Angular momentum Definition and 1000 Threads

Homework Statement A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ]. (i) Explain why we can interpret this as a particle moving...

Homework Statement Homework Equations I= sum m r2 L= r p or L=I W The Attempt at a Solution I= m1 r12 + m2 r22 I= 5.20 (0.9)2+ 2.20(0.9)2= 5.994 kg.m2 Then I used the second equation of second momentum L(Angular momentum) = I W L= 5.994 x 4.60 In the solutions sheet, he used the first...

Homework Statement (This is a problem I myself created, so it may sound a bit trivial/stupid.) A particle of mass m in the xy plane has velocity v and a radius vector r with respect to some origin. After some time Δt, the same particle has velocity v and a radius vector r' with respect to the...

I wonder what would the angular momentum vector look like for these gears. As it rotates, there is no clear direction on where the angular momentum vector is pointing. This object is symmetric. Here's the video about these.

Homework Statement A 4 g bullet traveling at 500 m/s strikes a disk of mass 1 kg and radius 10 cm that is free to rotate around an axis passing through its center. The bullet’s incoming path is 5 cm above the rotation axis and the bullet comes to rest in the position shown in the figure. At how...

So a light particle is orbiting a massive particle by gravity. We take both particles as spot particles. The light particle makes an eccentric orbit where maximum radius of the orbit equals 2 and minimum radius equals 1. I suppose the mass of the massive particle such that the speed of the...

Homework Statement Imagine that you are standing on the edge of a cliff looking out over the vista… a sudden gust of wind nudges you off balance and you start tilting out over the edge of the cliff…. Yikes! You start wind milling your arms to regain your balance. A) do you rotate your arms...

Homework Statement "The flywheel rotates with angular velocity of w=0.005theta^2 rad/s. Determine the angular acceleration after it has rotated 20 revolutions. Homework Equations I thought the equations were all but self-evident using the problem description! (See below.) alpha=dw/dt The...

Consider a flat 2D rigid body rotating about an axis perpendicular to the body passing through a point P that is (1) in the same plane as the body and (2) different from the body's center of mass (CM). In this case does Theorem 7.1 (eqn 7.9) still apply? In the last step of the derivation of...

Homework Statement Two ice skaters of mass ##m = 50\,\mathrm{kg}## each are moving towards each other frictionless on parallel paths with a distance of ##3\,\mathrm{m}##. They both have a velocity of ##v_o=10\,\frac{\mathrm m}{\mathrm s}##. Skater 1 is holding a massless rod of length...

Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...

Hi I have seen an example of commutator of the Parity operator of the x-coordinate , Px and angular momentum in the z-direction Lz calculated as [ Px , Lz ] ψ(x , y) = -2Lz ψ (-x , y) I have tried to calculate the commutator without operating on a wavefunction and just by expanding...

Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...

Homework Statement Let ##\left|\psi\right\rangle## be a non-degenerate stationary state, i.e. an eigenstate of the Hamiltonian. Suppose the system exhibits symmetry for time inversion, but not necessarily for rotations. Show that the expectation value for the angular momentum operator is zero...

Some observed neutron stars rotate hundreds of times per second. Speeds at the surface of these stars are as much as 15% the speed of light. These huge speeds are generated because angular momentum is conserved when a large rotating pre-super nova star collapses into a neutron star. The...

My textbook says that for a central force at the origin, the angular momentum is constant, because the derivative rxF is zero since F points radially outwards so it is in the same direction as r. Ok, but what about the angular momentum about a point other than the origin, or the angular momentum...

Hi, I am a physics student and i was asked to answer some questions about Hydrogen atom wavefunctions. I hope you can help me (sorry for my english, is not my motherlanguage, i will try to explain myself properly) 1. In order to find hamiltonian eigenfunctions of Hydrogen atom, we make then be...

Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...

OK, I understand that 'spin' is just an unfortunate name some someone gave to a particular quantum property and that particles do not actually spin. I also accept that I may never be able to understand what spin is without also understanding the mathematics involved. However, I am also told...

Hi Folks, Problem Statement How would one use the conservation of angular momentum to explain the attached picture? The rod is held fixed horizontally..the person holds on to the cork and then let's go...apparently the glass is saved due to this conservation... Relevant Equations Momentum...

Hi Folks, How would one use the conservation of angular momentum to explain the attached picture? The rod is held fixed horizontally..the person holds on to the cork and then let's go...apparently the glass is saved due to this conservation...

Homework Statement a spool of radius R1 and R2 (R2>R1) is kept on hortizontal surface. A force f= 2t N (where t is time ) acts on the inner radius tagentially find the angular momentum of the system about the bottomost point of the spool. Homework Equations v=u+at W=Wi+alpha(t) L=IW+mvrThe...

Homework Statement A uniform rod of length L and mass M hangs at rest from a frictionless pivot. The rod is hit a distance 0.8L below the pivot by a particle of mass m moving perpendicularly to the rod at speed v; the particle sticks to the rod. Following the collision, the maximum angle...

I am currently trying to model collisions of rigid balls. I have successfully been able to calculate collisions that only deal with linear momentum, but have run into trouble when I want to calculate angular momentum (e.g. when ballA glances the top of ballB, both balls should start spinning a...

Homework Statement A hydrogen atom is in the 3d state. Determine the orbital angular momentum. Homework Equations unnecessary The Attempt at a Solution I already know how to figure this out and have an answer but WHAT ARE the units?! It's not kgm/s^2!

Hi guys, This is basically a quick question to hopefully find some pointers on a topic I've been browsing the internet on to not much success. Basically the topic I'm trying to find more information on is the angular momentum problem with the "nebular hypothesis" of the formation of our solar...

