Angular momentum Definition and 1000 Threads

Homework Statement A 2 meter long bar weighing 90N hangs vertically from a frictionless pivot. The ball is hit at a point 1.5 Meters below the ceiling by a ball that weighs 3Kg and is traveling with a velocity of 10 m/s. The ball bounces back with a velocity of -6 m/s. Find the angular speed...

Homework Statement Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the xy-plane, with the sun at the origin, and label the planet's position by polar coordinates (r, \theta). (a) Show that the planet's angular momentum has magnitude L = mr^2 \omega, where...

Homework Statement A uniform bar of Length L and Mass M is hit by a blob of putty moving with velocity v. The blob hits the bar at a distance d from the center of the bar and sticks to the bar at the point of contact. Obtain expressions for the velocity of the systems center of mass and for...

The experiment of a quickly rolling wheel on a string is well known. How is this behavior explained in terms of the molecules of an atom? That is to say, why don't the individual atoms of the wheel fall down?

Hi, Both Ballentine in "Quantum Mechanics - a modern development" pages 160-162 and Sakurai in "Modern Quantum Mechanics" pages 193-196 use essentialy the same argument to show the existence of a set of eigenvectors of J² and J_z with integer spaced values of the J_z eigenvalues for fixed J²...

Homework Statement A particle with mass=m moves in the xy plane. It is under the influence of a repulsive central force described by: F(r)={A\hat{r} if r<R0 and 0 if r>R0} \hat{r} is the unit radial vector and R0 is the range of the force The initial conditions are x=-3 R0, y=0.5 R0...

Is several other threads some arguments depend on what circumstances angular momentum is conserved in relativity and that is what I would like to establish here. This Wikipedia article http://en.wikipedia.org/wiki/Relativistic_angular_momentum describes relativistic angular momentum as being...

I was thinking of a couple basic mechanics problems lately. What if you have a rod sitting in space at rest, and you shoot a bullet at its center. Linear momentum is conserved, and the problem is quite trivial. Now what if the bullet hit the rod slightly off of the rod's CG? I think linear...

Homework Statement Write down the 3×3 matrices that represent the operators \hat{L}_x, \hat{L}_y, and \hat{L}_z of angular momentum for a value of \ell=1 in a basis which has \hat{L}_z diagonal. The Attempt at a Solution Okay, so my basis states \left\{\left|\ell,m\right\rangle\right\}...

Homework Statement A block of mass m1 is attached to a block of mass m2 by an ideal rope passing over a pulley of mass M and radius R as shown. The pulley is assumed to be a uniform disc rotating freely about an axis passing through its center of mass (cm in the figure). There is no friction...

Spin and "intrinsic angular momentum" After searching this forum for what exactly spin is my inference is that it is a misnomer for an electrons "intrinsic angular momentum"...so some doubts; may be I am being too blunt; What is the difference between +1/2 and -1/2 spin? Is the electron...

Homework Statement A bike is going clockwise around a circle of radius R (see below). The moment of inertia of each wheel around its center I_cm is NOT negligible. What is the direction of the total Angular Momentum of the bike about the center of the circle (point Q)? Consider when the bike...

Homework Statement A solid disc of mass m = 5.0 kg and radius r = 0.45 m is spinning clockwise about the axis passing through the center of the disc. At t = 0, three forces are applied to the disc as shown. Part 1. What is the magnitude of the net torque acting on the disc about its...

Homework Statement A light rigid rod of length 3s where s = 1.5 m has small spheres of masses m = 0.24 kg, 2m, 3m and 4m attached as shown. The rod is spinning in a horizontal plane with angular speed w = 2.5 rad/s about a vertical axis. Find the magnitude of angular momentum of the rod in...

I'm looking for an equation similar to the change in forward momentum equation: Δmv=f*Δt But for angular momentum. I think it will be (change in angular momentum) = (torque) * (change in time) Here is how I derived it: Is this all correct? I cannot find this equation anywhere on the...

The apparatus above has an initial angular velocity of \omega_{1} as the rods are released. I need to find the angular velocity \omega_{2} of the apparatus at the bottom. I've tried 3 methods. First I tried a work-energy balance where I included a gravitational potential energy. KE_{1} + PE =...

Two questions 1) The total orbital spin angular momentum is given as L2=l(l+1). What is the source of or meaning of the (l+1). 2) Similarly for the electron the total spin angular momentum is given as S2-1/2(1/2+1) hbar2. Is the total angular momentum precessing to give sz 1/2 hbar object?

Homework Statement The question is to find the total angular momentum of the following atoms in their ground state - Na (11 electrons), and Rb (37 electrons). That's all the info given. Homework Equations I have no idea - that's what I can't find! The Attempt at a Solution I've...

Homework Statement I'm trying to demonstrate that if: $$\hat{L}_z | l, m \rangle = m \hbar | l, m \rangle$$ Then $$\hat{L}_z^2 | l, m \rangle = m^2 \hbar^2 | l, m \rangle$$Homework Equations $$\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$$ $$\hat{L}_z = -i\hbar \left [ x...

Why, for states with angular momentum l >0, do states with smaller total angular momentum J have a higher binding energy? For example, why does the 2p1/2 state have a higher binding energy than the 2p3/2 state? If the 2p orbital is filled (2p6), wouldn't Hund's third rule indicate that the...

I just want to test my understanding of angular momentum here... I rotate a sphere in space such that the axis of rotation passes through it's diameter, by applying a torque. At one moment of time, I just stop applying the torque. Now, the net torque on the sphere is zero.There is no change in...

Ok so this has always confused me and I still can't seem to find an answer anywhere! A general black hole has parameters M, Q, and J which are given the meaning of mass, charge, and angular momentum. My question is what what is the contribution to M by Q and J?? Presumably if you start with a...

