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!
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...
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...
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...
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).
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?
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...
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...
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...
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...
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...
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...
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...
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...
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} +...
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...
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...
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...
##\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 =...
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...
To show that when ##[J^2, H]=0 ## the propagator vanishes unless ##j_1 = j_2## , I did (##\hbar =1##)
$$ K(j_1, m_1, j_2 m_2; t) = [jm, e^{-iHt}]= e^{iHt} (e^{iHt} jm e^{-iHt}) - e^{-iHt} jm $$
$$ = e^{iHt}[jm_H - jm] $$
So we have
$$ \langle j_1 m_1 | [jm, e^{-iHt} ] | j_2 m_2 \rangle $$
$$ =...
I have trouble solving this problem any help would be appreciated.Problem statement
##J=\frac{mr^2}{2}##
a) Determine the motion of yoyos for ##n=1,2,3##
The case for ##n=1## is simple, however, I am having trouble with ##n=2## and ##n=3##.
for ##n=2## I started by drawing all the forces...
I know how to work through this problem but I have a question on the initial separation of the wave function. Assuming ##\psi(\rho, \phi) = R(\rho)\Phi(\phi)## then for the azimuthal part of the wavefunction we have ##\Phi(\phi)=B\left(\frac \rho\Delta cos\phi+sin\phi\right)##, but this function...
I can not solve this problem:
However, I have a similar problem with proper solution:
Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...
Hello,
The question I have pertains to conservation of Angular momentum on a motorcycle. I know that the dynamic friction is less than the static friction, so when you are braking on a (say a motorcycle) and the wheels lock up, the bike is bound to fall over. This is the reason ABS (Anti-lock...
A cylinder of radius R spins with angular velocity w_0 . When the cylinder is gently laid on a plane, it skids for a short time and eventually rolls without slipping. What is the final angular velocity, w_f?
The solution follows from angular momentum conservation. $$L_i = I \omega_0 = L_f =...
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...
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...
Hello everybody!
I have a problem with this exercise when I have to find the possible angular momentum.
Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange.
$$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} =...
Summary: Different sign in the combination of two ##\textbf{1/2}## isospins with opposite third component
Hello everybody!
I was doing an exercise regarding isospin and I noticed something from the Clebsch-Gordan coefficients that made me think.
For example, if I consider the combination...
The green dot shows the position of the Earth at the instant the Sun disappears. The distance from the Sun, ##d##, is the Earth's orbital distance and the velocity ##v## is the Earth's orbital velocity.
When the Sun disappears the Earth heads off in a straight line at constant velocity as shown...
I'm actually not even 100% sure about the formulas, as in my book they explain j, s and l quite unclearly. Could anyone give me a proper explanation as how to see these and if I'm using them correctly.
What i tried to do was determine the proton and neutron angular momentum, spin and parity...
I don't have too much of a clue of how to begin the problem.
I first wrote the angular moementum of the system of particles: →M=∑mi(→ri×→vi)M→=∑mi(r→i×v→i). Then I know that the angular momentum from of the moving reference frame would have the velocity as the sum of the velocity of the frame...
Hi guys, so in Arnold's mathematical methods of classical mechanics p43, he defined the moment M_z, or L_z, the angular momentum, relative to the z axis of vector F applied at the point r is the projection onto the z axis of the moment of the vector F relative to some point on this axis...
Looking into the infinitesimal view of rotations from Lie, I noticed that the vector cross product can be written in terms of the generators of the rotation group SO(3). For example:
$$\vec{\mathbf{A}} \times \vec{\mathbf{B}} = (A^T \cdot J_x \cdot B) \>\> \hat{i} + (A^T \cdot J_y \cdot B)...
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...
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...
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...
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...
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...
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 $$a_\alpha =...
Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...
Hello,
in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...
Homework Statement
Considering the atom made of an electron and a positron. The spin-orbit Hamiltonian is:
$$H=\frac{e^2}{4\nu^2c^2r^34\pi\epsilon_0}\vec{L}\cdot\vec{S}$$
with ##\vec{L}## the relative angular momentum, with ##\vec{S}## the total spin and ##\mu## the reduced mass. Finding the...
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...