Homework Statement Suppose we have a wavefunction with n=4. If we measure the orbital angular momentum along the z-direction(no spin in this problem) and get 2*hbar then what are the possible values of the total angular momentum and what is the most general wavefunction after the measurement...

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.0×104 m/s when at a distance of 2.6×1011 m from the center of the sun, what is its speed when at a distance of 5.2×1010 m . Express your answer using two significant figures I applied...

Homework Statement The nucleons in a nucleus have a net orbital angular momentum ##L = 1## and spin angular momentum ##S = \frac{1}{2}##. What are the possible values of the total nuclear spin ##J##, i.e. the total angular momentum of the nucleus, and what are the possible values of ##J_z## in...

I don't typically do this, but attached is a figure with a problem statement. This is not homework because I have already solved it! My question is a subtle one. Please see the attachments, one is the question and the other is my solution. I know my solution is correct, but at the end of...

The "color force" doesn't actually change the color of quarks because they don't actually have any color. We use the word "color" non-literally here. Now, I'm told that quarks don't "actually" "spin" either, so again, I infer that it's a term used out of convenience, but I'm also told that they...

Suppose you have a ball on a string, and you make the ball to move around in a circle. The force on the ball is caused by the tension of the string, and is called the centripetal force F = mv^2/r. If you were to let go at any moment, the ball would stop rotating and move with linear velocity...

My textbook talks about the average angular speed that ω = angular displacement / time for the angular displacement to take place. So the question is like there is m1v1 = m2v2, can the velocity be instead average angular speed to have the conservation of momentum equation like this? m1ω1 = m2ω2

I've been asked to replace a professor for a couple of classes in an undergraduate quantum mechanic course. I have to present some topics on angular momentum, including the addition of angular momentum. I have no problem with the general theory and can present it just fine. But I would like to...

Hello everyone, currently working on a physics project. I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can...

Homework Statement A 500.0-g bird is flying horizontally at 2.25 m>s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top(Fig. P10.85). The bar is uniform, 0.750 m long, has a mass of 1.50 kg, and is hinged at its base. The...

Homework Statement Particle is in a state with wave function \psi (r) = A z (x+y)e^{-\lambda r}. a) What is the probability that the result of the L_z measurement is 0? b) What are possilble results and what are their probabilities of a L^2 measurement? c) What are possilble results and what...

This (photo) is a very typical example of conservation of angular momentum, but my trouble arrises from trying to prove that the difference of energy will have to correspond to work, by calculating the work done by you to alter the moment of inertia. I have spent a lot of time in this, but I...

I've been reading a book that talks about the angular momentum of an extended body around a point 0 (H_0) being made up of the moment-of-momentum of an equivalent particle (representing the total mass at the centre of mass) with respect to the point 0 and the angular momentum around the centre...

Hi there guys. I'm new here, and I'm learning physics by myself. Please, if the answer to my question is too obvious, be kind hee hee, I'm a 13 and trying to learn physics by myself. So, I know that we have ## \textbf{L}= \textbf{r} \times \textbf{p} ## Then, we can write ## \frac{d}{dt}...

Hello everyone! I have a problem , to which I do not understand the law of conservation of angular momentum... I searched this problem on the web and it is obvious that I am making the mistake. So we have a rod of length ##L## and mass ##m## that is lying on a horizontal frictionless table. We...

Hi there, A friend of mine is creating a physics engine in java (mostly as a challenge I believe). Today he asked me a question about the results of collisions between objects. For example, imagine that these 2 objects collide: The results of such a collusion would be something like this...

This is from text [Introduction to Lagrangian and Hamiltonian Mechanics] on NTNU opencourse. Annnnd... I don't use english as my primary language, so sorry for poor sentences. I can't get two things in here. First, at (1.12) I can't understand how L dot derivated like that. Since I know...

Hello! I'm trying to derive the linear velocity vector from the position vector and the angular momentum vector. I've seen on the internet that V = W x R (V,W and R are all vectors and x is the cross product) but I cannot for the life of me derive it! I've tried doing it by writing out the...

I know that magnetic fields can align objects with spin. In that case, if we suspend an object and turn on a magnetic field such that a significant number of electrons become aligned with the field, could we observe a macroscopic change in angular momentum?

Hello. The quantum mechanics textbook shows the relation of J1 + J2 + J3 ≠ J1 + (J2 + J3). I believe Ji is total angular momentum operator for ith group of electrons (but actually I have not seen J1 operator while I have seen J12 operator so far). I don't know how to prove J1 + J2 + J3 ≠ J1 +...

Say there is a man swinging in space on a rope attached to a pivot. The man is rotating at some constant angular speed w. Now he climbs up the rope at some constant speed v. Apparently the angular momentum is conserved. As a result his speed increases. However, how does his speed increase if...

Homework Statement [/B] I messed up the original thread in terms of information, so I made a new better one. Ok here goes: I have a problem where a right circular cylinder with diameter .115meter and a mass of .03kg is rotating at 300 rev per min. Now an Ant which weighs .01kg collides with...

https://en.wikipedia.org/wiki/Balancing_of_rotating_masses See the image in that page. I know intuitively why a direction of torque is counterclockwise-because of a centrifugal force. But an direction of angular momentum of that shaft with attached weights (ignore the shaft mass) is southeast...

This is rewording of a question on a test I've just done. A vinyl record on a turntable has radius R=0.15 m, mass M=1.5 kg. The angular speed is reduced from 33.3 rev per minute to zero as a result of an applied torque, in 7 seconds. Moment of inertia given as I=1/2 M R^2 Calculate a) angular...