Angular Definition and 999 Threads

The Schwarzschild metric seems to model, for example, the earth’s gravity field above the earth’s surface pretty well, even though the Earth is not really a golf-ball sized black hole down at the center. Can the same be said for the Kerr metric? Does it model a rotating extended body’s gravity...

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...

[Mentor Note -- OP deleted his posts after receiving help. His posts are restored below] @ocean1234 -- Check your messages. Deleting your post is not allowed here, and is considered cheating. Problem was given: ##\theta(t) = at - bt^2 + ct^4## a) calculate ##\omega(t)## b) calculate...

Hi, I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...

The centre of mass of the rod would be at the middle of the rod i.e. at l/2=[50*10^(-2)]/2 The force responsible for torque will be acting downwards = mg The Torque = mg*l/2*sin(30) =mg*l/4 We know that Torque=I*alpha Hence alpha = mg*l/(4*I) Moment of inertia of rod about the end= ml^2/12 +...

Since the equations are, actually, the question, i will post the image with relevant equations here: it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms

θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t) When I calculate it out it is π /2 radians per second. Is this correct?

Angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved). There is a proof about this conservation?

is my solution correct?

"A smooth horizontal disc rotates with a constant angular velocity ω about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that point with velocity v0. Find the angular momentum M(t) of the disc relative to the point O in the...

given z(0) = 0 as well as ˙z(0)=0 How would one find the angular momentum along the x-axis in terms of t. Currently, I have formulated the following: $${\ddot{z} = \frac{g}{1+(\frac{4R}{s})^2}}$$

Hi With the 2-body problem relating to planetary orbits i have encountered the following ; the gravitational force on the reduced mass acts towards the large mass(Sun) and since it is a central force it exerts no torque about the fixed centre(Sun) so angular momentum is conserved. Conservation...

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...

Well I am pretty sure that the kinetic energy stays the same because in this case the velocity vector and energy make a ninety degree angle so no work is done, but I am lost about angular momentum. It could decrease maybe if the torque is clockwise while the ship is going in a counterclockwise...

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 a previous thread it was concluded that both torque and angular momentum are taken about a chosen origin, and these quantities are generally not invariant under translations of the origin (since ##\vec{r}## changes but ##\vec{v}## does not, etc.). The moment of inertia tensor doesn't...

Summary:: not constant spin How could I calculate the system lagrangian in function of the generalised coordinates and the conserved quantities associated to the system symmetries? I've been struggling for the case with not constant angular velocity, but I don't realize what I have to do...

I got the correct answer for the first part but I'm not sure why the answer for (b) is the same for (a). Wouldn't the rings falling off mean that I_f = \frac{1}{12}M_L L^2 only where I_F, M_L, L are the final moment of inertia, mass of the rod and length of the rod as opposed to I_f =...

I have tried this question and have gotten to an answer from the following steps So my angular separation is 2.85 millidegrees. Have I done this right with the formula I have made use of? Any help would be great, thanks!

This is a diffraction grating problem I have been given that I am trying to answer Made a attempt at it and just wanted to see if I done this correctly or not? I get an angular width of 0.71 degrees which is very small Any help is much appreciated! Thanks

Here is my problem I have given this a go and get 26.77 degrees as my angular position My concern is do I double this angle to get the angular width between both 2nd order maxima's (which would be 53.53 degrees) or do I just leave it as 26.77 degrees? Thanks for any help!

One part of König's theorem states that ##\vec{L} = \vec{L}_{\text{COM}} + \vec{L}^{'}##. The term ##\vec{L}^{'}## simply refers to the angular momentum wrt. the centre of mass. This is just a point, and doesn't have an axis implicitly associated with it (we have infinitely many choices!). The...

So in my textbook on oscillations, it says that angular frequency can be defined for a damped oscillator. The formula is given by: Angular Frequency = 2π/(2T), where T is the time between adjacent zero x-axis crossings. In this case, the angular frequency has meaning for a given time period...

Hi ; I have a few question regarding the conservation of linear and angular momentum. Would appreciate any help. 1 - When no external forces act are both linear and angular momentum conserved in all 3 directions separately or just the total linear/angular momentum conserved ? 2 - if I approach...

I have solved part a using the conservation of energy, getting a (correct) answer of 47.9 km/h, but I am unable to make headway with part b. Based on the flywheel rotating at 237rev/s when the car is moving at 86.5 km/h, I obtained omega = (237*2pi)v/24=62v. Differentiating both sides should...

