Circular motion In a rotating or orbiting object, there is a relation between distance from the axis, r,
tangential speed, v, and the angular frequency of the rotation. During one period, T, a body in circular motion travels a distance vT. This distance is also equal to the circumference of the path traced out by the body, 2\pi r. Setting these two quantities equal, and recalling the link between period and angular frequency we obtain: \omega = v/r. Circular motion on the unit circle is given by \omega = \frac{2 \pi}{T} = {2 \pi f} , where: •
ω is the angular frequency (SI unit:
radians per second), •
T is the
period (SI unit:
seconds), •
f is the
ordinary frequency (SI unit:
hertz).
Oscillations of a spring 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 \omega = \sqrt{\frac{k}{m}}, where •
k is the
spring constant, •
m is the mass of the object.
ω is referred to as the natural angular frequency (sometimes be denoted as
ω0). As the object oscillates, its acceleration can be calculated by a = -\omega^2 x, where
x is displacement from an equilibrium position. Using standard frequency
f, this equation would be a = -(2 \pi f)^2 x.
LC circuits The resonant angular frequency in a series
LC circuit equals the square root of the
reciprocal of the product of the
capacitance (
C, with SI unit
farad) and the
inductance of the circuit (
L, with SI unit
henry): \omega = \sqrt{\frac{1}{LC}}. 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. == Terminology ==