Angular momentum Definition and 1000 Threads

Hello, I believe this to be a rather simple problem but I am not quite sure if my thinking is correct. We have a particle in a j=1 state of angular momentum J. I am first asked to find some eigenvectors of the matrix J(y): J_{y}=\frac{\hbar}{\sqrt{2}i}\begin{pmatrix} 0 & -1 & 0\\ 1 & 0...

I got a homework problem the other day, and it was a conservation of angular momentum problem. Basically a bullet hits a rod, and a rod starts to spin. I needed to find how fast the rod was rotating. I didn't get the answer right, but I was looking up the answers, and it says that to convert...

Homework Statement We have a system of 2 indistinguishable spin-1 bosons. We shall adopt the center of mass frame. Let S = total spin L = relative orbital angular momentum J = L+S = total angular momentum Prove that J = 2m where m is an integer. If given that J=1, what are the permissible...

Energy, Angular Momentum, Torque, solid ball rolling down loop track? help!? A solid brass ball of mass .280g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 14.0 cm, and the ball has radius r<<R. (a) What is...

Hollow sphere, angular momentum, torque problem? help?? a hollow sphere or radius 0.15m with rotational inertia = 0.040 kg m^2 about a line through its center of mass, rolls without slipping up a surface inclined 30 degree to the horizontal. at a certain initial position,the sphere's total...

Homework Statement Consider a system that is initially in the state: \psi\left(\theta,\phi\right)=\frac{1}{\sqrt{5}}Y_{1,-1}\left(\theta,\phi\right) + \frac{\sqrt{3}}{5}Y_{1,0}\left(\theta,\phi\right)+\frac{1}{\sqrt{5}}Y_{1,1}\left(\theta,\phi\right) Part 1: Find <\psi|L_{+}|\psi> Part 2...

Two astronauts, each having a mass M are connected by a length of rope of length d have a negligible mass. They are isolated in space, orbiting their center of mass at an angular speed of ω0. By pulling on the rope, one of the astronauts shortens the total distance between them to 0.668d...

Homework Statement A rigid, uniform bar with mass m and length b rotates about the axis passing through the midpoint of the bar perpendicular to the bar. The linear speed of the end points of the bar is v . What is the magnitude of the angular momentum of the bar? Homework Equations...

Regarding the polarization correlation studies generated using parametric down conversion. All the studies appear to be done correlating the polarization of linearly polarized photons. Has any experiment been done showing the same effect with circularly polarized light? 1) If this...

Homework Statement A 1.4 kg object at x = 2.00 m, y = 3.10 m moves at 4.9 m/s at an angle 45° north of east. Calculate the magnitude of the object's angular momentum about the origin. Answer is 5.3 kg m^2 /s Homework Equations These were the only three I could think of: L=Iω L=mvr ω=v/r The...

Homework Statement A billiard ball strikes an identical billiard ball initially at rest and is deflected 45 degrees from its original position. Show that if the collision is elastic, the other ball must move at 90 degrees to the first and with the same speed.Homework Equations Momentum: mv =...

What is the significance of the ladder operators eigenvalues as they act on the different magnetic quantum numbers, ml and ms to raise or lower their values? How do their eigenvalues relate to the actual magnetic transitions from one state to the next?

Homework Statement A solid cylinder merry-go-round of mass 250kg and radius of 1.9m spinning at 1 revolution every 5 seconds has a 40kg child sitting at 1.1m from the axis. A 50kg child, running tangentially at 3m/s, jumps on the merry go round at the outer edge. What is the new rotation rate...

A small 0.531-kg object moves on a frictionless horizontal table in a circular path of radius 0.85 m. The angular speed is 6.30 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins...

Homework Statement Two equal, parallel and opposite forces at at both sides of a horizontal disk that lies on a smooth table, according to the picture. The mass is m and the moment of inertia is: kmR2 Angular momentum round the center point A: 2FR=kmR^2 \cdot \alpha. Angular momentum round...

In classical mechanics, p = mv L = Iω These correspond to linear and angular momentum, respectively. They're both called momentum, but...they don't have the same units. Why is that?? How can we call them both momentum when they don't seem to represent the same physical quality? Can we set...

