- Angular frequency
Classical mechanics History of classical mechanics · Timeline of classical mechanics
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.
- ω is the angular frequency or angular speed (measured in radians per second),
- T is the period (measured in seconds),
- f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν),
- v is the tangential velocity of a point about the axis of rotation (measured in meters per second),
- r is the radius of rotation (measured in meters).
In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. From the perspective of dimensional analysis, the unit Hertz (Hz) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω. This convention helps avoid confusion.
where x is displacement from an equilibrium position.
Using 'ordinary' revolutions-per-second frequency, this equation would be
Oscillations of a spring
Another often encountered expression when dealing with small oscillations or where damping is negligible is:
- k is the spring constant
- m is the mass of the object.
This is referred to as the natural frequency (which can sometimes be denoted as ω0).
References and notes
- ^ a b Cummings, Karen; Halliday, David (Second Reprint: 2007). Understanding physics. New Delhi: John Wiley & Sons Inc., authorized reprint to Wiley - India. pp. 449, 484, 485, 487. ISBN 9788126508822. http://books.google.com/?id=rAfF_X9cE0EC&printsec=copyright. (UP1)
- ^ Holzner, Steven (2006). Physics for Dummies. Hoboken, New Jersey: Wiley Publishing Inc. pp. 201. ISBN 978-0-7645-5433-9. http://books.google.com/?id=FrRNO6t51DMC&pg=PA200&dq=angular+frequency.
- ^ Lerner, Lawrence S. (1996-01-01). Physics for scientists and engineers. p. 145. ISBN 9780867204797. http://books.google.com/books?id=eJhkD0LKtJEC&pg=PA145.
- ^ Serway,, Raymond A.; Jewett, John W. (2006). Principles of physics - 4th Edition. Belmont, CA.: Brooks / Cole - Thomson Learning. pp. 375, 376, 385, 397. ISBN 9780534464790. http://books.google.com/?id=1DZz341Pp50C&pg=PA376&dq=angular+frequency.
- ^ Nahvi, Mahmood; Edminister, Joseph (2003). Schaum's outline of theory and problems of electric circuits. McGraw - Hill Companies (McGraw - Hill Professional). pp. 214, 216. ISBN 0071393072. http://books.google.com/?id=nrxT9Qjguk8C&pg=PA103&dq=angular+frequency. (LC1)
- Olenick ,, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe. New York City: Cambridge University Press. pp. 383–385, 391–395. ISBN 9780521175928. http://books.google.com/?id=xMWwTpn53KsC&pg=RA1-PA383&dq=angular+frequency.
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