Angular momentum Definition and 1000 Threads

Hi, friends! Let the quantity ##I\boldsymbol{\omega}## be given, where ##I## is an inertia matrix and ##\boldsymbol{\omega}## a column vector representing angular velocity; ##I\boldsymbol{\omega}## can be the angular momentum of a rigid body rotating around a static point or around its -even...

Hello there! I was doing my Gravitation problems and I found this problem that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force produced by a proton and a neutron is: U(r) = \frac{k}{r}e^{-\alpha r},\ k<0,\ \alpha > 0...

Hi I read that for Dirac equation, [ L , H ] =/ 0 , so Dirac found a operator S such that 1. [ S , H ] = - [L, H] ---> [ J, H ] = 0 where J = L + S , the total angular momentum. 2. S gives an eigenvalue of spin 1/2 ---> solutions of Dirac equation describe fermions. The total...

Homework Statement A child (mc = 36 kg) is playing on a merry-go-round (mm = 225 kg, R = 2.9m) that is initially at rest. The child then jumps off in a direction tangent to the edge of the merry-go-round. The child has a speed of 5.0 m/s just before she lands on the ground. What is the...

Homework Statement Homework Equations The Attempt at a Solution For a angular momentum ##J##, there exists the eigenvalue problems $$J^{2} \mid j \hspace{0.02 in} m \rangle = j(j +1)\hbar^{2} \mid j \hspace{0.02 in} m \rangle $$ $$ J_{z} \mid j \hspace{0.02 in} m \rangle = m \hbar \mid j...

Torque is defined as the cross product of position vector and force, i.e. \vec \tau = \vec r \times \vec F . However the force vector \vec F is fixed, but the choice of origin is arbitrary, making \vec r also arbitrary. Does it make the torque vector also arbitrary, which apparently shouldn't...

Homework Statement Problem statement - [/B] Klepner and Kolenkow 6.15 : A pendulum is made of two disks each of mass M and radius R separated by a massless rod. One of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centres are a distance l...

How the relative angular momentum of two particles can be detect by detector in two particle decay (center of mass frame)? I am curious about the signatures/differentiation between different relative momenta, means how one can decide that it is L=0, L=1,2,3,...? Of course the distribution would...

Homework Statement A particle with mass m can move freely in three dimensions. Explain why the stationary states of the particle are determinate states for angular momentum (L_z and L^2) Homework Equations L^2 = L_x^2 + L_y^2 + L_z^2 L = r \times p \hat{H} =...

Homework Statement Say a human is moving through space with constant acceleration due to gravity. There are no external forces/torques on the body other than the force of gravity. The person applies an internal torque at some joint, let's say the knees, so that they bend. Assume the rest of the...

It seems to be implied, but I can't find it explicitly - the order in which linear operators are applied makes a difference. IE given linear operators A,B then AB is NOT necessarily the same as BA ? I thought it was only with rotation operators that the order made a difference? I noticed this...

Some literatures say that the selection rule in electric dipole approx. for angular momentum ##\Delta j = 0,-1,1## some other say ##\Delta l = -1,1##. I follow the notation used in my references, despite the difference I think since j and l are both angular momenta which fulfill angular momentum...

Hello, For the spin angular momentum operator, the eigenvalue problem can be formed into matrix form. I will use ##S_{z}## as my example $$S_{z} | \uparrow \rangle = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \frac {\hbar}{2} \begin{pmatrix} 1 \\ 0...

Homework Statement A bird m_b=0.470kg, is flying horizontally at v_b=2.50 m/s, not paying much attention, when it suddenly flies into a stationary vertical rod, hitting it d=25cm below the top. The rod is uniform, L=0.740m long, has a mass of m_r =1.60kg and is hinged at its base. This time the...

The direction of the torques in the following working will be found using: \vec{\tau} = \vec{r} \times \vec{F}. When viewed from above, the counterclockwise rotation of the blades produces a torque out of the page: As the angular momentum (right-hand corkscrew rule) is also out of the page...

