Angular Definition and 999 Threads

Many texts state that in an elliptic orbit you can find angular momentum magnitude as $$ L = r m v = m r^2 \frac {d \theta} {dt} $$ I wonder if $$ v = r \frac {d \theta} {dt} $$ is valid at every point. I understand this approximation in a circumference or radius r but what about an arc...

Hello everyone! I've been watching the following Walter Lewin lecture, the part that illustrates my question is part 17:19 of the video Most things have made sense during this lecture, but one persistent question I have is the following: why does the bicycle tilt toward the inside of the...

I'm making a MATLAB code to propagate a gaussian field in the angular spectrum regime (fresnel number >> 1). After Fourier transforming the field, you propagate it: $$U(k_x,k_y,z) = U(k_x,k_y,0)e^{ik_z z}$$ The thing that I am having trouble with is the propagation factor, I have looked at this...

Summary: Consider a body which is rotating with constant angular velocity ω about some axis passing through the origin. Assume the origin is fixed, and that we are sitting in a fixed coordinate system ##O_{xyz}## If ##\rho## is a vector of constant magnitude and constant direction in the...

(OBS: Don't take the index positions too literal...) Generally it is easy to deal with these type of exercises for discrete system. But since we need to evaluate it for continuous, i am a little confused on how to do it. Goldstein/Nivaldo gives these formulas: I am trying to understand how...

I am using the following formula to solve this problem. $$ L_a= L_c + \text { (angular momentum of a particle at C of mass M)}$$ Because the point C is at rest relative to point A, so the second term in RHS of above equation is zero. Hence, the angular momentum about A is same as angular...

I think the the time given doesn't matter since no torque is acting on the system, but not sure. Therefore, all we need is to determine the angular momentum about the axis passing through O and perpendicular to the plane of disk. This will involve finding the moment of inertia of smaller disk...

When given a small displacement ##x##, the equation for m is: (i) N sin θ = m.a where N is the normal force acting on the ball and θ is angle of the ball with respect to vertical. (ii) N cos θ = m.g So: $$\tan \theta = \frac a g$$ $$\frac x R = \frac{\omega^{2} x}{g} \rightarrow \omega = \sqrt...

Hello everyone, I have a doubt regarding the conservation of angular momentum. When dealing with collisions between two objects, if the net external force is zero we know that the linear momentum is conserved; even when the system is not isolated, for instance because of gravity acting on the...

I thought the answer is B because the angular momentum in conserved in all 3 pictures. <Moderator's note: Use of external servers not allowed. Please upload all images to PF.>

Suppose we have a rotating body like a bicycle wheel in space away from gravity. This body stops after a while due to friction between the wheel and wheel axles. Is not the conservation of angular momentum violated?

I have no idea how to go about this. Any help would be appreciated thanks :) Edit: I converted the 1.5 rev/s to rad/s = 9.4 rad/s

Hello to everyone, first of all shame on me I has to ask and can not figure out it by myself... The problem is I am trying to code game where two homogenous discs with same mass and same diameter, no fricition due to gravitational forces, can collide. I can figure out the speed and direction...

One of the component of angular momentum operator is ##\hat{L}_{x}=\hat{y} \hat{P}_{z}-\hat{z} \hat{P}_{y}## I want it's position representation. My attempt : I'll find the representation of the first term ##\hat{y} \hat{P}_{z}##. The total representation is the sum of two terms. The...

I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...

a) We use the definition of linear speed in terms of angular speed: v = r*omega omega_f = v/r = (1.25 m/s)/(0.025 m) = 50 rad/s omega_0 = v/r = (1.25 m/s)/(0.025 m) = 21.55 rad/s b) We use the definition of linear speed: v = d/t d = vt = (1.25m/s)(74 min)(60 s/1 min) = 5.55 km c) We use the...

I am trying to build a simulation of a car engine and wheels for a game project. My model is currently this: Engine outputs a torque -> this spins up a flywheel over time (the physics step of 1/60s) -> the flywheel is coupled with the clutch and thus transmission -> the transmission multiplies...

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...

In other words, is there a rotational orientation of each atom in a monatomic gas (and corresponding rotational speed conserving angular momentum) that affects collisions, or does a substance need to have at least 2 atom particles to have the orientation/rotational ability to have particle...

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...

I understand that angular velocity is technically not a vector so does that mean the cross product of the radius vector and the angular velocity vector, the tangential vector, is also not a vector?

I don't understand why my solution is wrong. Here is my solution. $$ r_{\theta} = R\cos{\theta} \vec{i} + R\sin{\theta} \vec{j} $$ $$ v_{\theta} = v\cos(\theta + \frac{\pi}{2}) \vec{i} + v\sin(\theta + \frac{\pi}{2}) \vec{j} $$ $$ p_{\theta} = mvR(-\sin{\theta}) \vec{i} +mvR(\cos{\theta}...

Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion? My intuition is that, whether considered in a classical sense or quantum sense, the speed of a given electron in its motion within an atom will be constant and...

