Angular momentum Definition and 1000 Threads

Angular momentum is the product of its moment of inertia and its angular velocity. So can we infer that since angular momentum is conserved then if an object has more moment of inertia then it will have lesser angular velocity and vice versa? Since from common sense we can make out that moment...

Do we find out angular momentum for an object from a specific position? Since L= r x mv. R is the distance from the centre of mass. So can I say that angular momentum is 12 for a fixed position 4 metres away from centre of mass having mass of 1 kg and velocity of 3 metres per second north?

Hello all, I can understand the mathematics of this phenomena First, one can solve the Euler equations of motion numerically, using Runge-Kutta and plot the motion. Also, the path of the angular velocity vector will like on the kinetic energy ellipsoid and the angular momentum vector...

Homework Statement Hi everybody! I would like to discuss with you a problem that I am wondering if I understand it correctly: Find expressions for the cartesian components and for the magnitude of the angular momentum of a particle in cylindrical coordinates ##(r,\varphi,z)##. Homework...

1. Homework Statement When the 3.2-kg bob is given a horizontal speed of 1.5 m/s, it begins to rotate around the horizontal circular path A. The force F on the cord is increased, the bob rises and then rotates around the horizontal circular path B. (picture included) Homework Equations L = I ω...

For an equations such as this what goes into the θ? θ = sinθ or θ = θ? Let's say if the angle of displacement = 45° do I just plug 45° as θ into the equation below or should it be sin(45°)? Or is it θ = S/R ? ωf2 = ωi2 + 2 α (θf - θi)

I am having trouble visualizing which two tires of a car will be pushed down based on the angular momentum and torque of that car. Let's say if its angular momentum is point OUT while its torque is pointing UP in relations to the picture below. My guess is it's the two right wheels of the...

Homework Statement The period of a comet is 75.8 years. The perihelion distance is 0.596 AU (1 AU = 1.5 ⋅ 1011 m). The velocity at perihelion is vp = 5.45 ⋅104 m/s. a) Find the length of the major semi-axis of the elliptical orbit. b) Find the aphelion distance and the velocity at aphelion...

I need some clarification on a homework problem related to angular momentum. I understand how to calculate the angular momentum by using L= IW but when calculating the moment of intertia for the particle i don't understand why to use .5m as the radius instead of .4m due to being placed at the...

Imagine a hoop with mass M and radius R that will only roll without slipping on the floor. Place a point object with mass m on top of the hoop and then the system starts from at rest. Question: where does m leave M? If one fixes the hoop or let the hoop slide, solutions can be found using high...

Homework Statement A large wooden turntable in the shape of a flat disk has a radius of 1.50 m and a total mass of 100 kg. The turntable is initially rotating about its vertical axis through its centre with an angular velocity of 2.50 rad/s. From a very small height a 100 kg sand bag is...

Homework Statement A Person sitting firmly over a rotating stool has his arms stretched. If he fold his arms, his angular momentum about the axis of rotation : A.) Increases B.) Decreases C.) Remains Unchanged D.) doubles Homework Equations [/B]Conservation of Angular Momentum The...

Homework Statement An object is in uniform circular horizontal motion at the end of a chord of length L. Its tangential speed is v. The chord is pulled into length 0.5L in such a way that the tension in the chord remains constant. As a result, the tangential speed: a) remains constant b)...

Homework Statement A satellite is in a circular orbit of radius R from the planet's center of mass around a planet of mass M. The angular momentum of the satellite in its orbit is: I. directly proportional to R. II. directly proportional to the square root of R III. directly proportional to...

Homework Statement Two cars collide head on but offset from each others center of gravity. After the impact the two cars are locked together as one body. Due to the location of the collision point, the impact causes the two locked cars to spin clockwise. Car A- traveling west going 10 mph...

I'm looking through an old exam, and don't quite understand the solution given for one of the problems. We have given a wavefunction g(\phi,\theta) = \sqrt{\frac{3}{8\pi}}(-cos(\theta) + isin(\theta)sin(\phi)) and are asked what possible measurements can be made of the z-component of the...

