Angular momentum Definition and 1000 Threads

Is the spin of an electron still \hbar/2 in the direction transverse to its momentum? Classically angular momentum transforms non-trivially under boosts, so I was wondering if this applies to quantum mechanics too. A more general question would be: Is angular momentum quantized into units of...

Homework Statement In the calculation of the Zeeman Effect, the most important calculation is \langle L_z + 2S_z \rangle = \langle J_z + S_z\rangle Suppose we want to find the Zeeman Effect for ##(2p)^2##, meaning ##l=1##. In Sakurai's book, My question is, what is ##m##? They say that...

Hey, It's a simple question (hope so). How do you know (analitically) wether angular momentum is conserved based solely on the Lagrangian? Let me elaborate, for example to prove that the linear momentum is conserved you simply look for cyclic coordinates, i.e \frac{\partial L}{\partial...

Hi there! I have tried for hours to calculate the commutator of angular momentum in the differential form, but I cannot get the correct answer. This is my first experience with actually checking if two operators commutes, so there may be some beginner's misunderstandings that causes the...

Homework Statement Part (a): What is momentum operator classically and in quantum? Part (b): Show the particle has 0 angular momentum. Part (c): Determine whether angular momentum is present along: (i)z-axis, (ii) x-axis and find expectation values <Lz> and <Lx>. Part (d): Find the result...

Homework Statement Homework Equations The Attempt at a Solution I have tried inserting the first wavefunction into Lz which gets me 0 for the eigenvalue for the first wavefunction. Is this correct? For the second wavefunction, I inserted it into Lz and this gets me -i*hbar*xAe^-r/a which...

Homework Statement A thin rod of mass M and length L is suspended vertically from a frictionless pivot at its upper end. A mass m of putty traveling horizontally with a speed v strikes the rod at its CM and sticks there. How high does the bottom of the rod swing? Homework Equations The Attempt...

Hey there, I'm having trouble understanding where two of the formulas for angular momentum of an electron in the hydrogen atom tie together. The first relation L = nh/(2∏) which comes from the de Broglie momentum-wavelength relation and the requirement for the electron wavelength to equal an...

We read everywhere that a spinning wheel, a gyroscope, offers resistence to change the plane of rotation. Suppose a gyroscope has angular momentum L = 10 J*s: What force F must we apply, what work W is needed to rotate the spinning plane by 2π? - do we need to know only L or do we need to...

Hi, I was wondering if the stars in a galaxy are orbiting its centre with (for example) 'anticlockwise' angular momentum. Then would you expect the orbits of the galaxy around the centre of a galactic cluster (if it's in one) to be 'clockwise' or 'anticlockwise' or will it not make much...

Homework Statement Two concentric spherical shells carry uniformly distributed charges +Q (at radius a) and -Q (at radius b>a). They are immersed in a uniform magnetic field \vec{B}=B_0\hat{z}. (a) Find the angular momentum of the fields (with respect to the center). (b) Now the...

Really don't like this book, he's crazy ambiguous, I've looked it up myself on the internet and it makes far more sense, but it's our textbook so I have to understand what he's trying to say. We're coupling the angular momentum of an electron's orbital and spin based angular momentum. And he...

So I understand the commutation laws etc, but one thing I can't get my head around is the fact that L^2 commutes with Lx,y,z but L does not. I mean if you found L^2 couldn't you just take the square root of it and hence know the total angular momentum. It seems completely ridiculous that you...

Homework Statement Imagine a particle tracing a counter-clockwise circular path on a flat table with a certain speed. The particle is tied with a massless string of length R to a point P at the center of the circular path. Will the particle rotate about P forever at constant speed in the...

Homework Statement I'll provide picture for clearer understanding. The solid cylinder of mass ##m## and radius ##r## revolves about its geometric axis at an angular rate ##p## rad/s. Simultaneously, the bracket and shaft revolve about x-axis at the rate ##\omega## rad/s. Determine the angular...

