# What is Angular momemtum: Definition and 111 Discussions

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1. ### Electron moving in an electromagnetic field and rotation operator

Hello, The idea I had was to time evolve the state ##U(\hat{\textbf{b}}, \omega t)| \phi(t) \rangle##, but I'm confused on how to operate with ##H## on such state. I Iwould be glad if anyone could point some way. Thanks!
2. ### I How is the net force on the system equal to 0 initially?

I understand that in the initial condition both the net torque and net force are zero since the system is in a static state , the net torque remains zero as the mass down is being pulled , the two blocks get pulled towards the axis of rotation by a radial force but I am wondering what is...
3. ### Sequential Stern Gerlech experiment

So I thought that when the $m_l = 1$ beam passes through the second SG-magnet, it should split into 3 different beams with equal probability corresponding to $m_l = -1 , 0 , 1$ since the field here is aligned along z-axis and hence independent of the x-axis splitting. And I thought that the...
4. ### Angular momentum of rotating hoop

Problem: Official solution: My calculation: \begin{align*} \mathbf L &= M \mathbf R \times \mathbf V + \mathbf L_{cm} \\ &= M R (\hat j + \hat k) \times (- \Omega R \hat i) + MR^2 \Omega \hat j \\ &= MR^2 \Omega (\hat k - \hat j + \hat j) \\ &= MR^2 \Omega \hat k \end{align*}
5. ### Angular momentum of a particle

First, I have always consider that the angular momentum equals to inertia times angular velocity, but that’s not the case from the options perpective, is my memory wrong, or is there something wrong with the options? Another, I think I need to figure out the angle it went through, I think it has...
6. ### Explain the phenomenon of decrement of angular momentum

I tried to work out the net resultant postion of the normal force but could only come at a conclusion that normal force and mg, both pass through C.O.M(torques were considered about the edge of block).
7. ### I How to prove that the L and S (of the total angular momentum commute?

I read here https://en.wikipedia.org/wiki/Spin%E2%80%93orbit_interaction that L and S commute. these operators have not the same dimension. Do they act on a common Hilbert space?
8. ### Which system to apply conservation of momentum to?

For this problem I was very confused whether conservation of angular momentum should be applied to the person, the swing or the person-swing system. It seems to me that there is no net torque on any of the three systems I listed above. However, it seems that the angular momentums of the three...
9. ### I How to Land a Tree Flat in 3/4 Rotation: Solving the Equations

Can anyone tell me how to solve this problem? I have the stem of a tree that is X feet tall. It's just a cylinder as the top and all branches have been cut off. I want to cut off the top portion such that when it falls, it will do precisely a 3/4 rotation and land perfectly flat. What fraction...
10. ### B Doubt regarding the terms used in the solution

In the solution, the term Lcm and Icm is used. Explain the meaning of these terms? I think cm stands for centre of mass. why that is used in the subscript?does the term angular momentum from the centre of mass of the sphere makes sense? Is the term Lcm and Icm stand for angular momentum of the...
11. ### Tong QFT sheet 2, question 6: Normal ordering of the angular momentum operator

My attempt/questions: I use ##T^{0i} = \dot{\phi}\partial^i \phi##, ##\dot{\phi} = \pi##, and antisymmetry of ##Q_i## to get: ##Q_i = 2\epsilon_{ijk}\int d^3x [x^j \partial^k \phi(\vec{x})] \pi(\vec{x})##. I then plug in the expansions for ##\phi(\vec{x})## and ##\pi(\vec{x})## and multiply...
12. ### I Problem with understanding angular momentum

I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved. imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...
13. ### Kepler's Third Law vs Conservation of angular momentum

The classic way to go about this problem would be to use Kepler's laws and thus find the new time period of earth. However I encountered this question in a test on rotational motion which deals with conservation of angular momentum. The equation used here would be I1ω1= I2ω2 Replacing I with MR2...
14. ### Perfectly inelastic collision of two moving and rotating disks

two moving and rotating, uniformly weighted disks perfectly inelastic collide. The disks are rotating in opposite directions (see the diagram) At the moment of their collision, the angles between their velocity and the line connecting their centers are 45 degrees. The velocities are therefore in...
15. ### A bullet collides perfectly elastically with one end of a rod

A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...
16. ### Why is the angular momentum negative in a disk and stick collision?

figure 11.12 I need someone to explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?p.s. ##\Delta\vec{L}_{total} = \vec{L}_{f} - \vec{L}_{i} = (-rm_{d}v_{df} +...
17. ### What's the source of increase in rotational energy of carousel?

