Angular momentum Definition and 1000 Threads

Homework Statement A particle of mass m moves in a circle of radius R at a constant speed v, as shown below. The motion begins at point Q at time t = 0. Determine the angular momentum of the particle about the axis perpendicular to the page through point P as a function of time...

Imagine a body that is attached to a massless string and then rotated in such a manner that no external forces like gravity acts on the body in tangential direction. The body now has the angular momentum with respect to the axis of rotation Lo = Ro * Vo * m Where Ro = constant...

I got myself here a satellite rotating at a large distance around planet X. Distance from center of planet X = 100, mass of the satellite = 1 gram (really small), mass of planet X = 1.0 kg velocity of my satellite 10 m/sec and in this oddball universe the gravitational constant = 10**4...

If we look at the classical formula for the conservation of angular momentum, L=mvr, we can easily see that, if the radius of a rotating body is shortened, its velocity must increase in order to conserve L, and vice-versa. Again, the classical conception we have of this formula is its...

In Griffiths book, "Introduction to Electrodynamics" example 8.4 he calculates the angular momentum density for a set up that is a version of Feynman disk paradox. His answer for the angular momentum points in the z direction. But if we you assume that the r vector has component in the s...

Here's a little thought experiment that highlights a problem I'm having with angular momentum. Here's my little experimental gizmo, spinning freely and leisurely in space. It has a hub and a pair of robot arms (whose mass we can ignore) holding a pair of masses m each at a distance r from...

I'm working on a problem where I want to write the operator S_z down in terms of some operator(s) in the \vec{J} = \vec{L} + \vec{S} basis so that I can operate S_z on the states \mid \ell, s=1/2, j= \ell\pm1/2, m\rangle but I'm having trouble finding the correct combination of operators...

Consider two concentric circles of radius r1 and r2 as might be drawn on the face of a wall clock. Suppose a uniform rigid heavy rod of length | r2-r1 | is somehow constrained between these two circles so that one end of the rod remains on the inner circle and the other remains on the...

Lets imagine a binary system of two astronauts in space connected to one another via light rope. The rope is taut and they're spinning round and round with their axis of rotation being the the axis perpendicular to the their centre of mass. Now, my question is this. Let's say they each let go...

Hello! I am trying to show that the ADM definition of angular momentum is well-defined and finite. Here is the definition: J^{i} = -\frac{1}{2}lim_{r\rightarrow\infty}\int_{S_{r}}\epsilon_{ijm} x^{j} (k_{mn} - \overline{g}_{mn} tr k) dS_{n} I'm working with an asymptotically flat...

Hi all, I have a question about mass conservation and the way that I should apply it on my problem. Consider a NxN Mass Matrix, (lets assume 10x10 came from 1D 10 node bar element). I am going to modify this matrix so I add some different unknowns to all terms (100 terms) from Physics...

Homework Statement http://session.masteringphysics.com/problemAsset/1070538/5/12.EX46.jpg a)What is the magnitude of he angular momentum of the 200g particle relative to the origin. b) What is the direction of the angular momentum relative to the origin of the 200g particle? Into the page or...

Homework Statement An object of mass 2 kg is held in circular motion by a string of negligible mass. Initially the radius is 1 m and the tangential velocity is 4 m/s. The string is subsequently let out gradually until the radius doubles to 2 m. There are no frictional or resistive forces...

Sorry about the crude drawing but here's the question. If you have a ball in a hollow pipe, which is being rotated around one of it's ends. Why does the ball leave the pipe? I would think that the force the pipe applied to the point of contact would be in the tangent to the circle i.e. not...

I used kg*m/s*m so 1500 metric tons=1500000 kg 85 km/h=23.61 m/s ( 1500000 )*23.61*53=1.877x10^9 kg*m^2/s I feel like this is correct.

Homework Statement When a star like our Sun exhausts its fuel, thermonuclear reactions in its core cease, and it collapses to become a white dwarf. Often the star will blow off its outer layers and lose some mass before it collapses. Suppose a star with the Sun’s mass and radius (the radius of...