Homework Statement Consider a three-dimensional system with wave function ψ. If ψ is in the l = 0 state, we already know that Lzψ=0. Show that Lxψ=0 and Lyψ=0 as well. Homework Equations [Lx,Ly]ψ = i*h-bar*Lzψ The Attempt at a Solution I'm having trouble figuring out where to...

The two mass is similar. I read a line about this and i thought L should be conserved before. What is the background knowledge behind? Thank you.

Homework Statement http://postimg.org/image/qghh7y1vr/ can someone explain why angular momentum is conserved about O? Homework Equations M(P) = d/dt (h(P)) + v(P) x mv(G) h(P) = I(G)w + r(G/P) x mv(G) The Attempt at a Solution edit: nvm, I got it

Homework Statement I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, that's all I need help with. Progress Since the rod is...

3. A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. The collision takes place over a very short time span. During this collision a) the angular momentum of...

Homework Statement Homework Equations L = Iw v = wr The Attempt at a Solution Friction acts on the ball while it is skidding, but goes away when the hoop starts to roll, because the velocity is 0 at a point on the ground. This is when v = wr. When skidding, friction decreases...

I guess this question can apply in all the generality of the 3D Schrodinger eqn. with a central force, the case I'm thinking of however is the the hydrogen atom. When solving the equation, we derive the quantization of the angular momentum, which has me thinking that before we begin quantizing...

I'm having trouble with two review questions: 1) Julie has been hired to help pain the trim of a building, but she is not convinced of the safety of the apparatus. A 5 m plank is suspended horizontally from the top of the building by ropes attached at each end. Julie knows from previous...

Homework Statement A particle of mass m moves in a circle of radius R at a constant speed v. Assume: The motion begins from the point Q, which has coordinates (R, 0). Determine the angular momentum of the particle about point P, which has coordinates (−R, 0) as a function of time. The...

Homework Statement A classical electron in circular motion with radius r and velocity v. How would you find the quantum number l that gives quantized angular momentum close to the angular momentum of the classical electron? Homework Equations p=mvr L=(h/2pi)√[l(l+1)] Can anyone...

Homework Statement Homework Equations The Attempt at a Solution Angular momentum is the only parameter conserved. This is because there are no external torques acting on the system. Energy is not conserved because the collision is inelastic. Finally, linear momentum is not...

Homework Statement A batter swings a 0.9 m long bat. Calculate the angular momentum of the bat relative to its axis of rotation. Assume the bat has a mass of 0.6 kg and rotates at 3 rad / s (Hint: Approximate the bat by a rod, or a long thin cylinder, and find the moment of inertia.) Answer in...

A bicycle is traveling North. The direction of the angular momentum vector of it's front wheel is? I chose "North." The answer is West. Why? thanks

Homework Statement Express the units of angular momentum (a) using only the fundamental units kilogram, meter, and second; (b) in a form involving Newtons; (c) in a form involving joules. The Attempt at a Solution a) L = r x p = r x mv = Iω This can be simplified to kgm2/s...

Hi guys, This is a problem which is bothering me right now. The angular momentum operators (Lx, Ly, Lz), when expressed in spatial rotations consists of derivatives in \theta and \phi. This would suggest that there are, at any point in space, only two linearly independent operators (since there...

Homework Statement A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 42.0kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.400kg , traveling perpendicular to the door at 11.0m/s just before...

I have a question on the algebra involved in bra-ket notation, eigenvalues of \hat{J}_{z}, \hat{J}^{2} and the ladder operators \hat{J}_{\pm} The question has asked me to neglect terms from O(ε^{4}) I am using the following eigenvalue, eigenfunction results, where ljm\rangle is a...

Homework Statement Taken from Binney's Text, pg 143. Homework Equations The Attempt at a Solution From equation (7.36): we see that ##\delta a## is in the direction of the angle rotated, ##\vec{x}## is the position vector, and ##\vec{n}## is the unit normal to the plane of...

