Angular momentum Definition and 1000 Threads

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Suppose I have a system of two disks (identical in mass and size) one is fixed to a shaft at it's center point and rotating due to an external torque that's removed as soon as the rotational motion begins. The second disk is dropped from rest over the rotating disk and sticks together to the...

I am struggling to figure out how to calculate the expectation value because I am finding it hard to do something with the exponential. I tried using Euler's formula and some commutator relations, but I am always left with some term like ##\exp(L_z)## that I am not sure how to get rid of.

Not sure what to do here, except using the conversation of angular momentum. Even then, is angular momentum conserved in this case even after attaching an external object here? Else, what laws can I use to solve this problem? Using conversation of angular momentum: $$\dfrac...

Hello all! Hope everyone's been doing well! My question relates to the nebular theory of solar system formation. It is generally accepted that via the nebular hypothesis, matter in a nebula contracts on its own gravity and begins to spin, but I'm having trouble understanding why it must begin...

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

(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

In calculating the matrix elements for the raising operator L(+) with l = 1 and m = -1, 0, 1 each of my elements conforms to a diagonal shifted over one column with values [(2)^1/2]hbar on that diagonal, except for the element, L(+)|0,-1>, where I have a problem. This should be value...

As an analogue, if 5J of work is done on an object then the linear KE might increase by 2J and the angular by 3J, so the work is divided between the linear and rotational forms. Now suppose there is a sphere sliding on a frictionless surface. If an impulse of magnitude 1Ns is applied to the...

1) the motion equations for ##m_2## are: $$T-m_2 g=0 \rightarrow T=m_2 g$$ ##m_1##: $$T=m_1\frac{v^2}{r_0} \rightarrow \vec {v_0}=\sqrt{\frac{r_0 g m_2}{m_1}}\hat{\theta}$$ 2) This is where I am stuck, first I wrote ##m_2## motion equation just like before, but in polar coordinates...

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩

I have the moment of inertia for the core(initial) and full body(final) but my answer for the moment of inertia for the arms(initial) was incorrect. Arms(initial) moment of inertia:(1/12)(6)(1.7^2)=1.445 this is incorrect for some reason Core(initial) moment of inertia: .9558 Full...

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Summary: Consider a train carriage rolling along a curve that forms a left turn on the track. The carriage speed is directed along the y-axis (into the plane of the paper) in the figure. The trolley will have a tendency to curl in the curve in the specified direction. A flywheel is inserted...

Relevant Equations: Angular momentum density stored in an electromagnetic field: $$\vec{l}_{em} = \epsilon_0[\vec{r} \times (\vec{E} \times \vec{B})]$$ Electric field of an electric charge: $$\frac{q_e}{4\pi\epsilon_0}\frac{r - r'}{|r - r'|^3}$$ Magnetic field of a magnetic charge...

Hi, Since this is a question about COAM (Conservation of Angular Momentum), I will assume I can leave out the part on translation and just use the formula below: ##Initial Angular Momentum= Final Angular Momentum## whereby ##I = \frac {1}{12}ML^2## (of rod) So, ##\frac {1}{12}ML^2(1.5)=\frac...

I suppose that the principle of conservation of angular momentum holds also for a cloud of particles weekly interacting at low pressure, density and temperature. And it should be still applicable when the particles or the atoms would start condensing and forming fusion products or simply solid...

There is a cornering maneuver in rallying called the "Scandinavian flick" or the "pendulum turn". It involves steering away from the corner before actually steering into the corner. This creates a pendulum effect which makes the car turn more sharply into the corner. Sorry for the poor video...

I'm reading through "University Physics 14th edition" by Young and Freeman. Section 10.5 on angular momentum for a rigid body around a fixed axis of rotation is derived as L = Iω. However, it shows that this is only the case for the fixed axis of rotation being an axis of symmetry. In section...

In this video, around 2:28 He explains Earth maintain its same angular momentum even after sun disappears. I didn't get it. How Earth maintain its same angular momentum even after sun disappears?

a) Kepler's first law states that a planet like Earth displays an elliptical orbit with the sun in focus. Using M = dL/dt, prove that a planet cannot leave its plane of orbit. Note: M here is an externally applied torque that the sun exerts on the planet. diagram of the situation described b)...

3. Find the hamilton equations 4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved. I got in ##3##: How can I prove 4?

What I know is the following: The total angular momentum of the nucleus is just the total sum of the angular momentum of each nucleon. If the nucleons are even the total angular momentum in the ground state will simply be ##0+##. If the odd number of nucleons is close to one of the magic...

I was wondering why in the video the moment of inertia for the clay ball (upon collision) was simply 1ml^2. That is the constant for a hollow cylinder. The problem specifies that the object is a ball, so the cylinder classification makes no sense, and also I'm pretty sure clay is rather dense...

So, I was reading my textbook in the section regarding net torque, and they gave an example of a seesaw with one person at each end, and they said that there is a net external torque due to the force of gravity on each person. I completely understand that; however, when I was reading another...