In relativistic limit the spin and the angular momentum are not of conservation because of spin-orbit interaction.Then the symmetry SU(2) is broken because vector spin does not commute with the interaction Hamintonian.The SO(3) symmetry is also broken for the same reason.So I do not understand...

Homework Statement The professor very generally created a very simple conceptual problem as a basis for harder ones, but I don't understand how to answer it. A piece of clay, with mass (m) and speed (v) collides with a motionless stick of length L (with uniform mass density and total...

Can someone please explain why angular momentum involves a cross product? Why is it r x p and not r . P Why a cross product and not a dot product?

If I had two cylinders of equal weight and size, but cylinder one had the weight distributed around an outer radius and cylinder two had it distributed around an inner one, would it change their angular momentum going down an incline? Would they be equal, or would cylinder two have greater...

HI,i am aiming to show that 1/(2)^1/2(|spin up>|spin down> + |spin down>|spin up>) is an eigenvalue to the total angular momentum operator in a two-electron system. I know that i should end up with getting the eigenvalues of the separate spins; L1|spin up> and L2|spin down> and so...

If the incident radiation is linearly polarized can the scattered radiation be circularly or elliptically polarized? If the scatter is a lossless dielectric the scattered radiation is not elliptically polarized. How about if the scatter is conducting? if the scattered radiation is elliptically...

In Newton's problem,and other central force problems in Classical Mechanics, you can get with decreasing the center of mass movement to the lagrangian: L=1/2m(r' ^2+r^2 \varphi'^2)-V(r) because \varphi is cyclic, you can write: \frac{d}{dt}(mr^2 \varphi')=0 or, defining the angular...

Homework Statement about what point and about what kind of axis can we conserve angular momentum?can we conserve it about a point moving in circular motion? Homework Equations The Attempt at a Solution its just a understanding based question to apply to problems

I have to find the expectation value of the z component of the angular momentum for a particle on a ring and the expectation value of the z component of the angular momentum squared for a particle on a ring. The wavefunction is e^((± imx)) I've determined that the expectation value for the...

Homework Statement a ring of mass M and radius r lies on its side on a frictionless table.it is pivoted to table at its rim.a bug of mass m walks around the ring with speed v,starting at the pivot.what is the rotational velocity of the ring when the bug is a) halfway around b)back at the pivot...

Homework Statement A cockroach with mass m rides on a disk of mass 6.00m and radius R .The disk rotates like a merry go round around its central axis at angular speed ω_i=1.50rad/s.The cockroach is initially at radius r=.800R,but when it crawls out to the rim of the disk .Treat the cockroach...

If ψ is normalize-able and a function of nx, ny, nz, is the maximum energy degeneracy 6? I.E. There can be degeneracy at the same Energy with each state taking a different value of n, yet adding up to some (nx^2+ny^2+nz^2)=Same E, due to the linearity of the operators involved. I guess the...

Why does the magnitude of angular momentum remain constant in gyroscopes?

This isn't really a homework question, it came along in my studying of the chapter, but it is a homework "type" question so I assumed this would be the best place to post this. I am trying to show that [L_x,L_y]=y[p_z,z]p_x+x[z,p_z]p_y=i \hbar L_z This is all the work the book showed. So I...

Confusion over derivation of angular momentum equation Hello, I'm a little confused over the relation between torque and angular momentum. When L=r×mv \frac{dL}{dt}=r×m\frac{dv}{dt}+mv×\frac{dr}{dt} According to Wikipedia, v=\frac{dr}{dt} mv×\frac{dr}{dt}=mv×v=0 So...

Homework Statement t seems to me all momentum is angular momentum. An ice skater pulling in her arms will rotate faster, and obversely, extending her arms will slow her rotation. If her arms are extended to the radius of the planet, her rate of spin will slow to unnoticeable (to us)...

Imagine a semi-classical birdcage of radius R with N regularly spaced bars individually separated by a spacing a. Now imagine there is a linear light source centered along the cylinder's axis z. Use the dual wave/particle nature of light to show that angular momentum is quantized in the...

http://physicsworld.com/cws/article/news/2011/jul/25/was-the-universe-born-spinning http://arxiv.org/ftp/arxiv/papers/1111/1111.3873.pdf Is there any particular reason why the universe cannot have a net angular momentum? If it did indeed have a net angular momentum are there any...

