# What is Angular frequency: Definition and 127 Discussions

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function.
Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.One revolution is equal to 2π radians, hence

ω
=

2
π

T

=

2
π
f

,

{\displaystyle \omega ={\frac {2\pi }{T}}={2\pi f},}
where:

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).

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1. ### Angular frequency of two hanging bobs of different masses

This is a the representation of the two masses. . Using Newton's second law I got the following equations assuming x1>>x2: m*x1''(t) = -k(x1-x2) m*x2''(t) = 0.5kx1-kx2 I put it in matrix form m| x1''| = | -k k| *|x1| |x2''| =| 0.5k -k| |x2| After some simplification assuming...
2. ### I What Determines the Use of Normal vs Angular Frequency in Quantum Transitions?

This might be silly, but I am a bit confused by the conventions used for transitions in atoms/molecules. Usually these are given in nm and using the formula ##\lambda = c/\nu##, from here we can get the normal frequency ##\nu## and the angular frequency would be given by ##\omega = 2\pi\nu##. In...
3. ### Definition of angular frequency in nuclear structure

Hi all I am a little bit confused about the definition of angular frequency in the context of nuclear rotation, some times its defined in the regular way as $$E=\hbar \omega$$ and other time from the rigid rotor formula $$E=\frac{\hbar^{2}}{2I} J(J+1)$$ where ##I## is the moment of inertia...
4. ### I Question about Waves -- "frequency" versus "angular frequency"

I've been reading many references that said "frequency" and "angular frequency" are two different things. I'm writing a report about damped oscillations experiments (that's a task from a subject in my college). Can someone tell me which one is the resonant frequency (natural frequency)? f or ω...
5. ### Derive angular frequency for mass spring system

tried writing the x position as x = Acos(wt) (ignoring the phase) so that d2x / dt2 = -w2x Substituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass

32. ### Block on Spring SHM, Finding angular frequency

Homework Statement An "ideal" spring with spring constant 0.45 N/m is attached to a block with mass 0.9 kg on one end and a vertical wall on the other. The floor has negligible friction, and you give the block a push and then let go. You observe that the block undergoes simple harmonic motion...
33. ### Angular Frequency of a Piston with Ideal Gas

Homework Statement A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A. Assuming that the pressure and...
34. ### The period, angular frequency of a piecewise function

Homework Statement The function ##f## is defined as follows: \begin{equation*} f(t) = \begin{cases} 1, \text{ when } 2k < t < (2k+1),\\ 0, \text{ when } t = k,\\ 2, \text{ when } (2k-1) < t < 2k, & k \in \mathbb{Z}\\ \end{cases} \end{equation*} What is the period ##T## of the function ##f##...
35. ### Determining angular frequency and amplitude for SHM

Homework Statement A mass "m" is attached to a spring of constant "k" and is observed to have an amplitude "A" speed of "v0" as it passes through the origin. a) What is the angular frequency of the motion in terms of "A" and "v0"? b) Suppose the system is adjusted so that the mass has speed...
36. ### B For oscillations, why do we use angles in waves and oscillat

For example, the term angular frequency, it units is radian per second. For phase, it is also measured in radians or degrees, why is that? Why is the math the same when you use angles to describe oscillations?
37. ### Atomic units of frequency and angular frequency

To calculate the Keldysh parameter, I need to use the optical frequency of a laser in atomic unit. Since for the time: 1 a.u. = 2.42×10-17 s, I would assume that for the frequency: 1 a.u. = 4.13×1016 s-1 which is juste the inverse of the time one. However, I found several sources such as...
38. ### Question regarding angular frequency of a SHM

1. Homework Statement Homework Equations KE=½m(ωa)2 The Attempt at a Solution So first I did this: 2.4x10-3= ½ mω2(1.5x10-2)2 To find mω2=21.33 And substitute that into the KE eqn to find the new amplitude, which is 1.30x10-2 But I only did that because that was the only way I could think...
39. ### Angular frequency of plank attached to spring

Homework Statement A horizontal plank (mass 2kg, length 1m) is pivoted at one end. A spring (k=1000N/m) is attached at the other end. Find the angular frequency for small oscillations. Answer: ω=39rad/s Homework Equations ω = √(mgd + kΔxd/I) I think I would be treating the plank as a long...
40. ### Can the angular wave number(k) or frequency(w) be negative?

1.Homework Statement The wave function for a wave on a taunt string is: y(x,t)=(0.350)(sin(10(π)(t)-3(pi)(x) +(π)/4) where x and y are in meters and t is in seconds. If the linear mass density(μ) of the string is 75.0g/m, (a) what is tha average rate at which energy is transmitted along...
41. ### Finding the velocity of a wave

I am currently studying a course on waves, which has a real ambiguity in the lecture notes. Essentially, I don't know how the professor got from equation \ref{eq:surf_x-y} to equations \ref{eq:vel_u} and \ref{eq:vel_w}. I have tried to work backwards to find a method but am not sure of its...
42. ### Describing elliptic orbit as a parametric function

Hi PF I've beent rying to model the lunar orbit around the sun (cardioide) as a parametric function, but have run into a problem. f(t) = r(t) : x = a cos(ωt) y = b sin(ωt) z = k t The angular frequency ω as well as the distance from to the center varies around the orbit. Is...
43. ### Calculate the angular frequency w using the Euler equations

Homework Statement Consider the Earth as a rigid body with moment of inertia I1, I2 and I3. The Earth is symmetric around the z-axis (I1 = I2). Calculate the angular frequency w using the euler equations Homework EquationsThe Attempt at a Solution
44. ### If the angular frequency of the generator exceeds 1/sqrt(LC)

Homework Statement If the angular frequency of the generator exceeds 1/sqrt(LC), the average energy stored in the inductor is greater than the average energy stored in the capacitor. True of False? Can someone explain to me the derivation of this answer? Homework EquationsThe Attempt at a...
45. ### Dependence of Phase Velocity on Wavelength

Homework Statement This is Problem 7.6 from Electronic Properties of Engineering Materials by Livingston. "Over a wide range of frequencies, the dielectric constant of a polymer is found to be proportional to the inverse square root of frequency. (a) How does the phase velocity of EM-waves...
46. ### Cyclotron Motion Due to Earth's Magnetic Field

1. Say that an electron is heading towards the Earth from the sun with an initial known velocity v. And we know that at Earth's surface the magnetic field is given by B1. This B varies as (R1/R2)^2 where R1 is the radius of the earth. How can I find the location in space, R3/R1, where R3 is the...
47. ### Angular Frequency vs. Angular Velocity

In S.H.M omega denotes?I am really confused where to put pi=3.14 and where to put pi=180 degrees.In one question while solving for omega when Time period is given from formula T=2pi/omega i took pi=3.14 and got right but in other question in similar situation i.e solving for omega when Time...
48. ### Determining angular frequency in an electric field using velocity.

1. There are 2 negatively charged plates opposite each other. In between them, there is a vacuum tube (50 cm long), containing only 1 electron. Assume it is completely isolated. The charge value for the plates is equivalent to 10000 electrons. Initially the single electron is directly in the...
49. ### Simple Harmonic Motion and angular frequency

Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...
50. ### How do I normalize angular frequency for circuit optimization?

Hey all, This question may sound daft, but how do I normalize angular frequency? For a little background: I'm trying to optimize some circuits, and I've managed to write some successful code using the "Design of Ultra Wideband Antenna Matching Networks" book, but the code requires normalized...