Homework Statement We model a dirt bike as a rod of mass (M) 100 kg, and length (L) 2 m to which are attached two wheels of mass (m)=40 kg kg, and radius R=0.5 m. The bike goes off a spine ramp with angle ##\phi=1deg.## to the vertical on either side (see diagram below). Our question is, at...

Homework Statement Homework Equations Torque = r X F The Attempt at a Solution r is 2.5m since that's the length of the red (minus 0.5), and F should be the weight, so ma? That gives something like (5 * 2.5/3) * 9.8 * 2.5, which doesn't give me an answer at all :(

Homework Statement http://tinypic.com/r/vsew5k/8 Homework Equations Angular momentum for rigid bodies Kinetic energy of rigid bodies The Attempt at a Solution I tried to start by using conservation of energy, but I can't find the center of mass of the rod. I'm also not sure where to put the...

Homework Statement What is the direction of the red ball's angular momentum about the point A? (see figure) Same as the momentum. Out of the page. Zero magnitude. Opposite to the momentum. Same as rA. Into the page. [/B] Homework Equations Angular Momentum[/B] The Attempt at a...

Homework Statement I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - http://www.kwon3d.com/theory/moi/iten.html I follow clearly to the...

Homework Statement Homework EquationsThe Attempt at a Solution This whole thing about angular momentum has me totally confused and stumped, but I am trying this problem given in a youtube video lecture I watched. I know of this equation ##L^{2} = L_{\pm}L_{\mp} + L_{z}^{2} \mp \hbar L_{z}##...

Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM. What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation? If not, are the 3...

Hey all, I'm not understanding why the bits highlighted in red are equal? Any help appreciated, thanks.

Homework Statement If the angular momentum of Earth in its motion around the Sun were quantized like a hydrogen electron, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? Would that energy release be detectable? What would be the...

(Based on a problem from the 59th Polish Olympiad in Physics, 2009) Let's consider a ball of mass ##m##, radius ##r## and moment of inertia ##I = 2/5mr^2## approaching a wall with linear velocity ##v_0##, rolling without sliding with angular velocity ##\omega_0##. It collides with a wall. Its...

Essentially just a consequence of inertia and gravity?

Homework Statement Prove that ## e^{2\pi i \mathbf{n\cdot J}/\hbar} |j,m\rangle = (-1)^{2j}|j,m\rangle ##. This equation is from Ballentine's QM book. The term in front of the ket state in the LHS is a rotation operator through ##2\pi## angle about an arbitrary direction ##\mathbf{n}##...

Question: A streetcar is freely coasting (no friction) around a large circular track. It is then switched to a small circular track. When coasting on the smaller circle its speed is: a) greater b) less c) unchanged Relevant Formulas: w = v/r KE = 1/2mv2 My teacher said the normal force from...

In a discussion with someone claiming to be a physicist (whether PhD or something less he did not say) we got into a hypothetical discussion related to Hitchhiker's Guide to the Galaxy. An alien civilization wants to move the Earth out of the way because it's impeding a galactic highway...

I have been busy with rotating objects and I have a question which I don't understand. http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_AngularMomentum.xml (last question of the page, about the clay on the rod) What I don't understand is that the clay has a kinetic energy...

Homework Statement I was trying to learn about this force, and came across a youtube video: . At 4.00 in the video, he says, "if the parcel of air continues to get deflected..." Why would it continue to get deflected? At 4.40 in the video, a girl rolls a ball while moving on a merry go round...

Homework Statement I am studying the topics listed above and have been having great difficulty getting my problems going. To explain, I am having difficulty seeing where the problem should go and attacking in that direction. I can draw out free-body diagrams but I can't see how to solve the...

Homework Statement Homework EquationsThe Attempt at a Solution I can't understand what is ɛ in this problem, and why should we adopt it. Could you explain me please?

So a particle has intrinsic parity ##\pm 1 ## . The parity of a system of particles is given by product of intrinsic parities and the result is: ##(-1)^l ## (1). Questions: 1) How does this result follow? and what exactly is ##l## here? so it's the orbital angular momentum, so say a particle...