A carousel has the shape of a circular disc with radius 1.80 m and a mass of 300 kg. There are two people with masses of 30 and 45 kg out on the edge while carousel rotates with the angular speed 0.6 rad / s. The people move towards the center of the carousel Calculations show that the...
18. ### I Changing the RPM of a frictionless spinning wheel in a box

Imagine a spinning wheel built into a hand size vacuum box. There is no friction between the axe bearings of the wheel and the box. Let's say that the wheel rotates with 60 RPM. Am I right if I assume: 1. The wheel continues to rotate, approximately as if in space. 2. It is not possible to...
19. ### What is the final angular displacement of a disk hit by two masses?

1) By conservation of linear momentum: ##m_1 v_1-m_2v_2=(m+m_1+m_2)v_{cm}\Rightarrow v_{cm}=\frac{m_1}{m+m_1+m_2}v_1-\frac{m_2}{m+m_1+m_2}v_2=\frac{3}{8}\frac{m}{s}##; 2) By conservation of angular momentum: ##-Rm_1v_1-Rm_2v_2=I_{total}\omega=(I_{disk}+m_1R^2+m_2R^2)\omega## so...
20. ### Angular momentum of a particles in the form of ##L = mr^2\omega##

##\vec{L} = \vec{P} \times\vec{r}## ##L = mvr sin \phi##, where P = mv Since ##\vec{r}## and ##\vec{v}## are always perpendicular, ##\phi## = 90. Then, ##L = mvr## At this point, I don't see how to get ##L = mvr = mr^2\omega##, using ##\omega = \dot{\phi}## I know that ##\omega =...
21. ### I Time derivative of the angular momentum as a cross product

I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...

29. ### Angular Momentum Vector and Torque Vector

In studying gyroscopic progression, the angular momentum vector is added to the torque vector. As intuitively these two vectors seem to be qualitatively quite different, how do we know that both vectors are in the same vector field and that they can be manipulated using the rules of vector...
30. ### Angular momentum of a baseball

k̂ direction = 0 kg*m^2/s ĵ direction = 0 kg*m^2/s î direction = (0.145kg) (20m/s) (6m) = 17.4 kg*m^2/s
31. ### Angular momentum of a falling ball

(L) = (radius) * (mass*velocity) velocity= 0+ (9.8m/s^2) (0.7s) = 6.86m/s (L) = (0.77m) * (2kg*6.86m/s)= 1.05 kg*m^2/s angular momentum points towards Polly
32. ### I Relativistic Energy of Rotating Thin Ring: Quick Qs

Quick question about the relativistic energy of a rotating thin ring, hoop or cylinder. Is there any reason why the relativistic energy would be anything different than ##E=\gamma_t m_0 c^2## where ##\gamma_t## depends on the tangential velocity ##v_t## observed by someone at rest with the...

41. ### How Do You Calculate the Ratio h/R for a Spinning Billiard Ball?

1. Homework Statement A spherical billiard ball of uniform density has mass m and radius R and moment of inertia about the center of mass ( ) 2 cm I = 2/ 5 mR^2 . The ball, initially at rest on a table, is given a sharp horizontal impulse by a cue stick that is held an unknown distance h above...
42. ### Conservation of Energy and Angular Momentum in a Rotating Train-Disk System

Homework Statement [/B] A train stands in the middle of a rotating disk with an initial angular velocity of $\omega_i$. The mass of the train is m and the moment of inertia of the train-disk is I. At one point the train departs on a straight track to a distance R from the disk's centre. (R...
43. ### Lagrangian for relativistic angular momentum

Hi everyone, I have a question that can't solve. Does exist a lagrangian for the relativistic angular momentum (AM)? I can't even understand the question because it has no sense for me... I mean, the lagrangian is a scalar function of the system(particle,field,...), it isn't a function FOR the...
44. ### Year1 Mechanics (angular momentum)

Homework Statement A circular plate with radius 0.5 m and mass 5 kg is hung on the wall, fixed at a point that is 0.3 m above its center. The plate can freely rotate about the fixed point with no friction. A very short-duration impulse of 5 N sec, along a direction that is tangential to the...
45. ### Determining Eigenvalues and Eigenvectors in a Coupled 2-Particle System

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...

50. ### Need help finding angular momentum of a particle

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...