# What is Angular: Definition and 999 Discussions

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant.
In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics. Unlike momentum, angular momentum depends on where the origin is chosen, since the particle's position is measured from it.
Just as for angular velocity, there are two special types of angular momentum of an object: the spin angular momentum is the angular momentum about the object's centre of mass, while the orbital angular momentum is the angular momentum about a chosen center of rotation. The total angular momentum is the sum of the spin and orbital angular momenta. The orbital angular momentum vector of a point particle is always parallel and directly proportional to its orbital angular velocity vector ω, where the constant of proportionality depends on both the mass of the particle and its distance from origin. The spin angular momentum vector of a rigid body is proportional but not always parallel to the spin angular velocity vector Ω, making the constant of proportionality a second-rank tensor rather than a scalar.
Angular momentum is an extensive quantity; i.e. the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a continuous rigid body or a fluid the total angular momentum is the volume integral of angular momentum density (i.e. angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body.
Torque can be defined as the rate of change of angular momentum, analogous to force. The net external torque on any system is always equal to the total torque on the system; in other words, the sum of all internal torques of any system is always 0 (this is the rotational analogue of Newton's Third Law). Therefore, for a closed system (where there is no net external torque), the total torque on the system must be 0, which means that the total angular momentum of the system is constant. The conservation of angular momentum helps explain many observed phenomena, for example the increase in rotational speed of a spinning figure skater as the skater's arms are contracted, the high rotational rates of neutron stars, the Coriolis effect, and the precession of gyroscopes. In general, conservation limits the possible motion of a system but does not uniquely determine it.
In quantum mechanics, angular momentum (like other quantities) is expressed as an operator, and its one-dimensional projections have quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, implying that at any time, only one projection (also called "component") can be measured with definite precision; the other two then remain uncertain. Because of this, the axis of rotation of a quantum particle is undefined. Quantum particles do possess a type of non-orbital angular momentum called "spin", but this angular momentum does not correspond to a spinning motion.

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1. ### B Inertia and flying

As someone who only knows elementary physics (so pardon me for maybe getting some things wrong), I have a question which troubles me and I'm having difficulties in finding an answer to: If a plane takes off at the equator and flies east to west, counter to earth's rotation, how it would be able...
2. ### Inelastic collision of two squares

I know that the speed of the centre of mass is ##v_{cm}=(mv_0+mv_0)/(2m)=v_0##. But I don't know how to proceed from here with the angular speed around the centre of mass of the system. Any help will be appreciated.
3. ### I What Causes the Einstein - de Haas Effect in Iron Rods?

This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod. Is there a classical thought...
4. ### I Angular Momentum problem v2 (mass moving inward or outward)

Hello, simplified the Angular momentum problem that comes up when i try to solve a mass moving inward or outwards and it does not conserver the angular momentum properly. I have tried this is many software by now, or by someone else and we all have found that there is no angular momentum...
5. ### I Angular momentum associated with a current carrying circular wire

How should I calculate the angular momentum carried by a current carrying circular wire? Is it correct to consider the angular momentum of the electrons moving with drift velocity? Like ##L = n m_e v_{drift} r## where ##r## is radius of the loop, and ##n## is total number of electrons moving in...
6. ### Angular Velocity of a Large Pendulum on Earth as seen from the stars

I don't understand the question. how am I supposed to find the magnitudes and directions of the velocity from the figure?
7. ### Solving Orbital Speed with Energy & Angular Momentum Conservation

I've already solved the orbital speed by equating the kinetic and potential energy in the circle orbit case. $$\frac{1}{2}mv^2 = \frac{1}{2}ka^2.$$And so $$v^2 = \frac{k}{m}a^2$$Now when the impulse is added, the particle will obviously change course. If we set our reference point in time just...
8. ### Final Angular Momentum of a Space Station

Li = Lrf +Ltf Iωo = Iωf + mvRsinθ I = MR^2 (MR^2)ωo = (MR^2)ωf + mvRsinθ ωf = (MR^2ωo -mvRsinθ)/MR^2 = 3.99
9. ### I Angular velocity of a rod and what formula to use while solving.

The question is: A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming...
10. ### I Can angular motion exist outside of a gravity field?

I can't find the answer anywhere here's my question. can a centrifuge exist outside a field of gravity. More specifically, in a theoretical void of nothing without stars in view or any point of reference for comparison how could motion like spinning or acceleration exist?
11. ### 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...
12. ### I Maximizing S/N in Angular Power Spectrum Signals

The signal-to-noise ratio for angular power spectrum signal Cl under theoretical noise Nl, where Cl and Nl are functions of multipole l, is given as (S/N)^2= \sum (2l+1) (Cl/Nl)^2To increase the S/N we bin the power spectrum signal, if bin width \Delta l, this in principle decreases Nl by a...
13. ### B How to show that particle spin includes angular momentum?

