Angular momentum Definition and 1000 Threads

Hi, I,ve been looking through some notes on Lagrangian mechanics but they have got me confused so i'll start from the beginning. If a point mass is moving in the x-y plane with constant velocity v at a y-coordinate r then it has linear momentum mv which is a constant but it has an angular...

Hi guys, this might be a stupid question but if I wanted a general expression for the time evolution of the angular momentum operator is it just the same as Hamiltonian? i.e ih ∂/∂t ψ = L2 ψ Solving this partial differential gives the time evolution of the angular momentum operator...

What are the "matrix elements" of the angular momentum operator? Hello, I just recently learned about angular momentum operator. So far, I liked expressing my operators in this way: http://upload.wikimedia.org/math/8/2/6/826d794e3ca9681934aea7588961cafe.png I like it this way because it...

Hello :) Homework Statement The Earth of mass m_{e}, moves with an approximately circular orbit of radius r = 1.5 * 10^{8}km around the sun of mass M_{s} = 2 * 10^{30}kg. (a) Determine the numerical value of the speed of the earth. (done, got an answer of 29821 ms^{-1} by equating the...

Homework Statement Electron in Hydrogen atom can be described with wavefunction ##\psi =\frac{1}{2}(\psi _1+\psi _2+\psi _3+\psi _4)## where ##\psi _1=\psi _{200}##, ##\psi _2=\frac{1}{\sqrt{2}}(\psi _{211}+\psi _{21-1})##, ##\psi _3=\frac{i}{\sqrt{2}}(\psi _{211}-\psi _{21-1})## and ##\psi...

In my textbook there is an equation for the precession frequency: Ω = τ/Iω The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t...

Attached file shows where my problem occurs. I understand how to get the angular momentum just before the collision. But what confuses me is is within the square. Why mvg(r) is only on the left hand side when I've had similar equations with it on both sides. Why is Ig used and why isn't Ib used...

Homework Statement I'm running through practice papers for my 3rd year physics exam on atomic and nuclear physics: This is the operator we found in the previous part of the question L = -i*(hbar)*d/dθ Next, we need to find the eigenvalues and normalised wavefunctions of L The...

Homework Statement A finger presses a ball and throws it away with angular velocity ω0 and velocity V0 like in the picture. the coefficient of friction is μ. what is the ratio ω0 to V0 so that they both are zeroed at the same time Homework Equations I_C=\frac {2}{5}mr^2 Torque=\dot{L}...

Homework Statement 4 small balls of mass m each are connected with light rods like in the picture. the system is rotating with angular velocity ω0. When the system is in the rightmost position the upper ball disconnects from the system. What is the angular velocity of the 3 remaining balls...

Homework Statement A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l? Homework Equations n>l, l is bigger or equal to m The Attempt at a Solution The allowed l= 3,2,1 The allowed m for...

Homework Statement Consider an electron with spin \frac{1}{2} and orbital angular momentum l=1. Write down all possible total angular momentum states as a combination of the product states | l=1 , m_l > | s = \frac{1}{2} , m_s > Homework Equations Lowering operator : J_- |j, m> =...

L = Ʃ rn x mnVn The general equation for calculating the angular momentum is given above, from what I understand would you use the rn x mnVn part of the equation for each particle, and then sum these values all together? This isn't a homework or coursework question, I study Physics as a...

Hello! I have a system composed by a particle attached to four springs that lie on the xy plane. The motion of the particle occurs on the xy plane. I wanted to know if the angular momentum is conserved. Thanks for your help :)

If the units of angular velocity, ω, is expressed in rad/a what then is the units of angular momentum? L=Iω From this I can gather that the units are Kgm^2*rad/s Is this a suitable way to express angular momentum?

When solving for the spherical harmonic equations of the orbital angular momentum this textbook I'm reading.. Does this mean that there must be a max value of Lz which is denoted by |ll>? Normally the ket would look like |lm>, and since m is maxed at m=l then |ll> is the ket consisting of the...

1. Homework Statement [/b] Consider a thin rod of mass m_{r} and length L hanging from a pivot at its upper end. A ball of clay of mass m_{c} and of horizontal velocity v_{0} strikes the lower end of the rod at a right angle and sticks, causing the rod + ball to rotate. What is the angular...

Homework Statement A thin rod of mass M and length L rests on a frictionless table and is struck L/4 from its CM by a clay ball of mass m moving at speed v. The ball sticks to the rod. Determine the translational and rotational motionHomework Equations Irod=1/12 mr^2 Irod=1/3 mr^2 L=mrv=Iw...

