Circular motion Angular frequency

in rotating or orbiting object, there relation between distance axis, tangential speed, , angular frequency of rotation:

ω
=
v

/

r
.


{\displaystyle \omega =v/r.}



oscillations of spring

an object attached spring can oscillate. if spring assumed ideal , massless no damping, motion simple , harmonic angular frequency given by

ω
=



k
m



,


{\displaystyle \omega ={\sqrt {\frac {k}{m}}},}

where

k spring constant,
m mass of object.

ω referred natural frequency (which can denoted ω0).

as object oscillates, acceleration can calculated by

a
=
−

ω

2


x
,


{\displaystyle a=-\omega ^{2}x,}

where x displacement equilibrium position.

using ordinary revolutions-per-second frequency, equation be

a
=
−
4

π

2



f

2


x
.


{\displaystyle a=-4\pi ^{2}f^{2}x.}



lc circuits

the resonant angular frequency in series lc circuit equals square root of reciprocal of product of capacitance (c measured in farads) , inductance of circuit (l, si unit henry):

ω
=



1

l
c




.


{\displaystyle \omega ={\sqrt {\frac {1}{lc}}}.}

adding series resistance (for example, due resistance of wire in coil) not change resonate frequency of series lc circuit. parallel tuned circuit, above equation useful approximation, resonate frequency depend on losses of parallel elements.