I understand how a massive, electrically charged spinning ball would have both angular momentum and a magnetic dipole, and i can see how the Stern–Gerlach experiment shows that the magnetic dipole of an electron is quantized. What kind of experiment demonstrates a connection between electron...
14. ### Angular acceleration problem for a pulley used to raise an elevator

I tried to multiply 1/8 g (1.22625) by the radius (1.25 m) and got 1.53 rad/s^2. This is actually the linear acceleration of the elevator. How do I get the angular acceleration of the disk? Thanks!
15. ### Angular momentum <Lx^2> and <Ly^2>

Hi, I have a question. Let us say we have the wave function as with eigen value and base eigen value of: ##!\psi >\:=\:\frac{1}{6}\left(4!1,0,0>\:+\:3!2,1,1>\:-1!2,1,0\:+\:\sqrt{10}!2,1,-1>\right)## I need to find <Ly^2> the solution of the problem according to answers, is demanding that...
16. ### Question involving clockwise angular movement

v=1.00*8=>v=8 rad/s ar=>100*8^2=>ar=64 rad/s^2 at=1.00*4=>at=4 rad/s^2 The only question I have is ar=-64 rad/s^2, not 64 rad/s^2 as I calculated. I believe this is because the wheel is accelerating in a clockwise direction. However this is not indicated by the mathematical equation. How do I...
17. ### Question involving angular acceleration of a spinning wheel

wfinal=98.0 rad/s, dt=3.00s w=(37 revs/3)=>w=(37 revs*(2*pi/1))/3=>w=77.493 a=(98-77.493)/3=>a=6.8357 My answer is exactly half of the correct answer. Where did I go wrong?
18. ### I Angular momentum and rotations

Cohen tannoudji. Vol 1.pg 702"Now, let us consider an infinitesimal rotation ##\mathscr{R}_{\mathbf{e}_z}(\mathrm{~d} \alpha)## about the ##O z## axis. Since the group law is conserved for infinitesimal rotations, the operator ##R_{\mathbf{e}_z}(\mathrm{~d} \alpha)## is necessarily of the form...
19. ### B Spin And Angular Momentum of Large Objects

I read that quantum spin is the measure of the angular momentum of a quantum object. Suppose you have a rotating Thing 1. Quantum objects bounce off of it then collide with Thing 2. Will this transfer angular momentum from Thing 1 to 2, causing it to rotate?
20. ### Puck collision with rod using angular momentum conservation

For this problem, Why for part (a) the solution is, Is the bit circled in red zero because since the putty is released at a very small distance above the rod it velocity is negligible? Also for part (d) the solution is I did a computation of the initial and finial kinetic energies of the...
21. ### Engineering How do I know that the angular acceleration is the same for both wheels?

how do I know that both angular accelerations are the same for both wheels here? should I apply relative motion analysis for the acceleration at A(with ##a_x,A and a_y,A##) and B(with ##a_{x,B} and a_{y,B}##) here, or is just a_A=r*alpha_C and a_B = r*alpha_D enough from which a_A=a_B and thus...
22. ### Average value of components of angular momentum for a wave packet

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.
23. ### Angular deceleration of a circular saw blade

I tried the formula I showed up there but got 0.399 instead of 7.88rad/s^2.
24. ### Change in Angular Velocity While Orbiting With No Torque

The planet is faster when it is closer to the planet because when it is closer to the planet it has less rotational inertia, and rotational momentum is conserved in this system, so less rotational inertia means a greater angular velocity. This explains why it is slower when it is farther away...
25. ### Motion with Time-Dependent Angular Acceleration

I am not understanding how to even start the question
26. ### Calculate orbital angular momentum

The section Kepler’s Second Law here describes the above equation. In this problem, ##\text{r = D, m = M and v = V}## What is the way to go about finding out ##\theta## as shown in Figure 13.21?
27. ### Angular deceleration of the Earth

365 rotations - 365 days 365 days - 31536000 s apart from that I do not know how to continue the question
28. ### Angular deceleration of a washing machine spin cycle

6.0 rev - 1 s 1 rev - 1/6 5.0 rev - (1/6) x 5 = (5/6) s = 0.833 s I do not know how to calculate the angular acceleration

30. ### Angular velocity of an airplane

Speed = 900km/hour tan(α)=900t/10000 α=arctan(900t/10000) Derivative is 900/(10000+81 t^2)
31. ### System of particles, impulse and conservation of angular momentum

So i was able to solve the angular velocity part but i don't know how to find the velocity of centre of mass . For the first part i simply conserved momentum about COM because if i consider the particles as a part of the same system as rod the collision are internal forces . I am mainly...
32. ### I How do I check if the canonical angular momentum is conserved?