A boy sitting on a rotating chair (ignore friction) with his hands stretched outwards, pulls in his hands thus reducing the moment of inertia of the chair-boy system. The angular velocity will increase to conserve the angular momentum. The kinetic energy of the system will also increase (as...

Fred, mass 36 kg, stands at the center of a merry-go-round that has mass 50.0 kg and radius 2.0m and that rotates one full revolution every 4.5 seconds. Treat the merry go round as a solid disc, and Fred as a point object. As it turns, he walks to the edge of the merry-go-round, then jumps off...

Hi, I'm basically wondering why there is any residual angular momentum in the universe left over from the big bang at all. Can this be explained by the Anthropic principle and could statistics surrounding angular momentum tell us anything about the early universe? Cheers, Taylrl

Homework Statement A merry-go-round of radius 2m has a moment of inertia 250kg*m^2, and is rotating at 10rpm on a frictionless axle. Facing the axle and initially at rest, a 25kg child hops on the edge of the merry-go-round and manages to hold on. What will be the new angular velocity of the...

Homework Statement For an assignment, I was shown a video where two identical pucks were launched at each other. They were not spinning when launched. They had Velcro on their edges so they stuck to each other when they collided. They hit off-center from each other. Due to conservation of...

In a simple case of hydrogen, we can have simultaneous eigenstate of energy, angular momentum L_z, \hat{\vec{L}^2} . I'm thinking of constructing a state that is an eigenstate of energy but not the angular momentum: \left | \Psi \right > = c_1\left |n,l_1,m_1 \right > + c_2\left |n,l_2,m_2...

Homework Statement Given the parametric equations for a satellite in orbit around a spherical mass find angular momentum L in terms of ε, a, k, m, where k=GMm. Also, find the energy E in the same terms. Lastly, I can only use the equations provided and "fundamental definitions." Homework...

Homework Statement If a particle has spin 1/2 and is in a state with orbital angular momentum L, there are two basis states with total z-component of angular momentum m*hbar l L,s,Lz,sz > which can be expressed in terms of the individual states ( l L,s,Lz,sz > = l L,Lz > l s,sz > ) as l...

Homework Statement http://puu.sh/5rfl9.png Homework Equations CM = Σmr / Σm L = Σ (r x p) The Attempt at a Solution CM = 0.118 * (0.0036 + 0.00657) / (0.0723 + 0.118) = 0.00630614818 m (from the centre of top disk) L = Σ (r x p) = [0.118 * (0.0036 + 0.00657) /...

Homework Statement What are the possible results of the measurement of the sum of the x and z components of the spin angular momentum of a spin-1/2 particle? Sx = Spin angular momentum operator x Sz = Spin angular momentum operator x Homework Equations The Attempt at a...

Hi guys, I need help on interpreting this solution. Let me have two wave functions: \phi_1 = N_1(r) (x+iy) \phi_2 = N_2(r) (x-iy) If the angular momentum acts on both of them, the result will be: L_z \phi_1 = \hbar \phi_1 L_z \phi_2 = -\hbar \phi_2 My concern is, \phi_1 and \phi_2...

Homework Statement Determine the angular momentum of the Earth about its rotation axis (assume the Earth is a uniform sphere). Homework Equations L = Iω I = (2/5)Mr^2 ω = 2\pi/T The Attempt at a Solution I = (2/5)(6.0 X 10^24 kg)(6.4 X 10^6m)^2 ω = 1.992 X 10^-7 rad/sec L =...

Homework Statement What is the angular momentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.35m at an angular speed of 10.4 rad/s? Homework Equations I am using L = Iω The Attempt at a Solution I put I = (2/5)(0.210 kg)(1.35m)^2 ω = 10.4 rad /...

When combining N spin 's' states, is it always true that each multiplet has even or odd symmetry? I know that's the case for N=2 and s=1/2 or 1. For s=1/2, the triplet is symmetric and the singlet is antisymmetric. For s=1, the pentlet is symmetric, the triplet antisymmetric, and the singlet...

Homework Statement On a frictionless table, a glob of clay of mass 0.240kg strikes a bar of mass 1.560kg perpendicularly at a point 0.390m from the center of the bar and sticks to it. a) If the bar is 1.260m long and the clay is moving at 9.300m/s before striking the bar, what is the final...