I am reading Tong's lecture notes and I found an example in which there are several aspects I do not understand. This example is aimed at: - Understanding what is the analogy in field theory to the fact that, in classical mechanics, rotational invariance gives rise to conservation of angular...

Hi there ... How do I calculate the change of angular velocity, when demonstrating conservation of angular momentum? I mean the change of angular velocity depends on the ratio between the two (rotating) masses that moves a distance along radius, and the (rotating) mass of the system itself. In...

I'm trying to write a program to solve a series of dynamic equations, and ran into one stumbling block that seems like it should be easy to resolve. Basically, I'm trying to solve for the angular position of an object rotating around a circle, and to specify certain conditions on the circle...

In quantum mechanics one sees what J^2 can offer but why do we even consider looking at the eigenstates and eigenvalues of J^2 and a component of J, say J_z? Why don't we just use J?

Hello! I am reading some papers and I often noticed that it is mentioned that a strong magnetic field is able to decouple certain angular momenta from each other. For example in this paper: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.100.023003 they present a Hamiltonian (second column...

My understanding is that the terms are synonymous but I'm just wondering if there is a subtle difference between the two terms which I am unaware of.

As ##P=ccte## we can find final velocity considering a plastic collision ##m_0 . v_0 =(2m+m_0).V## But what about the angular velocity? Because, as the bullet hits the centre of mass of the string, it won't have angular velocity

Please refer to the image

Consider the following experiment from the point-of-view of classical mechanics and classical electromagnetism: An originally free electron then passes through a magnetic field that is oriented so that it causes the electron to turn to, say, the right. During the “turning” of the electron (a...

Tell me if I'm right: A) Angular momentum is conserved because there are no external torques. Linear momentum isn't conserved because gravity is acting on the spacecraft . Mechanical energy isn't conserved because it has to change between different orbits. B) Parabolic orbit...

Hi everyone I had this argument with someone told. About angular acceleration. His opinion: Since both pulleys are connected by a string then both of them must have the same angular acceleration. My opinion: Since a2 "acceleration of the second mass" is half a1. Then angular acceleration of the...

When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.

This is a very special case. In my 50 years studying physics I have never seen any discussion of photons having orbital angular momentum. Any angular momentum for photons in orbit around a black hole must be a GR question. I have not specialized in GR but I don’t recall any discussion of it. I...

Lets do it for the left (the right will be similar): ##r_{left}=[(L-a\sin\theta)\sin\phi,(L+a\cos\theta)\cos\phi]## so ##v_{left}=[-a\dot{\theta}\cos\theta\sin\phi+(L-a\sin\theta)\dot{\phi}\cos\phi,-a\dot{\theta}\sin\theta\cos\phi-(L+a\cos\theta)\dot{\phi}\sin\phi]##. Is this right?

The balls used in the game of lawn bowls are biased so that they travel in a curved path of decreasing radius. When a bowl in motion collides at a glancing angle with another bowl at rest, it -appears- to increase its velocity. Due to conservation of linear momentum the post-collision velocity...

I can solve the two particle system easily enough: Using ##j_1 = 1## and ##j_2 = 1##, the possible total angular momentum values are ##j = 2, 1, 0##. With ## m = -j , -j+1, ..., j ##, ##j = 2: m = 2, 1, 0, -1, -2 ## (5 states) ##j = 1: m = 1, 0, -1## (3 states) ## j = 0: m = 0 ## (1 state) I...

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...

Homework Statement:: Ball of mass mb and velocity vb hits rod of length L , Rod pivots about the center. What is the angular momentum aafter impact? Homework Equations:: I = 1/12 (mR^2) I = mR^2 See the attached figure. I understand the concept of linear and angular momentum separately but I...

The area of ​​Angular Land is described by inequalities | x + 5y − 28 | ≤30 and | 3x + 5y −34 | ≤30, where the point with coordinates (x, y) is the point distant x kilometers east of a certain reference point (in the case of x negative, this is a point | x | kilometers west) and y kilometers...

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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...

So this question has something probably due to the conservation of angular momentum. I am able to find the moment of inertia about the pivot, which is : $$\dfrac {1}{3}mL^{2}+\left( \dfrac {1}{12}ML^{2}+mL^{2}\right) =\dfrac {17}{12}ml^{2} $$ Now to find angular velocity when angle =0, how am I...

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.