Consider addition of two angular momenta J = J1 + J2 , with j1=j2=1. Find the eigenstates of the total angular momentum I jm > in terms of the product states I j1 m1 j2 m2 > in two ways (a) Make use of the tables of the Clebech _Gordan coefficients (b) The state with m1 = m2 = 1 must be a...

Homework Statement A thin rod of length l and mass M rotates about a vertical axis through its center with angular velocity ω. The rod makes an angle φ with the rotation axis. Determine the magnitude and direction of L (angular momentum). So we're given: mass - M, length - l, angular velocity...

Hello, See attached PDF for basic depiction of an issue I am currently working on. If lid starts off with angle = 0 (closed) and I fling it open until it hits the "stop" (interferes with bottom causing it to stop), how fast must lid being traveling to tip over entire assembly? From this I want...

So basically, I was doing my AP Physics 1 homework and came across the spinning ice skater question yet again. The question states, "An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the...

1. Homework Statement A small cube is sliding on a round dish (see attached figure) . The cube is always in contact with the (vertical) edge of the dish (which prevents the cube from falling outside the dish itself). There is friction between the cube and the dish. The dish can rotate around...

If one can't ever know all the three components of (QM) angular momentum, then can it even be considered as a "vector"? Is it only cause it transforms as a vector in a coordinate transformation?

Homework Statement A projectile of mass m is launched with an initial velocity [PLAIN]https://www.webassign.net/images/boldv.gifi making an angle θ with the horizontal as shown below. The projectile moves in the gravitational field of the Earth. Find the angular momentum of the projectile...

Homework Statement Word for word, from the problem: "A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman...

I'm confused about situations involving rotating frames in which the angular momentum is conserved and the initial velocity does not change. I'll make an example. Take a rotating carousel (constant angular velocity) with no friction on it and a ball. At the initial time instant the ball has the...

Homework Statement A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0m/s flies into this door at its center and bounces back at 2.0m/s in the opposite direction...

Homework Statement In the figure, a small 0.235 kg block slides down a frictionless surface through height h = 0.471 m and then sticks to a uniform vertical rod of mass M = 0.470 kg and length d = 2.36 m. The rod pivots about point Othrough angle θ before momentarily stopping. Find θ. Homework...

Torque ##\tau## should be in the same direction as the change in angular momentum ##\Delta L##, but the following example seems to suggest otherwise. Consider a cone rolling on its side without slipping on a flat surface. Let the apex be the origin and the initial coordinate of the center of...

Consider a central force. The central force is radial by definition, so ##\vec{F}=f(r) \hat{r}##. Therefore, by definition, the acceleration caused by the force, in the direction of ##\hat{\theta}## must be zero, ##\vec{a_{\theta}}=0##. In presence of central force angular momentum is...

I'm trying to understand the relations between the existence of Coriolis force and the conservation of angular momentum. I found this explanation on Morin. I do not understand the two highlighted parts. In particular it seems that Coriolis force is there to change the angular momentum of the...

For the rotation of a rigid body about a fixed axis z the following holds. $$\vec{\tau_z}=\frac{d\vec{L_z}}{dt}= I_z \vec{\alpha} \tag{1}$$ Where \vec{\tau_z} is the component parallel to the axis z of a torque \vec{\tau} exerted in the body; \vec{L_z} is the component parallel to the rotation...

Homework Statement A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with...

I find difficulties in identify the forces acting behind the acceleration of objects that are considered consequence of conservation principles (for istance of KE and angular momentum). I'll make an example to explain. The same string-mass system is linked to a rod. In case (a) a force pull the...

I don't understand why the conservation of angular momentum can imply an acceleration, in absence of a force. Consider for istance planetary motion. The angular momentum \vec{L} of the planets is conserved and that means \mid \vec{L} \mid=mr^2 \dot{\theta}=mrv_{\theta} is conserved too...

Homework Statement How much torque is needed to change the speed of spinning rate of a 3.50 kg sphere with a radius of 7.50 m from 900. rpm to 200. rpm in 3.0 s? [-1924  -1.92 x 103 Nm] Homework Equations t = I * α I = (2/5)mr^2 t = F * r The Attempt at a Solution just can't get a crack at...