Homework Statement On a frictionless table, a glob of clay of mass 0.380 kg strikes a bar of mass 0.9 kg perpendicularly at a point 0.550 m from the center of the bar and sticks to it. a) a) If the bar is 1.300 m long and the clay is moving at 8.100 m/s before striking the bar, what is the...

I've got 3 problems that I got wrong on my most recent test (college 1st year physics). I need to figure out what I did wrong and hopefully someone here can help me. I know all my answers are wrong because I got marked wrong but I'm unsure why, or if there's another way or a better way to go...

Homework Statement In the graph shown in the picture, an expression for the acceleration of the pulleys is obtained. Homework Equations The Attempt at a Solution The thing i don't understand is, how do we find the angular momentum for the system? In class, I was told that the angular...

Homework Statement Derive m*= mM/(m+M) *hint* total angular momentum Iω=m*r2ω equals the sum of the individual angular momenta, where r = re + rn; re and rn are the distances of the electron and nucleus respectively from the center of mass. Homework Equations Angular Momentum = mvr...

It's confusing to me how black holes can conserve angular momentum in relativity. In order to define rotation, there needs to be a 1 dimensional line that represents a radius. Considering that a black hole singularity has no dimensions, it seems impossible that a singularity, and hence a black...

Homework Statement A paint ball fires a ball of putty at a pendulum at a speed of 14 m/s, with a mass of 53g, at an angle of 42 degrees below the horizontal. The pendulum is made of a thin bar 51 cm long and mass of 310 g. The sphere fixed to the end of the pendulum is 17 cm in radius and has...

I'm trying to understand why the eigen value of the total angular momentum L^{2} is \hbar ^2 l(l+1). The proofs I have seen go like this. Using the ladder operators L_{\pm} = L_x \pm iL_y we can see and the |l, m \rangle state with maximum value of m (eigen value of L_z ) \langle l,m_{max} |...

Homework Statement A particle is in a state described by the wave function: \Psi = \frac{1}{\sqrt{4}}(e^{i\phi} sin \theta + cos \theta) g(r), where \int\limits_0^\infty dr r^{2} |g(r)|^{2} = 1 and \phi and \theta are the azimuth and polar angle, respectively. OBS: The first...

Imagine that two electrons interact by exchanging a virtual photon. Electron A gains momentum ##-\vec{p}## and electron B gains momentum ##\vec{p}##. If the two momentum vectors are not collinear then there will be extra angular momentum left over from the interaction. In a simple Coulomb...

Homework Statement Solve for ##L^2_x## ##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry! Homework Equations Solve for ##L^2_x## ##L_x = \frac{\hbar}{i}...

Homework Statement Figure: http://i.imgur.com/E2D1hkW.png A massless rod of length 2R is attached at the middle to a pivot point that allows it to rotate in the vertical plane. Masses m and 2m are attached to the rod at the locations depicted in the figure. Initially the rod makes an angle of...

1. The problem statement. Two boys are sliding toward each other on a frictionless, ice-covered parking lot. Jacob, mass 45 kg, is gliding to the right at 7.98 m/s, and Ethan, mass 31.0 kg, is gliding to the left at 10.7 m/s along the same line. When they meet, they grab each other and hang on...

In a central force problem, angular momentum is conserved. we quantized one of the component of L, say Lz. Also, we quantized the angular momentum, L = √l(l+1)h_bar If we know Lx and Ly without uncertainty, then we know the direction of L. Hence we know the motion of the particle is confined...

Homework Statement An infinite wire of linear charge density \lambda lies on the z axis. An insulating cylindrical shell of radius R is concentric with the wire and can rotate freely about the z axis. The charge per unit area on the cylinder is \sigma = -\lambda/2\pi R while the mass per unit...

Homework Statement Given a photon polarization state lphi> = lx> 3/5 + ly> 4i/5 , a beam of photons transmit N photons per second in such a state. An L-polarized photon has an angular momentum hbar along its direction of motion, and an R-polarized photon has an angular momentum of the same...

Hello, could somebody please explain to me why in 4 of these solutions, the angular momentum final term about point p is mVfR + Icmω ? It is in huge attached solutions my teacher posted. Thank you very much in advance Here is the problem in case you are interested of Horne context. 4. A...

I have angular momenta S=\frac{1}{2} for spin, and I=\frac{1}{2} for nuclear angular momentum, which I want to add using the Clebsch-Gordon basis, so the conversion looks like: $$ \begin{align} \lvert 1,1\rangle &= \lvert\bigl(\tfrac{1}{2}\tfrac{1}{2}\bigr)\tfrac{1}{2}\tfrac{1}{2}...