Homework Statement You and your best friend are at sea on your ship. Your ship is designed to withstand seas during 120 knot winds. You measure the winds outside your ship at 30 knots. From satellite images and Global Positioning System (GPS) data, you pinpoint your position at 60...

Homework Statement So I'm told I can't do it this way but I was wondering if anyone could clarify as to why? We're given |J=\frac{1}{2},M = \frac{1}{2}\!> where j_1 = 1 \, and \, j_2 = \frac{1}{2} Homework Equations The Attempt at a Solution So this can be composed as a linear...

Homework Statement from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) Homework Equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 The Attempt at...

Say we have two particles of mass m which repel each other, V = V(seperation). Let these particles be constrained to move on a circle of radius r. The particles want to stay at opposite sides of the circle because they repel each other. We want to treat this as a quantum problem so the particles...

A horizontal plane supports a stationary cylinder of radius R and a disc A attached to cylinder by a thread of length l , initial velocity given to to disc is v0 .how long will it move until it strikes the cylinder . (no friction) I guess this question is somewhat like tetherball , though i...

I'm reading about the derivation of the lande' g-factor which comes about when one considers an electron moving about a nucleus which is put in an external magnetic field. This gives rise to a perturbative hamiltonian H = - (\vec \mu_s + \vec \mu_s) \cdot \vec B_{ext} = \frac{e}{2m}...

Homework Statement For the third electron of Lithium atom moving in its permissible orbit, the values of angular momentum and the energy are? Homework Equations E= -2π2e4mZ2/n2h2 Third electron is in the second orbit The Attempt at a Solution The value for energy should be...

Homework Statement When a block is dropped to a disc that is rotating with a constant angular velocity about its centre, at the end, we know that both of them will rotate with the same new angular velocity which is slower than the previous one. Question: What is the force that makes the...

Hi everyone! Which is the formula and the proof of the projection of the angular momentum of a rigid body along the rotation axis? I searched on the web and on my mechanics book but cannot find anything... does somebody know this curiosity ?

It's theorized that most black holes have rotational speed. Also, I'm guessing, event horizons are always spherical or close to spherical because they are a function of the gravity well extending from center mass of the black hole. My question is this, could a black hole ever rotate with such...

Homework Statement Show that < l,m | Lx2 - Ly2 | l,m > = 0 Homework Equations L2 = Lx2 + Ly2 + Lz2 [ Lx, Ly ] = i h Lz [ L, Lz ] = i h Lx [ Lz, Lx ] = i h Ly The Attempt at a Solution I tried substituting different commutation values in place of Lx and Ly, but I'm...

I always read that conservation of angular momentum is with respect to an origin of our choice, so if we want to compare the angular momentum of two situations, we have to calculate the angular momentum in these situations with respect to the same origin. However - I've seen in some questions...

Two point masses, with masses of m and 2m, are connected through a string that has a length of L. The two bodies are put on an horizontal frictionless table as in the figure, so that m is at the origin. The body 2m is above it (on the y axis) at a distance of L/2 m. At a certain moment they give...

Maybe this is a simple question but, all the stuff I've been reading so far keeps talking about protostars and their angular momentum being a consequence of the surrounding nebula. Why do they inherit that in the first place? Is is just a consequence of the gravitational collapse?

My understanding is that spin angular momentum is just as real as bulk angular momentum. So, if we get the spin of some electrons in an object to flip, then the object should start spinning in the opposite direction to conserve angular momentum. Right? If we mount a permanent magnet in an...

Homework Statement I do not understand equal signs 2 and 3 the following Angular momentum operator identity: Homework Equations \hat{J}^2 = \hat{J}_1^2+\hat{J}_2^2 +\hat{J}_3^2 = \left(\hat{J}_1 +i\hat{J}_2 \right)\left(\hat{J}_1 -i\hat{J}_2 \right) +\hat{J}_3^2 + i...