A solid balsa cube of side length L = 16.0” and mass M = 8.60 kg is at rest on a horizontal table top. It is constrained to rotate about a fixed and frictionless axis, AB, along one edge of the cube. A bullet of mass m = 50.0 g is fired with speed v at the other side of the cube, at height a =...

Homework Statement I'm just stuck on one part of a larger problem. I need to find the range of total angular momentum values for an electron in a j-j coupling scheme. Homework Equations j= l + and - 1/2 The Attempt at a Solution The electrons here are in a 5d 6s configuration. So for the...

A 2.3kg , 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rpm, just after this event?I first cacluted the angular...

Homework Statement Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 10^14 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid...

The bond distance for HCl is 1.29 A. At the lowest rotational state the energy is zero. What is the energy and angular momentum Lz corresponding to the first nonzero rotational state? I m not sure if I am approaching this problem right. first I did 1.2 A = 8.3 x 10^7 cm^-1 Then I used this...

Homework Statement Use the spin##-1## states ##|1,1\rangle, \ |1,0\rangle, \ |1, -1\rangle## as a basis to form the matrix representations of the angular momentum operators. Homework Equations ##\mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle##...

Homework Statement By evaluating the "volume" of the relevant region of its phase space, show that the number of microstates available to a rigid rotor with angular momentum less or equal to M is (M/ħ)2. Homework Equations Consider the motion in the variables θ and φ, with...

Could someone explain to me how the author goes from 2nd to 3rd step I think the intermediate step between 2 and 3 is basically to split up the commutator as [y p_z, z p_x] - [y p_z,x p_z] - [z p_y,z p_x] + [z p_y, x p_z] 2nd term = 0 3rd term = 0 so leftover is [L_x, L_y] = [y p_z, z p_x]...

As you can see, solid disk is rotating at steady angular speed, without any external force beeing applied. If i stop it gradualy within 60 second, by applying some linear load, how many kWh can i extract from this moving object?

Homework Statement Figure 10.30 shows two disks: an engine flywheel (A) and a clutch plate (B) attached to a transmission shaft. Their moments of inertia are and initially IA and IB, they are rotating with constant angular speeds ωA and ωB, respectively. We push the disks together with forces...

Homework Statement if the distance between the Earth and the sun were to be cut in half, what would be the number of days in the year? Homework EquationsThe Attempt at a Solution I can solve this question using simple centripetal force = gravitational force of attraction and then halving the...

Homework Statement Prove that ## [L_a,L_b L_b] =0 ## using Einstein summation convention.Homework Equations [/B] ## (1) [L_a,L_b] = i \hbar \epsilon_{abc} L_c ## ## (2) \epsilon_{abc} \epsilon_{auv} = \delta_{bu} \delta_{cv}- \delta_{bv} \delta_{cu}## ## (3) \epsilon_{abc} = \epsilon_{bca}...

ok i just learned that spin comes up when l (azimuthal quantum number) is half integer but then my book says that each elementary particle has a specific and immutable value of spin. Ok now does this mean that l (azimuth quantum number) takes two values at once - One value corresponding to spin...

1. Pluto moves in a fairly elliptical orbit around the sun. Pluto's speed at its closest approach of 4.43×109km is 6.12 km/s.Homework Equations : L=mvr, F_g: (GMm/r^2), A_c: mv^2/r[/B]The Attempt at a Solution : I found the answer here, but I'm more interested in why we would use angular...

Homework Statement [/B] A thin spherical shell of radius R = 0.50 m and mass 15 kg rotates about the z-axis through its center and parallel to its axis. When the angular velocity is 5.0 rad/s, its angular momentum (in kg ⋅ m2/s) is approximately: a . 15 b. 9.0 c. 12 d. 19 e. 25 Homework...

Spin or angular momentum in my book is formulated in the basis of eigenstates of the operator that measures the angular momentum along the z-axis. But in principle I guess this could just as well have been done in the basis of eigenstates of Ly or Lx. Will that change anything in the equations...