Homework Statement We just started matrix representation of operators. For the life of me I can't figure out how to construct any of the matrices. For example, the L+ matrix for l=1 (which gives m=-1,0,1). I plug in the 3 values of m into the L+ equation and get sqrt(2), sqrt(2), and 0. Then I...

Homework Statement A rotating uniform-density disk of radius 0.6 m is mounted in the vertical plane. The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5.8 kg. A lump of clay with mass 0.5 kg falls and sticks to...

This is a question that I remember hearing a few years ago: If the law were changed so that traffic in Great Britain traveled on the righthand side of the road instead of on the left, would the length of the day increase, decrease or be unaltered? I remember the answer was increase...

Homework Statement A small 13.0g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 65.0g and is 120cm in length. The...

I fully expect to be taken out to the intellectual wood shed by any number of candidates (GhWells, DaleSpam come to mind), but I do not understand how you can have relative motion and angular momentum? Angular momentum seems to suggest there is some absolute type of motion, i.e. rotation of...

Homework Statement I am getting confused by the QM selection rules. Photons have an angular momentum of 1. So when a transition of some sort occurs and a photon is emitted, the atom must lose 1 unit of angular momentum. My question is, is a electron transitioning from spin up to spin down...

Hi guys, I have a question which is probably stupid. I am studying angular momentum and I have found almost everywhere that, if we have orbital angular momentum higher than \ell=0 then it brings powers of the momentum of the system like k^\ell. What is the reason of that? Can someone suggest a...

Homework Statement I am just confused about Angular momentum. Homework EquationsKE(rotational)= 1/2Iw^2 Angular momentum= Iw The Attempt at a Solution Why can I do the change in KE rotational to calculate the her final angular velocity in 3 revs? very confused! :( both equations relate to...

The angular momentum of the electromagnetic field is defined as, $$ \vec{L_{em}} = \int \vec{l_{em}} d^3r. $$ To solve this for a rotating sphere I must consider the cases where r < R and r > R. When I did this problem I thought that there would be two solutions, one for both cases; however...

In short: Why are galaxies flat? In more detail: A very large mass M is at rest in vacuum, rotating at point O. Its axis of rotation is the xz-plane with angular momentum \vec{L} directed along the positive y-axis. What forces do the following masses experience? (Units of distance are...

Homework Statement Using the operator identity: \hat{L}^2=\hat{L}_-\hat{L}_+ +\hat{L}_z^2 + \hbar\hat{L}_z show explicitly: \hat{L}^2 = -\hbar^2 \left[ \frac{1}{\sin^2\theta} \frac{\partial^2}{\partial\phi^2} + \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}...

What is the definition of angular momentum that is to be conserved in the Schwarzschild solution of general relativity, expressed in coordinate time? I am trying to put together an expression for gravitational acceleration that is to emulate the Schwarzschild solution. I need to test whether...

Hi there Iive been reading the intro chapter to Peskin and Schroder's 'An intro to QFT' I have a question regarding the conservation of angular momentum during particle collisions/scatterings As an example they talk about e+ e- --> μ+ μ- The take the Centre of Mass (CM) frame...

Homework Statement A uniform beam with mass M = 156 kg and length L = 2.3 m slides broadside down along the ice at a speed of v0 = 9 m/s. A man of mass 88 kg, who is initially at rest grabs one end of the beam as it goes past and hangs on as the beam and man go spinning down the ice. Note...

Homework Statement Wow, the site looks way different from when I was last here. Nice job to whoever did this! Now, to business... My question pertains to part 2a of the HW. I've gotten the wavefunction in terms of the spherical harmonics, but I need help bringing it on home, so to...

Homework Statement A 1.9kg , 20 cm-diameter turntable rotates at 150rpm on frictionless bearings. Two 480g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. what is the objects angular velocity in rpm right after this event? Homework...

L = r x p What's the significance of angular momentum, L, acting along the z axis? Angular momentum is being compared to translational momentum, p = mv, but translational momentum is acting the same direction of the velocity, right? Thanks for any help! edit: this is a nice gif...

