Angular momentum Definition and 1000 Threads

I find conservation of energy and linear momentum to be quite natural to understand, but I find conservation of angular momentum really, really tricky. Let me give two examples: (a) I call my system as a stick with identical springs at its ends, facing opposite directions, each spring is coiled...

This took a lot of time and effort and I understand if you wish to skip past everything and just read my questions about it in the The too long didn't read summary (TL;DR) at the bottom. Homework Statement The 10-g bullet having a velocity of v = 750 m/s is fired into the edge of the 6-kg...

Homework Statement Consider a 2-particle system where the two particles have angular momentum operators ##\vec{L}_1## and ##\vec{L}_2## respectively. The Hamiltonian is given by $$H = \mu\vec{B}\cdot (\vec{L}_1+\vec{L}_2)+\gamma \vec{L}_1\cdot \vec{L}_2.$$ Determine explicitly the eigenvalues...

I know that spin is a type of intrinsic angular momentum. For electron spin is (1/2)ħ . But unit of (1/2)ħ is J.s, which is not the unit of angular momentum. Can you please explain this discrepancy?

Taking the Earth orbiting the sun as an example, when I consider the angular momentum of the Earth about the sun, should the spin angular momentum be counted? I'm confused that if it's counted, the spin angular momentum, Lcm=Icm×ωspin, is different from other angular momentum regarding the...

Hello, I'm trying to calculate the measurement of the orbital angular momentum of the state l=1 and m = -1. The operator for the angular momentum squared is ## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial}{\partial \theta}(sin\theta\frac{\partial}{\partial \theta}))...

Homework Statement (Problems/diagrams referenced are attached as images.) Homework Equations Net torque about an origin = time derivative of the angular momentum vector about the same origin. The Attempt at a Solution I've solved these problems before, but I'm now looking back at them and...

I know that total magnetic moment of an electron (I am not sure if it is magnetic moment of electron or atom, please clarify this) is sum of magnetic moment caused by orbital motion and spin angular momentum. So, Total magnetic moment = Orbital magnetic moment + spin magnetic moment Do I have...

Homework Statement A point particle travels in a straight line at constant speed, and the closest distance it comes to the origin of coordinates is a distance l. With respect to this origin, does the particle have nonzero angular momentum? As the particle moves along its straight-line path...

Good afternoon I just have this little doubt: imagine the osculating orbit of Mars changing slowly in its elements along the centuries. The semi major axis changes, the period, etc. Is the specific angular momentum allways equal in all the osculating orbits Mars has in those centuries? Or does...

Homework Statement Two pucks are lying on ice where they can slide and rotate with almost no friction. A string is tied to both pucks but it is tied to the middle of the first puck and wrapped around the second puck. You pull on both strings with the same force, F. The first puck moves without...

I have a 5.0 m tractrix and am trying to work out angular momentum and total angular momentum for two hitchpoint speeds 60 & 70 km/h. My result shows a higher total angular momentum for the lower speed. This is not what I expected. Here are my equations Positions: Derivatives Angular velocity...

I'm trying to deduce the angular momentum ( for a rigid body ) on my own, and here is the problem I face. By introducing the angular momentum of a tiny piece in rigid body (" i ") as : Li = ri × pi Li = ri × mi vi --------------------------------- [ Line 1 ] Li = ri × mi ri ωi To find the...

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the rules help to select the lowest energy state of a configuration). As far as I understood: Hund’s...

I've started on "Noether's Theorem" by Neuenschwander. This is page 35 of the 2011 edition. We have the Lagrangian for a central force: ##L = \frac12 m(\dot{r}^2 + r^2 \dot{\theta}^2 + r \dot{\phi}^2 \sin^2 \theta) - U(r)## Which gives the canonical momenta: ##p_{\theta} = mr^2...

Hello, I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two...

Homework Statement Not a HW problem, but a "me re-thinking things" problem. Please tell me where my thinking is flawed: You have an ice skater with no net external torques acting on him/her. (We are analyzing the time after they have to get an external torque on them by pushing off of the...

Homework Statement A uniform thin rod AB is equipped at both ends with the hooks as shown in the figure and is supported by a frictionless horizontal table. Initially the rod is hooked at A to a fixed pin C about which it rotates with a constant angular velocity w1 . Suddenly end B of the rod...

Homework Statement A particle (5 kg) moves with constant velocity 2 m/s along the straight line 2y=3x+4, the angular momentum of the particle about origin is? Homework Equations L=r x p The Attempt at a Solution For a 2d problem we take the component of velocity perpendicular to the point...

I have a disc that is rotating due to air being blown at its outer radius. The incoming relative velocity of the air is high, therefore the effect of friction supersedes the effect of conservation of angular momentum. The tangential portion of this velocity decreases due to the friction as it...

Homework Statement A disk of radius ##r## and mass ##m## rolls down an inclined plan. It reaches the end of the plane with velocity ##v_{f}## and collides with a vertical rod of length ##L## and mass ##M## sticking with it. See figure. What is the angular momentum magnitude and direction...

Homework Statement A ball of mass ##m## is attached to a massless string of length ##L##. The ball is released from rest as shown in the figure and as it reaches the bottom of the circle, the string wraps around a nail which is a distance ##d## below the center of the circle. What is the...

1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...

Homework Statement A 2.4 kg particle-like object moves in a plane with velocity components vx = 25 m/s and vy = 80 m/s as it passes through the point with (x, y)coordinates of (3.0, −4.0) m. (Express your answers in vector form.) (a) What is its angular momentum relative to the origin at this...