Specifically given a purely magnetic hamiltonian with some associated vector potential : $$H = \dfrac{1}{2m} (\vec{p} - q\vec{A})$$ How can I deduce if $$\vec{L} = \vec{r} \times \vec{p}$$ is conserved? ( $$\vec{p} = \dfrac{\partial L}{\partial x'}$$, i.e. the momentum is canonical)
33. ### I Can a Satellite Maintain its Angular Velocity with Continuous Low Thrust?

Suppose two satellites are in a circular heliocentric orbit with radius R and with angular velocity O'. Satellite 2 then undergoes a low continuous thrust. Can Satellite 2 (the one that undergoes the continuous low thrust) maintain the same angular velocity O' about the sun? It seems that...

35. ### What is the smallest value of angular displacement of the raft?

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...
36. ### Solving an Inertial Mystery: Angular Acceleration and Mud

So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall...
37. ### Orbital angular momentum Hamiltonian

I think that the quantum numbers are l=1 and ml=0, so I write the spherical harmonic Y=Squareroot(3/4pi)*cos(theta). I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.
38. ### Angular Velocity from KE, radius, and mass

I tried using the equation w^2 = (4*K)/(mr^2) but I don't think this is right... I got my answer to be 3.2243 and that's not correct
39. ### 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
40. ### I The Inertia Tensor .... Determining Components of Angular Momentum ....

I am reading Tensor Calculus for Physics by Dwight E. Neuenschwander and am having difficulties in following his logic regarding proceeding to derive the components of Angular Momentum and from there the components of the Inertia Tensor ... On page 36 we read the following: In the above text...
41. ### I Changes to a spinning skater's angular velocity

Can we describe what is happening as the skater's angular velocity increases/decreases using F=ma rather than invoking L = constant?
42. ### Getting wrong answer in an (angular) impulse momentum problem

I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α) And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.
43. ### Tong QFT sheet 2, question 6: Normal ordering of the angular momentum operator

My attempt/questions: I use ##T^{0i} = \dot{\phi}\partial^i \phi##, ##\dot{\phi} = \pi##, and antisymmetry of ##Q_i## to get: ##Q_i = 2\epsilon_{ijk}\int d^3x [x^j \partial^k \phi(\vec{x})] \pi(\vec{x})##. I then plug in the expansions for ##\phi(\vec{x})## and ##\pi(\vec{x})## and multiply...
44. ### I Kepler's second law derivation from angular momentum conservation

Many texts state that in an elliptic orbit you can find angular momentum magnitude as $$L = r m v = m r^2 \frac {d \theta} {dt}$$ I wonder if $$v = r \frac {d \theta} {dt}$$ is valid at every point. I understand this approximation in a circumference or radius r but what about an arc...
45. ### I Angular momentum and turning a bicycle

Hello everyone! I've been watching the following Walter Lewin lecture, the part that illustrates my question is part 17:19 of the video Most things have made sense during this lecture, but one persistent question I have is the following: why does the bicycle tilt toward the inside of the...
46. ### I Propagation of Angular Spectrum Code

I'm making a MATLAB code to propagate a gaussian field in the angular spectrum regime (fresnel number >> 1). After Fourier transforming the field, you propagate it: $$U(k_x,k_y,z) = U(k_x,k_y,0)e^{ik_z z}$$ The thing that I am having trouble with is the propagation factor, I have looked at this...
47. ### Angular Velocity in the Rotating systems

Summary: Consider a body which is rotating with constant angular velocity ω about some axis passing through the origin. Assume the origin is fixed, and that we are sitting in a fixed coordinate system ##O_{xyz}## If ##\rho## is a vector of constant magnitude and constant direction in the...
48. ### Noether theorem and angular momenta

(OBS: Don't take the index positions too literal...) Generally it is easy to deal with these type of exercises for discrete system. But since we need to evaluate it for continuous, i am a little confused on how to do it. Goldstein/Nivaldo gives these formulas: I am trying to understand how...
49. ### Angular momentum of a disk about an axis parallel to center of mass axis

I am using the following formula to solve this problem. $$L_a= L_c + \text { (angular momentum of a particle at C of mass M)}$$ Because the point C is at rest relative to point A, so the second term in RHS of above equation is zero. Hence, the angular momentum about A is same as angular...
50. ### Determining $L_{o}$: Finding Angular Momentum of System

I think the the time given doesn't matter since no torque is acting on the system, but not sure. Therefore, all we need is to determine the angular momentum about the axis passing through O and perpendicular to the plane of disk. This will involve finding the moment of inertia of smaller disk...