Homework Statement For the linear momentum operator ##\hat{\mathbf{p}}## and angular momentum operator ##\hat{\mathbf{L}} ##, prove that ##\begin{eqnarray} [\hat{\mathbf{L}},\hat{\mathbf{p}}^2]&=&0\end{eqnarray}##: [Hint: Write ##\hat{\mathbf{L}}## as the ##x##-component of the angular...

In the image showed in the link below I've illustrated a mechanism in which a small gear rotates about a large gear when the motor is spinning. The large gear is rigid and both of the gears are masless, except for the motor. The small gear has a radius of 25mm and the large gear has a radius of...

Homework Statement Imagine that you toss the drumstick of a turkey to your friend across a table. Approximate the leg as a baton consisting of two equal masses connected by a stiff spring. Let the masses, m and M, each equal 0.1 kg (we’ll modify this assumption later) and connect them with a...

Hi I attempted to solve this question but got a different answer, I don't know what's wrong with my solution. Homework Statement http://prntscr.com/wdmmo Homework Equations The Attempt at a Solution At point P before collision, the angular momentum from the top disc has two...

In the section "Angular momentum in quantum mechanics" of the angular momentum page in wikipedia,one can find the following: But we know that spin is an intrinsic property of a particle,a property that can be used for its identification.So how is it that it is not conserved? I mean,we say...

hi all, these days i m going through Arther Beiser's modern physics book where i read about the total angular momentum in many electron atoms..now i could understand the LS coupling and spin orbit effect how they combine to form total angular momentum but if i m given the magnitude of L=2...

Homework Statement A molecular cloud 0.2 light years across rotates once every 1.4 ×107 years. If it were to collapse to the size of our Sun, how long would it take to rotate once if it conserved angular momentum given by mvr, where m is mass, v is the circular rotation speed and r is the...

Homework Statement a planet of mass m orbits a star. The Velocity at point A = 10^4 m/s the Radius at point A = 10^7, Vb = (10^4)/3, Rb = 3*10^7 Numerically calculate the angular momentum! Homework Equations The main question is how would you calculate the mass? The Attempt at a Solution L =...

Homework Statement A bicycle with 0.8 m diameter tires is coasting on a level road at 5.6 m/s. A small dot has been painted on the rear tire. What is: a) the angular speed of the tire b) the speed of the dot when it is 0.8 m above the road in m/s? c) the speed of the dot when it is 0.4 m...

Greetings, My task is to prove that the angular momentum operator is hermitian. I started out as follows: \vec{L}=\vec{r}\times\vec{p} Where the above quantities are vector operators. Taking the hermitian conjugate yields \vec{L''}=\vec{p''}\times\vec{r''} Here I have used double...

I am sure there must be a better way to do this, but I just used the method I thought would work. Essentially, I just want to find n and put that in p=nh2π, but my method to find n will give me a complex answer, which is clearly not what I am looking for. If someone could either tell me what...

Homework Statement Show that the Hamiltonian H = (p^2/2m)+V commutes with all three components of L, provided that V depends only on r.Homework Equations In previous parts of the problem, I've worked out the following relations: [L_z,x] = i\hbar y, \quad [L_z,y] = -i\hbar x, \quad [L_z, z] =...

This is a very basic question, but what is orbital angular momentum actually? I know it can be quantized as zero, 1, etc. What is it in layman's terms? I tend to understand it in terms like the Earth orbiting the sun. Spin on the other hand is either right or left spin. So what do the different...

Here's the scenario: A uniform stick of length L and mass M lies on a horizontal surface. A point particles of mass m approaches the stick with velocity v on a straight line perpendicular to the stick that intersects with the stick at one end. After the collision, the particle is at rest...

Hi everybody, A seemingly straightforward example from lecture is causing me some confusion. The example was about calculating the angular momentum of a sliding disk (not rolling) about a point on the floor. The result given in lecture says the distance to the point on the floor is unrelated...

I know that L and S commute, but does this mean they do not anticommute? [L,S]=0. \left\{L,S\right\}=0?

Hi guys, basically i have a few questions with regards to Prof Walter Lewin's videos. Firstly, this is the video of him explaining the flywheel concept with energy involved: My question is, why does a flywheel actually spin when the car goes downwards? how does the flywheel actually converts...