Lets consider the angular momentum tensor (here ##m=1##) \begin{equation} L^{ij} = x^iv^j - x^jv^i \end{equation} and rortational velocity of particle (expressed via angular momentum tensor) \begin{equation} v^j = \omega^{jm}x_m. \end{equation} Then \begin{equation} L^{ij} =...

I had a question about the equation (1/2)mv^2... Why is the velocity squared? Why not simply (1/2)mv? Does it have anything to do with the intrinsic angular momentum ie does the intrinsic angular momentum change in anyway as velocity increases in a particular reference frame leading to the...

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...

n is the principal quantum number. l is the angular momentum quantum number. ml is the magnetic quantum number. The possible values of l are 2, 3, and 4. I'm not sure if l can be equal to 4. On the answer key, it shows l = 2, 3.

Why is angular momentum conserved for a charge in an electric field?

When do we use L=r x P and L=I x Omega (angular velocity)? in old 8.01x - Lect 24, I pasted here link of the lecture, which will take you at exact time (at 27:02)he says "spin angular momentum" in classical physics lecture and why? I expected to hear "angular momentum" vector. Normally...

1. A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it as shown above. Outside edge of the disk is moving at a linear speed of V and the clay is moving at speed v/2. How does angular momentum of system after the clay sticks compare to the angular...

Given the figure, how can i arrive to this formula knowing that angular momentum is conserved? I know that p = mv and L = p x r. So the initial momentum will be L1 = mV x R and the final momentum will be L2 = mv x r. I am not sure how R will equal to b since the distance between the...

I understand that in a system composed of two articles, the total angular momentum is: J = J1 + J2 From the operators: J^2, Jz, J1z, J2z，J^21z，J^22z, I get two possible sets of operators that commute: {J^2, Jz, J^21z, J^22z} and {J^21z, J^22z, J1z, J2z} What I don't understand is why the...

So,this is problem from David Morin's Classical Mechanics(Screenshot 1). I solved the problem. Then I went to see the solution in manual hoping for out of box thinking. As in screenshot 2 is solution by Morin. My question is why he conserves angular momentum about the point (R-h) below C.M...

Statement of the problem : "Using the definition L = r ##\times## p, prove that the direction of L is constant for an alpha (##\alpha##) particle whose scattering is shown in the diagram below. " Relevant equations : We are aware that the scattering takes place via a central force F = F(r)...

Good day dear forum, greetings from Argentina. I am studying the Lamb Shift, which says that in the atomic orbitals, an upward energy shift occurs due to an interaction of the electron with itself. This means that a level s can have an energy slightly greater than a level p. So far so good, but...

Homework Statement A system has a ball and a uniform rod. The rod is rotating about point X on a frictionless table until it strikes the ball. The rod stops and the ball moves away. Variables: Rod's mass: m1 Ball's mass: m2 Rod's original angular velocity: ω Ball's final velocity: v Rod's...

Statement of the problem : A ball shown in the figure is allowed to swing in a vertical plane like a simple pendulum. Answer the following : (a) Is the angular momentum of the ball conserved? No, the angular momentum ##L = mvl##, where m is the mass of the ball and v is its speed at an...

Can someone explain to me how we find it? Examples Y10X-= = |1,0>|1/2,-1/2> = √2/3 |3/2,-1/2> + √1/3|1/2,-1/2> Y11X-= = |1,1>|1/2,-1/2> = √1/3|3/2,1/2> + √2/3|1/2,1/2> Y2-1X- = = √4/5 | 5/2, -3/2> + √1/5 | 3/2, -3/2> I understand it goes like YlmX± = |l,m>|s,ms> = a |jmax, ?> + b |jmin, ?>...

Homework Statement Homework Equations For this problem I got the angular momentum conservation equations, mv(l+h)=mv'(l+h)+Ml2ω and momentum conservation equation as mv(l+h)=mv'(l+h) m=colliding mass,v and v' velocity before and after collision. M=mass of the rod. 2l=length of the rod...

Homework Statement Not an actual homework problem but a discussion that came up in class while we were learning about torque. A tall box is sliding across a surface with friction f, mass m, and velocity v. What equations would you use to figure out if the box would tip over while sliding to a...

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...

This question is about the conservation of angular momentum: So far, I have understood the reason as to why an object with a high moment of inertia has a small angular acceleration whereas an object with a low moment of inertia has a larger angular acceleration. The reason for this is that if...

Greetings. So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is \mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r} where \mu is the reduced...

Homework Statement 4 masses attached by a cross with no mass are spinning on a smooth table around the center of the cross. The distance between any mass to the center is L. The angular velocity is ω0. m1=m3,m2=m4 Suddenly, at t=0 (the time described in the picture), m4 disconnects from the...

Homework Statement Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic...

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...

Last week I posted in General Physics some questions about what happens in a collapsing gas cloud, and I was advised that total angular momentum is conserved. I thought of asking for extra clarification here, as that seems really amazing -- I apologize for asking the same thing twice. I use a...