If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...

Dynamics Rigid body Kinematics problem, looking for angular acceleration of link BD and ED. AB has constant angular velocity of 45 rad/s CCW. Could y'all verify any mistakes in my solution? Thanks!

My line of thinking is as follows: \omega_{PQ} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2} Similarly for rod ##QR## \omega_{QR} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2} Is my reasoning correct?

First case, descends with the wheel: mgh = .5(I)(w^2) ———- GPE converted to wheel energy w = .1095. ———- rotation result is .1095 Second case, allow to free fall and impulse: mgh = .5(m)(v^2). ———- GPE converted to kinetic energy v = 7.746 ———-...

for (a) ##T=\frac {2\pi}{\omega}## $$\omega=\frac {2\pi}{T}$$ $$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$ $$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$ for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...

I(i)w(i)= I(f)w(f) I(i)= 1.08 x 10-3 kg·m2 w(i)= 0.221 rad/s I(f)= mr^2 + I(i) = (5 x 10^-3)(.138)^2 + (1.08 x 10^-3) (1.08 x 10-3)(.221) = ((1.08 x 10^-3)+9.22 x 10^-5))w(f) w(f) = (2.3868 x 10^-4)/(0.00117522) w(f)= 0.203094 rad/s This is my attempt; however, I cannot seem to get it...

I calculate the gravity force F = mg = (-9806.6)*(5.26e-1) = -5158 (mm^2*kg)/s^2 I get the moment M = F*r = (-3.5e5)*(-6.81e1) = 3.5e5 (mm^2 * kg) / s^2 Where r is the y coordinate distance from origin to centroid J = (Ix'...

https://www.physicsforums.com/threa...f-a-translating-and-rotating-pancake.1005990/ So,I think I posted this in the wrong place. So, I will move it to here. Here, in post #6, it is stated that ##\int R dm = M R##. As far as I know, R change from time to time and it is not constant. Hence, isn't...

So far I have: The velocity of the belt will be the same for pully A and D, so we can calculate the angular velocity of pulley D: ## V_A = V_B ## ## \omega_A r_A = \omega_D r_D ## ## ((20*3)+40)(0.075) = \omega_D (0.025) ## ## \omega_D = 300 Rad/s ## My next step was to determine the angular...

Hi everyone :)! I resolve this problem with components method and trigonometry method. My results with components method its okay, but i can´t obtain the correct VE velocity. Im sure that the problem its in the angles, but i don't know how to fix it. The correct answers: -Angular velocity...

Hello, I am trying to solve a problem involving a mass with known moment of inertia about an axis with a lever arm at angle theta and length r with a non-constant spring force acting at the tip of the lever arm and fixed distance away from the axis of rotation. I am wondering what the best...

Hi! everyone! ;) I have a problem with the development of this problem. I need to resolve it with 2 procedures: trigonometry and instant centers. My advance can be see in the next image: The instant centers procediment its (1) up and trigonometry procediment its (2) down. I know that the...

I am currently reading David Morin book and found this statement : ##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM" Is it really alright to choose the center of a...

Hello, I am currently working on a computer program to move on object undergoing circular motion in a spiral of decreasing radius. I hope this is illustrated clearly below (forgive me but it is a sketch and thus not precise in scale): The scenario is as follows: 1. The object starts angular...

There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...

I was thinking a little about how the absorption of angular momentum occurs from the point of view of QM. For example, suppose we have an atom A and an electron $e^-$. The electron $e^-$ is ejected from a source radially in direction of the center of the atom. Suppose that the atom has net...

##\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 =...

While physics is generally believed to be CPT symmetric, there are processes for which such symmetry is being questioned - especially the measurement. One of examples of (allegedly?) going out of QM unitary evolution is atom deexcitation - we can save its reversibility by remembering about...

I have read Classical Mechanics book by David Morin, and there are some parts that I do not understand from its derivation. Note : ## V## and ##v## is respectively the velocity of CM and a particle of the body relative to the fixed origin , while ##v'## is velocity of the particle relative to...

Hello. I am not familiar with spherical trigonometry while I am reading a solution in a GR problem book. It reads, I study spherical trigonometry on Wikipedia and some other sites, but I am still not sure how to calculate the angular excess. First, is angular excess equivalent to spherical...

Hi! I would like to know how I could define an equation for α with given the two lengths of the rods and angle theta (θ). I sketched the situation below, the problem arises when the rod Lab has pasts the 180 degrees. Like to hear.

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...

Hello! I found this formula in several places for the total angular momentum of a particle with intrinsic spin 1/2 and angular momentum l=1 in the non-relativistic limit: $$\frac{1}{\sqrt{4 \pi}}(-\sigma r /r )\chi$$ where ##\sigma## are the Pauli matrices and ##\chi## is the spinor. Can someone...

I made a new version of the falling cat video, with narration. It explains how cats turn around while having zero net angular momentum during the fall:

I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis. I've seen the following approach...