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







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

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. questionas

    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. K

    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. patric44

    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. sinus

    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. S

    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
  6. S

    Angular frequency of a mass performing SHM

    When given a small displacement ##x##, the equation for m is: (i) N sin θ = m.a where N is the normal force acting on the ball and θ is angle of the ball with respect to vertical. (ii) N cos θ = m.g So: $$\tan \theta = \frac a g$$ $$\frac x R = \frac{\omega^{2} x}{g} \rightarrow \omega = \sqrt...
  7. C

    Resultant Frequency and Wavelength of Interfering Sound Waves

    ##-w1## and ##-w2## are to shift the cosine graph to the right, and ##\frac{2pi}{\lambda}## is to stretch the graph. But I can't seem to draw an appropriate ##y1+y2## graph (quite irregular) and I struggle to find the resultant frequency and wavelength. Also, why is there angular frequency in a...
  8. H

    Angular Frequency of a two-object system

    I calculate as follow and get a correct answer, but I wonder why the weight of the ladder 6 kg is not included in the mass (m) in the numerator. w= √(mgd/I) = √ { (42*10*1)/ [(1/12)(6)(2^2)+42*1] } = √ (420/44) = 3.06
  9. H

    What is the angular frequency of oscillation?

    ω^2 - (ωo)^2 = 2 (-630) (0.32) = -403.2 This is what I have now and I stuck here.
  10. Hamiltonian

    Real life example of the composition of two SHMs with same angular frequency

    Under the topic of simple harmonic motion comes the composition of two SHM's with the same angular frequency, different phase constants, and amplitudes in the same directions and in perpendicular directions. composition of SHM's in same direction: say a particle undergoes two SHM's described by...
  11. J

    Find ω, the angular frequency of oscillation of the object

    The hint says to use the moment of inertia of the rod, however i have not covered this on my course and I don't know what it is. After googling moment of inertia of a rod I found that it is a quantity expressing a body's tendency to resist angular acceleration, and for a rod I=1/3ML^2. So...
  12. Tony Hau

    Angular frequency of a damped oscillator

    So in my textbook on oscillations, it says that angular frequency can be defined for a damped oscillator. The formula is given by: Angular Frequency = 2π/(2T), where T is the time between adjacent zero x-axis crossings. In this case, the angular frequency has meaning for a given time period...
  13. Negatratoron

    I Uncertainty between position and angular frequency - is this correct?

    Motivation: In my thermodynamics + statistical physics class, we derived the equipartition theorem for ideal gasses using Boltzmann factors, dividing the phase space of a gas particle in position+momentum space into units of size x*p=h based on the quantum nature of the space of states that are...
  14. A

    Angular frequency of the small oscillations of a pendulum

    Homework Statement One silly thing may be I am missing for small oscillations of a pendulum the potential energy is -mglcosθ ,for θ=0 is the point of stable equilibrium (e.g minimum potential energy) .Homework Equations Small oscillations angular frequency ω=√(d2Veffect./mdθ2) about stable...
  15. U

    How Do You Calculate the Natural Angular Frequency of a Dual-Spring System?

    Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...
  16. Y

    Angular frequency of an ammonia molecule

    Hello 1. Homework Statement The dipole moment of an ammonia molecule is ##d_0=5*10^{-30} C.m##.If we apply a static electric field of ##\mathcal { E }=1*10^{6 }V*m^{-1}## to an ammonia molecule initially in the state ## |ψG⟩## where the nitrogen molecule is considered to be on the left,we make...
  17. I

    Angular frequency of a non-sinusoidal pulse

    Hey all, so I’ve been learning nonlinear acoustics and have encountered a conceptual hurdle in my studies. When using a model, such as a form of the classical Burgers equation, to propagate sound waves, you generally have a “characteristic angular frequency” in the equation (often represented by...
  18. S

    Difference between angular velocity and angular frequency

    I have seen so many questions and confusion about the difference between angular velocity/speed and angular frequency. Usually, answers were always given in the context of uniform circular motion (angular speed) and simple harmonic oscillation (angular frequency), but this is what causes the...
  19. B

    The difference between angular frequency and frequency?

