Angular momentum Definition and 1000 Threads

Homework Statement The 1.8kg , 5.2-cm-diameter disk is rotating as shown. What is the angular momentum of the disk about the axle? Homework Equations L=Iω=(mr^2)ω The Attempt at a Solution r=.026m m=1.8 kg ω=600rpm*(1minute/60seconds)*(2pi radians/1rotation) = 62.83 rad/sec L=(1.8kg *...

Homework Statement Prove that ## [L_a,L_b] = i \hbar \epsilon_{abc} L_c ## using Einstein summation convention. I think I have achieved the solution but I am not sure of my last steps, since this is one of my first excersises using this convention. Homework Equations [/B] ## (1)...

Homework Statement Before anything, please address this first question: Angular momentum, at least for pure rotation, is defined about the axis of rotation only, correct? [/B] We are given a wooden ring of mass M, radius R. I place a small particle of mass M on its circumference. Now the wooden...

Homework Statement I have a rod of mass m and length l on a table without any kind of friction. I give it an impulse J in any point of distance d from the center of the rod, parallel to the table and perpendicular to the rod. Find the angular velocity ω and the velocity of the center of mass...

My understanding of the angular momentum quantum number is that a different number indicates a different region of space that the electron can occupy. So does the principle quantum number determine the size of that region? For example, is 2s the same as 3s in shape, but the 3s has a greater...

Homework Statement Let e and f be unit vectors. Le = eL is the definition of the component of angular momentum in direction e. Calculate the commutator [Le,Lf ] in terms of e, f and L Homework Equations [A,B]=(AB-BA) The Attempt at a Solution we know that L=r x p, in classical mechanics, and...

Let ##L(\vec{r},\dot{\vec{r}})## be the lagrangian function, usually to get angular momentum conservation one impose ##\delta L=0## and form there we get ##\sum \vec{r}\wedge m\vec{v}=const##. There is however a conceptual problem with this procedure related to the fact that invariance under...

One can represent the mean of the angular momentum operator as a vector. But what is the (mathematical) justification to represent the operator by a vector which has a direction that the operator has not. Yet worse, l(l+1) h2 is the proper value of operator L^2 and from such result it is assumed...

The question: Consider two masses of 0.1 gm each, connected by a rigid rod of length 0.5 cm, rotating about their center of mass with an angular frequency of 800 rad/s. a.) What is the value of l corresponding to this situation? b.) What is the energy difference between adjacent l-values for the...

Homework Statement The puck in the figure shown below has a mass of 0.120 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 80.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the...

Hello there. I am trying to proove in a general way that [Lx2,Lz2]=[Ly2,Lz2]=[Lz2,Lx2] But I am a little bit stuck. I've tried to apply the commutator algebra but I'm not geting very far, and by any means near of a general proof. Any help would be greatly appreciated. Thank you.

Homework Statement Verify by brute force that the three functions cos(θ), sin(θ)eiφ and sin(θ)e−iφ are all eigenfunctions of L2 and Lz. Homework Equations I know that Lz = -iћ(∂/∂φ) I also know that an eigenfunction of an operator if, when the operator acts, it leaves the function unchanged...

Homework Statement Homework Equations PE spring = .5 kx^2 KE rotation = .5 I w^2 The Attempt at a Solution I tried to do a conservation of energy (Note: I = moment of inertia, L = length) 3*.5*k L^2 = .5 I w^2 I =3 M R^2 ---> a^2 = b^2 + c^2 -2bc cos(a) (the reason why I am using law of...

Homework Statement Hi all! I have a very simple problem, which seems to get two different answers depending on whether you use conservation of angular momentum, or energy. Both quantities seem to be conserved: Initially we have a disk of radius a spinning about its center of mass at known...

Hello, I have a few questions about rotation and relative motion. Suppose we transport the proverbial spinning ice skater used to demonstrate conservation of angular momentum to beginning physics students to a universe with only her and two planets. She is now spinning in deep space...

I read the following example in a thread in this forum: A ball (m = 1 Kg , v = p =+22 m/s, Lm = +11, Ke = 242 J) hits the tip of a rod (M = 10Kg , length = 1m, i = 5/6 ). the ball bounces back with v, p = -11.846 m/s , L = -5.923, (Ke = 70.16) the rod translates with v = 3.3846m/s , p = 33.846...

Homework Statement A small ball of mass m suspended from a ceiling at a point O by a thread of length l moves along a horizontal circle with constant angular velocity ##\omega##. Find the magnitude of increment of the vector of the ball's angular momentum relative to point O picked up during...

My book says that for uniform rotational flow, the velocity at any point is proportional to r (v = wr.) In vortex flow, the velocity at any point is proportional to 1/r (angular momentum is conserved.) However, in uniform rotational flow, isn't angular momentum also conserved so the same logic...

Homework Statement A straight line with charge density ##\lambda ## is in the middle of a large isolation cylinder, that can rotate around it's axis (line). Moment of inertia for that cylinder per unit of length is ##l## and electric charge density applied on the cylinder is ##\frac{\lambda...

When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum. However, photons can have arbitrarily high integer quantities of orbital...

I read this article, and I'm confused about several things. http://scitation.aip.org/content/aip/magazine/physicstoday/article/57/5/10.1063/1.1768672 Apparently, light can have orbital angular momentum as well as spin. But I don't see how this is possible, at least in vacuum. Is this in vacuum...

Just a quick question on photon orbital angular momentum. In the equation for photon energy: E2 = p2c2 + m2c4 Is OAM counted in the p2c2 part? Or does the above equation only apply to photons with normal momentum and there is another term for the angular momentum? The normal relation for p...