Homework Statement A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I Homework...

According to the book "transport phenomena" by Lightfoot, Byron and Stewart if you take the cross product of the equation of motion (for very small element of fluid) and the position vector ##r## you get the equation of change of angular momentum. After some manipulation of vectors and tensors...

Homework Statement I'd like to show, if possible, that rotational invariance about some axis implies that angular momentum about that axis is conserved without using the Lagrangian formalism or Noether's theorem. The only proofs I have been able to find use a Lagrangian approach and I'm...

Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring...

My intuition is if an object is orbiting a centre, it is accelerating as the direction of its vector constantly changes, i.e a ball orbiting a stick because they are tied by a string. I don't understand why Earth's spin does not slow down, if we think of Earth as lots of individual atoms, those...

Homework Statement Consider two pairs of operators Xα, Pα, with α=1,2, that satisfy the commutation relationships [Xα,Pβ]=ihδαβ,[Xα,Xβ]=0,[Pα,Pβ]=0. These are two copies of the canonical algebra of the phase space. a) Define the operators $$a_\alpha =...

Homework Statement A certain odd-parity shell-model state can hold up to a maximum of 4 nucleons. What are its values of J and L? What about an odd-parity shell-model state with a maximum of 6 nucleons? Homework Equations Parity = (-1)L J = L+S Total angular momentum, J, is equal to orbital...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Homework Statement A rod (mass M, length L) is placed vertically on a smooth horizontal surface. Rod is released and after some time velocity of COM is v downwards and at this moment rod makes 60 degrees with horizontal. Find angular momentum of rod about Instantaneous center of rotation...

Homework Statement A circular ring (2m, R) with a small insect of mass m on its periphery, is placed upon smooth horizontal surface (axis of rotation passing through center and perpendicular to the ground i.e disk is lying horizontally) . The insect starts moving with velocity v w.r.t ground...

Homework Statement suppose you're sitting on a rotating stool holding a 2kg mass in each outstretched hand, if you suddenly drop the masses, will your angular velocity increase, decrease or remain the same? Homework Equations dL/dt=net torque when net torque is 0, L=constant=Iw therefore...

Homework Statement Assertion- If linear momentum of particle is constant, then its angular momentum about any axis will also remain constant Reason-Linear momentum remains constant when net force is 0, angular momentum remains constant when net torque is zero which of these statements is/are...

Homework Statement A uniform rod (M, L) is rotated about a point L/3 from its left end. Angular momentum about O Homework Equations 1) L=I(cm)w for purely rotating body 2) L(orbital)= M*v(cm)*perpendicular distance(r) 3) L(spin)= I*w The Attempt at a Solution I got the correct answer in two...

Homework Statement A disk is undergoing pure rolling motion with speed v. The radius of the disk being R and mass M. Then the angular momentum of the disk about the 1)bottom most and 2)top most point Homework Equations 1) L(orbital) = m*v*r where v is the velocity of cm which is...

Homework Statement A 7.3-cm-diameter baseball has mass of 150 g and is spinning at 230 rad/s . Treating the baseball as a uniform solid sphere, what is its angular momentum? I'm about to pull my hair out because I feel like I understand everything about this problem perfectly and yet I'm still...

Homework Statement Four particles of mass 1 Kg each, are moving on a plane with the velocities given in the figure. Homework EquationsThe Attempt at a Solution First I calculated the position of the CoM: Xcm=7/4(i + j) Then I calculated the velocity of the CoM: Vcm= ½i + ¼j For the internal...

Hello, in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...

From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following: h = wr^2 = ab * n How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or...

Homework Statement Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...

Homework Statement 4 persons each with mass m stand out on the edge of the carousel that rotates with angular velocity W0. carousel has mass 4m, radius r and inertia I = 2mr^2. The 4 persons then go all the way to the center of the carousel. Show that the final angular velocity W1 = 3W0 See...

Homework Statement A point charge q sits at the origin. A magnetic field ##\mathbf{B} (\mathbf{r})=B(x,y)\mathbf{\hat{z}}## fills all of space. The problem asks us to write down an expression for the total electromagnetic field angular momentum ##\bf{L_{EM}}##, in terms of q and the magnetic...

Homework Statement A long board is free to slide on a sheet of frictionless ice. A skater skates to the board (laid horizontally relative to the skater's motion) and hops onto one end, causing the board to slide an rotate. In this situation, are angular and linear momentum conserved...

In the Dirac equation, the wave-function is broken into four wave-functions in four entries in a column of a matrix. Since there are four separate versions of the wave-function, does each version have the spin angular momentum of h-bar/2? This seems overly simplistic. How does spin angular...

Hi, I found some back of envelop calculations which show that Jupiter accounts for over 60% of the solar system's angular momentum. http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html Is that correct? A previous thread here on the subject ( now locked for some reason ) claimed...

1. At the instant of the figure, a 6.70 kg particle P has a position vector of magnitude 4.30 m and angle θ1 = 43.0° and a velocity vector of magnitude 3.40 m/s and angle θ2 = 32.0°. Force , of magnitude 7.40 N and angle θ3 = 32.0° acts on P. All three vectors lie in the xy plane. About the...

Homework Statement I am working on the derivation of Kepler's Second Law based on torque and angular momentum. I understand that the vector "L" is equal to the mass (m) times the cross product of the vector "r" and the vector "v." The source I am following then states that L = mrvtheta. I do...