Homework Statement Mass m is attached to a cylindrical post of rdius R by a string. Initially it is distance r from the centre of the post and is moving tangentially with speed v_{0}. In case (a) the string passes through a hole in the centre of the post at the top. the string is...

Homework Statement a drum of mass M_{a} and radius a rotates freely with initial angular velocity ω_{a}(0). A second drum with mass M_{b} and radius b greater than b is mounted on the same axis and is at rest, although it is free to rotate. a thin layer of sand with mass M_{s} is distributed...

This is problem 3 from section 9 of Mechanics, Landau Lifgarbagez. I have been trying to understand the problem but I have no idea how to solve it. Can someone give me a hand please? any comment or suggestion is very welcome. Thanks for your time. Best regards.

A man of mass m1 is standing at the edge of a disc of mass m2 which is pivoted about its CM. The man starts waling along the rim of the disc with a velocity μo. Find the angular velocity acquired by the disc by the motion of the man along the rim? I couldn't do this on my own so I turned to the...

Let an electron is orbiting in a orbit with the principal quantum number n =1. According to wave mechanics its angular momentum is √ l(l+1) h/2∏ and angle : cosθ = ml/ √ l(l+1) How one can explain the electron angular momentum and its possible orientations for l =0? Off course for n =2, l...

I'm looking for the general formula for Angular Momentum radiated away from quadrupolar electromagnetic radiation. I searched the usual books (Jackson, Landau-Lifchitz, ...) and just found the usual dipolar contributions. Using dimensional analysis and energy radiated away, I found this...

Homework Statement A particle of mass m moves along a straight line with constant velocity v in the x direction, a distance b from the x axis. (a) Does the particle possesses any angular momentum about the origin? (b) Explain why the amount of its angular momentum should change or should stay...

Hi all: I have been wondering: picture a cylinder sitting above a sheet of sand paper, assume static friction between the sheet of paper and the cylinder. if i start pulling the sheet of paper at velocity v along a direction of rolling (to the left), the moment caused by static...

Homework Statement Hi. I'm given a 3-dimensional subspace H that is made up of the states |1,-1\rangle, |1,0\rangle and |1,1\rangle with the states defined as |l,m\rangle and l=1 as you can see. The usual operator relations for L_{z} and L^{2} applies, and also: L_{+} = L_{x}+iL_{y} L_{-} =...

had a thought. suspect that i am wrong but not sure where. no idea of the maths involved but suspect As an object approaches the speed of light relativistic forces come into play – effecting time dilation density etc Can the same theory be rearranged to show that As you approach the density &...

Hello everyone, I'm going through some lecture notes and there are some things I don't understand about the whole derivation of the angular momentum multiplet. It's said that the skew-symmetric 3x3 matrices J_i are the infinitesimal generators of the rotation group SO(3). Later, however...

While dealing with a circling particle in an spherical symetric potential our professor said that we can replace an operator of ##z## component of angular momentum ##\hat{L}_z## with the expectation value - he denoted it just ##L_z## - of the angular momentum if ##L_z## is constant. Why is that...

Hi, I'm confused by a sentence in a set of lecture notes I have on quantum mechanics. In it, it is assumed there is some representation \pi of SO(3) on a Hilbert space. This representation is assumed to be irreducible and unitary. It is then said that the operators J_i, which are said to...

If any of you have the Third Edition of Classical Electrodynamics by John David Jackson, turn to section 11.8, as that's where I'm getting all this from. If not, you should still be able to follow along. In said section, Jackson gives us this equation that relates any physical vector G in a...

Homework Statement i need to calculate the orbital angular momentum for 3D isotropic harmonic oscillator is the first excited state The Attempt at a Solution for the first excited state...

Homework Statement Prove the commutation relation ##\left [L_x, p_y \right] = i\hbar \epsilon_{xyz} p_z## Homework Equations ##L_x = yp_z - zp_y## ##p_z = i\hbar \frac{\partial}{\partial z}##The Attempt at a Solution ##\left [L_x, p_y \right] = (yp_z - zp_y)p_y - p_y(yp_z - zp_y)## ##\left...

Hey all! I am trying to figure out physical situations when angular momentum is and is not conserved. If anyone could share some theory here and illustrate with a few "real life" examples this would be very helpful! Thanks for your help! josh

Ok so I have two very different questions, both closely tied to the concept of relativistic angular momentum. Question #1: Why do people claim there is a minimum radius for a classical model of electrons with spin? The typical argument is that if the radius were to fall below some minimum...

Homework Statement In an experiment an individual throws a rock with an initial horizontal velocity of v0 = 20 ft/s at time t=0. The rock is thrown from the edge of a cliff (directly above the base of the cliff) at height h=50 ft from the ground. The origin is assigned at the base of the...

Homework Statement m1 and m2 are two blocks tied with a rope with a pulley inbetween, like those in this picture http://labella.altervista.org/images/mechanicsoftwopoint_2.png there are no frictions. find: the linear acceleration of the blocks and the tension of the rope on both m1 and m2.The...

Homework Statement A point mass "m" moving at speed "v" strikes the end of a stationary uniform thin rod of length "l" and the same mass "m" at a right angle. The point mass does not stick to the rod; the collision is elastic. There are no pivot or anchor points. The system is floating freely...

From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 196. Equation (3.6.4), 1-i \left( \frac{\delta \phi}{\hbar} \right) L_z = 1 - i \left( \frac{\delta \phi}{\hbar} \right) (x p_y - y p_x ) Making this act on an arbitrary position eigenket \mid x', y', z' \rangle...

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...