In the Griffiths textbook for Quantum Mechanics, It just gives the ladder operator to be L±≡Lx±iLy With reference to it being similar to QHO ladder operator. The book shows how that ladder operator is obtained, but it doesn't show how angular momentum operator is derived. Ive searched the...

I'm reading Sakurai's "Advanced Quantum Mechanics" (which is different from his "Modern Quantum Mechanics"). In chapter 3, which is about the Relativistic Quantum Mechanics of spin 1/2 particles, after discussing the covariance of the Dirac equation, he goes on to give some examples to clarify...

Homework Statement Consider the rigid body in the picture, rotating about a fixed axis z not passing through a principal axis of inertia, with an angular velocity \Omega that can vary in magnitude but not in direction. Find the angular momentum vector and its component parallel to z axis (...

Consider the rotation of a rigid body about a fixed axis z, not passing through a principal axis of inertia of the body. The angular momentum \vec{L} has a parallel component to the z axis (called \vec{L_z}) and a component perpendicular to it (called \vec{L_n}). I have some doubts on...

Homework Statement [/B] Consider a barbell with two equal masses m that rotates around a vertical axis z not passing through its center with angular velocity \vec{\omega}. The barbell is forced to stay in this position by an appropriate support. Identify the forces exerting torques on the...

One of the best explanations of orbital angular momentum for the electron comes from Dirac himself. At around 39:30 of this youtube video (you will need headphones, but it is well worth it), Dirac talks about the non-commutation of operators, how quantum mechanics is more general then classical...

Homework Statement Homework Equations Find Angular Momentum. How to find velocity of a particle. The Attempt at a Solution If i differentiate with `dt` both sides, I'm getting velocity y-component=velocity x-component. Then i feel helpless:cry:

If we were to assume that the electron moves around the proton with radius a, the Schrodinger equation becomes: ##\frac{1}{a^2}\frac{d^2\psi}{d\phi^2} + \frac{2m}{\hbar^2}|E|\psi = 0## The question in my textbook asks me to solve the above equation to obtain values of energy and angular...

I 'd like to clarify some doubts about the rotational motion around a fixed axis of a rigid body, in the case the angular momentum vector \vec {L} is not parallel to the angular velocity \vec {\omega} . In particular, consider a horizontal barbell with two equal masses m , forced to rotate...

Homework Statement Hi everyone! I'm preparing an exam and reviewing some old problems until then, to clear up some misconceptions I might have! A stiff massless bar is frictionless rotatable about a point O. Two mass points m1 and m2 are fixed at its ends, respectively at distances d1 and d2...

If an electron does not orbit the nucleus in the classical sense, then how can we define an angular momentum operator that is analogous to the classical angular momentum? \hat{\mathbf{L}} = \hat{\mathbf{r}} \times \hat{\mathbf{p}} This angular momentum depends on both the position of the...

Homework Statement The torque ## \vec{τ} ## on a body about a given point is found to be equal to ## \vec{A} × \vec{L} ## where ##\vec{A}## is a constant vector, and ##\vec{L}## is the angular momentum of the body about that point. From this it follows: (Multiple answers correct) (A) ##...

Homework Statement Homework Equations I guess kepler's law but most importantly conservation of angular momentum are key here. The Attempt at a Solution [/B] I put down E as the answer, but the solutions have D as the correct answer. Why is this the case? Thanks in advance for the help!

Homework Statement A uniform stick 1.00 m long with a total mass of 270 g is pivoted at its center and is initially stationary. A 30 g piece of clay is thrown at the stick midway between the midpoint of the stick (pivot) and one end. The clay piece is going at 50 m/s and sticks to the stick...

Hi everybody! I'm preparing myself for upcoming exams, and I struggle a little with conservation of angular momentum. Can anybody help me understand how to solve such problems? 1. Homework Statement (for a better comprehension, see the attached image) We have a wooden cylinder of mass mZ =...