Say a uranium-238 nucleus with angular momentum II decays to thorium-234 plus an alpha particle. Will the sum of the angular momenta of the thorium-234 nucleus and the alpha particle equal II? What if a photon was emitted during this process, would Ithorium+Iα+hbar=II? thanks

Homework Statement A ring of mass Mb, radius b, is mounted to a smaller ring of mass Ma, radius a and with the same centre, and they are free to rotate about an axis which points through this centre and is perpendicular to the rings. Dust of mass Ms is distributed uniformly on the inner...

Homework Statement A thin, uniform metal bar, 2.00 m long and weighing 90.0 N, is hanging vertically from the ceiling by a frictionless pivot. Suddenly it is struck 1.50 m below the ceiling by a small 3.00-kg ball, initially traveling horizontally at 10 m/s The ball rebounds in the opposite...

Hi there, I'll come straight out with this, I'm really struggling to understand the conservation of angular momentum. A common example involves someone sitting on a rotating chair holding a rotating wheel. If the wheel is held so that the axis of rotation is vertical then the person...

Homework Statement "A particle of mass m moves in a circle of radius R. Using dimensional argument, determine the particle angular momentum." Homework Equations L = mvr The Attempt at a Solution Because L = mvr, the dimensionality would be ML2T-1. I don't know where to go from here...

We say that spin is an intrinsic angular momentum which does not have anything to do with space. But is it possible that it is the orbital angular momentum of some internal constituent particles (a yet unknown fine structure)?

[SOLVED] What have I done wrong? (torque and angular momentum) Homework Statement A billiardball is hit from rest by the cue at height "h" from the table with a force F in the time interval Δt. The mass M and radius R of the ball is known as well as the moment of inertia which is...

Homework Statement look photo Homework Equations The Attempt at a Solution LOOK THE PHOTO

When we add the angular momenta of two particles, J1 and J2, we get that the resulting total angular momenta is in the range |J1-J2| < J < J1+J2 but according to the Clebsh-Gordan table some coefficients are zero. Does it mean that not all combinations between |J1-J2| and J1+J2 are possible?

Homework Statement How do you find the Angular Momentum, J, if you are given the Angular Velocity, ω of a Kerr Black Hole. Homework Equations J = I*ω ##I = mass*r^2## Event Horizon: ##r_+ = M + (M^2 − (J/mass/c)^2)^{1/2}## Static Limit and the Ergosphere: ##r_0 = M + (M^2 −...

Note: physics conventions, \theta is measured from z-axis We have a vector operator \vec{L} = -i \vec{r} \times \vec{\nabla} = -i\left(\hat{\phi} \frac{\partial}{\partial \theta} - \hat{\theta} \frac{1}{\sin\theta} \frac{\partial}{\partial \phi} \right) And apparently \vec{L}\cdot\vec{L}=...

Homework Statement At one instant, force F: 4.0j N acts on a 0.25 kg object that has position^vector^V : (2.0t - 2.0k) m and velocity vector /: (-5.0i + 5.0k) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b)the torque acting on the object...

Homework Statement Hello, guys. I'm not a native english speaker, so don't mind if I wrote something incorrectly (if you find any error or difficulty in what I wrote just inform me, please). A little ball is hold by a thread of negligible mass which moves round a vertical axis with constant...

Does the first diagram in the Wikipedia page: https://en.wikipedia.org/wiki/Coriolis_effect (that of the ball rolling on a rotating disk) properly illustrate the Coriolis effect or does it simply illustrate the conservation of angular momentum. I understand that these are two different principles.

Homework Statement A sphere on top of a table is attached to a rope which goes through a hole in the table and is attached to a bucket at the other end. The sphere moves in a uniform circular motion with radius R. Water is then added to the bucket and the radius for the sphere's circular...

Why is angular momentum conserved around the bottom left corner in the following set up (see attachment)? The attachment shows a square of side a and mass 4m, and a body of mass m leaping with velocity v0 as shown in the attachment towards the opposite side of the square. I have found the new...

The spin angular momentum of a spin 1/2 particle is given by S = √(s(s+1))ℏ. If s =1/2, S= ((√3)/2)ℏ So, if s=1 is S= √2ℏ ?