Homework Statement A rod of mass ##M## and length ##l## is pivoted at the center(##O##) in horizontal position. An object of equal mass(having velocity ##v##) falls vertically on the rod at distance ##\frac{l}{4}## from ##O## and sticks to it. Find the angular velocity of the rod just after...

Homework Statement [/B] An Atwood's machine consists of two masses, mA and mB, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius R0 and moment of inertia I about its axle, determine the acceleration of the masses mA and mB. Homework...

Homework Statement A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is IP. The person holds a spinning bicycle wheel with its axis horizontal. The wheel has a moment of inertia Iw and angular...

Homework Statement if a disk is rotating on another stationary disk and someone standing on the stationary disk stops it what will the final angular velocity of both the disks be? the catch is that both the disks are not co axial. assume ω angular velocity, M mass of big disk.m mass of small...

Homework Statement A uniform disk of radius R=1m rotates counterclockwise with angular velocity ω=2rads/s about a fixed perpendicular axle passing through its center. The rotational inertia of the disk relative to this axis is I=9kg⋅m2. A small ball of mass m=1 is launched with speed v=4m/s in...

Do photons obey the conservation law of angular momentum?

Homework Statement What is the commutation relation between the x and y components of angular momentum L = r X P Homework Equations None. The Attempt at a Solution I do r X p and get the angular momentum componants:L_{x} = (-i \hbar) (y \frac{d}{dz} - z \frac{d}{dy}) L_{y} = (-i \hbar) (z...

Homework Statement An Atwood machine consists of two masses, M and m, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses M and m. Homework Equations...

Consider a particle with velocity "v" has the collision with a rotating disc. How can I analyze the final angular velocity this system? If the mass of particle is very negligible related to the mass of rotating disc, definitely particle will turn back after collision. In this case, how can I...

Homework Statement For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily...

Homework Statement Below is the question: I only have an issue with the last step of the problem. Why wouldn't you factor in the translational AND rotational energy of the ball and then solve for maximum height?

Homework Statement I was reading the textbook section on angular momentum, and I'm having some difficulty grasping angular momentum. Here is a question: In the book, it says that the angular momentum L is equal to vector r cross vector p for a particle. But, for a rigid body, the equation...

Homework Statement The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m2 and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs...

Keplers second law: An imaginary line joining a planet and the sun sweeps out an equal area of space in equal amounts of time. So this shows that the Earth would move faster if it was near the sun. Why? I have read that an abject will move faster if the mass has become smaller. If mass has...

Homework Statement I'm trying to understand an example from my textbook about angular momentum. This is the example given: For the part in red: I don't understand where the cosine theta term came from. When you're calculating the magnitudes of torques, don't you just use FRsin(theta)? If...

Homework Statement The following figure shows an overhead view of a thin rod of mass M=2.0 kg and length L = 2.0 m which can rotate horizontally about a vertical axis through the end A. A particle of mass m = 2.0 kg traveling horizontally with a velocity $$v_i=10 j \space m/s$$ strikes the rod...

Homework Statement Find the eigenvalues of the angular-momentum-squared operator (L2) for hydrogen 2s and 2px orbitals... Homework Equations Ψ2s = A (2-r/a0)e-r/(2a0) Ψ2px = B (r/a0)e-r/(2a0) The Attempt at a Solution If I am not wrong, is the use of L2 in eigenfunction L2Ψ = ħ2 l(l+1) Ψ...

Homework Statement A wooden block of mass M resting on a frictionless, horizontal surface is attached to a rigid rod of length l and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v...

In case it's relevant, the context of my question is finding the allowed states of an atom. For example, given a nitrogen atom with (1s)2(2s)22p3, how do we find the possible states in terms of total orbital angular momentum L, total spin S, and total angular momentum J = L + S. It seems that...

Homework Statement The problem is a Lagrangian problem that solves for a differential equation. I need to write a program to solve the Lagrangian numerically. My professor said you do not need mass for the program, but I'm not sure how. The problem is a vertical cone with a bead rolling around...

Homework Statement We have the initial orbital angular momentum state in the x basis as |l,ml>x=|1,1>x. We are asked to find the column vector in the z-basis that represents the initial orbital angular momentum of the above state. It then says "hint: use an eigenvalue equation". Homework...

For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1. As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the...

Suppose I have particle in three dimensional space whose position space wavefunction in spherical coordinates is ##\psi(r,\theta,\phi)##. The spherical harmonics ##Y_{\ell,m}## are a complete set of functions on the 2-sphere and so any function ##f(\theta,\phi)## can be expanded as...

Suppose a point mass B (m = 2 Kg) is rotating on a massless string (r = 2m) at v = 3m/s. Then KE = 9 J, p = 6 Kg m/s and L = p * r = 12 Nm (left in the sketch) Suppose B collides with A (m=2) the bob of a pendulum on a massless rod r = 1m. Is L conserved? It seems that there is no external...

Homework Statement Mass 2 collides with mass 1 as shown in the image, mass 1 is attached to the stick and it is initially stationary. Consider that the stick is massless and can rotate around the point O. The entire system is on a frictionless table. Which magnitudes are conserved in the system...

Homework Statement Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations Homework Equations l=r×p lx=ypz-zpy ly=zpx-xpz lz=xpy-ypx l+=lx+ily...

Homework Statement I'm supposed to calculate all the states for a system with ##l=1## and ##s=1/2##. Let's say ##\vec{J} = \vec{L} + \vec{S}##. I want to find the Klebsch-Gordon coefficients. I know that said system has 2 towers, one with ##j=3/2## and the other with ##j=1/2##. I've...

Homework Statement At time t, particle with mass m has displacement ##\vec r (t)## relative to origin O. Write a formula for its angular momentum about O and discuss whether this depends on choice of origin. The second part is what I'm more unsure of. Homework EquationsThe Attempt at a...