    I looked up and read the definitions in several different books, but still don't get it. Is someone willing to explain it to me on a really simple level?
  20. W

    Self-Induced Emf and Angular Frequency

    The context is an ac circuit with only one element - the inductor. My textbook says that the self-induced emf increases with increasing angular frequency, but I'm having trouble seeing this mathematically. If self-induced emf = ε = -L(dI/dt) and L = X/ω, then emf and ω are inversely related...
  21. Wrichik Basu

    What is the need of angular frequency in S.H.M.?

    While studying S.H.M., I found that the term ##\omega## is used quite a lot. The book says that this ##\omega## is the angular frequency. What is this angular frequency? Why do we use ##\omega## rather than ##\nu##, that is, the normal frequency? All equations in S.H.M. are made with ##\omega##...
  22. M

    Understanding DTFT Angular Frequency: Mike's Questions

    Hello everyone. Iam trying to understand the discrete time Fourier transform for a signal processing course but Iam quite confused about the angular frequency.If I have a difference equation given, what values should I choose for my angular frequency if I do not know anything about the sample...
  23. N

    Simple Harmonic Motion: conceptual idea of angular frequency

    One of the conditions to distinguish Simple Harmonic Motion from other harmonic motions is by the relation that a∝x where x is the displacement from the point that acceleration is directed towards But what confuses me is the constant of proportionality introduced to this relation: ω2 ω is...
  24. Pushoam

    Angular frequency of a physical pendulum

    Homework Statement For calculating angular frequency of a physical pendulum, I consider its center of mass motion. The COM motion is a simple pendulum motion. Considering a coordinate system whose origin is the pivot point. Then, the COM is the length of the corresponding simple pendulum. Is...
  25. S

    Can we say Angular Velocity is a 'moment' of tangential velocity?

    If a rigid link pin joint-fixed on ground and is rotating freely about the same point with uniform ang. vel., can we say the vector form of angular vel. (omega) is nothing but moment of the tangential (perpendicular) vel. at the other end?
  26. F

    Calculating angular frequency and velocity after a collision

    Homework Statement The Problem is the following: We have a uniform disk of radius r laying still with its center at the origin. Two bullets, with equal mass m and negligible size are approaching the disk, both with trajectories parallel to the x-axis and at distance h, -h from the y-axis...
  27. ltnghia1304

    The frequency of two parallel springs and one weight system

    Homework Statement I want to find the angular frequency of the system below Homework Equations F = -kx U = 1/2*k*x^2 The Attempt at a Solution But here's the answer: I don't know how come this solution. Any one help me? Thank you so much.
  28. S

    Low Pass: Why did my professor use frequency and not angular frequency?

    Homework Statement We are given a passive RC low pass filter with an input voltage of 5 Vrms at a frequency of 1 kHz. The resistor has a value of 22 kΩ, the capacitor a value of 100 nF. There is a current i across the resistor. (see picture below) We are to calculate the magnitude and phase...
  29. R

    Determine the angular frequency of the system in SHM

    Homework Statement Determine the angular frequency of the system in the image. The cable is ideal but the pulley is not. I will present the same solution but with different coordinate axes. For some reason they arent the same and neither of them are correct. Given data: R is the radius of...
  30. N

    Magnetic Torque on Dipole; Oscillating Magnet question

    Homework Statement A cylindrical bar magnet whose mass is 0.08 kg, diameter is 1 cm, length is 3 cm, and whose magnetic dipole moment is <5, 0, 0> A · m2 is suspended on a low-friction pivot in a region where external coils apply a magnetic field of <1.4,0,0> T You rotate the bar magnet...
  31. T

    Finding the angular frequency of an object

    Homework Statement An object undergoes simple harmonic motion along an x-axis with a period of 0.50s and amplitude of 29mm. Its position is x = 12mm when t = 0s. Determine the value of ω in the equation of motion. Suppose that ω > 0. Homework Equations $$ω = \frac {2π} {T}$$ The Attempt at...
  32. S

    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. P

    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. TheSodesa

    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. Elvis 123456789

    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. C

    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. Ecthe

    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. J

    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. vetgirl1990

    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. Ethan Godden

    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. H Smith 94

    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. T

    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. M

    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. Luke Cohen

    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. K

    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. M

    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. gracy

    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. F

    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. A

    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. A

    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...