is assumed to be ideal and massless with no damping, then the motion is simple and harmonic with an angular frequency given by[7]
where
Adding series resistance (for example, due to the resistance of the wire in a coil) does not change the resonant frequency of the series LC circuit. For a parallel tuned circuit, the above equation is often a useful approximation, but the resonant frequency does depend on the losses of parallel elements.
Although angular frequency is often loosely referred to as frequency, it differs from frequency by a factor of 2π, which potentially leads confusion when the distinction is not made clear.
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Cummings, Karen; Halliday, David (2007). Understanding physics. New Delhi: John Wiley & Sons, authorized reprint to Wiley – India. pp. 449, 484, 485, 487. ISBN978-81-265-0882-2.(UP1)
Olenick, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe. New York City: Cambridge University Press. pp. 383–385, 391–395. ISBN978-0-521-71592-8.