Angular Definition and 999 Threads

Suppose there is a disc rotating around axis through its centre, with force F acting on the rim. The equation of torque is simple, however, what happens if it is written about an arbitrary point on the rim? How can the angular acceleration about that point be understood? Do I have to transition...

What does this formula mean ? I can't find it anywhere. Vmax=Wmax x L. And Wmax=Wθmax. It came up in the pendulum chapter. L is string length.

So my first approach was to use L=Iw. Computing I, moment of inertia,I=$$I_{center} = \frac{md^2}{4}$$ $$L_{center} = I_{center} \omega = \frac{md^2\omega}{4}$$ And hence I obtain an answer. However, when I further thought about the question, I realised that L is a vector and I can probably do...

Hi, Unfortunately, I can't quite work out the terms in the task The expression in the integral (4) corresponds to the Lagrangian and since ##t## and ##\varphi## are cyclic variables, the following follows: $$-\frac{d}{dt} \frac{d L}{d \dot{t}}=0 \quad \rightarrow \quad -\frac{d L}{d...

Proof: Let ## \epsilon=0 ##. Then the unperturbed equation is ## \ddot{x}+x=0 ## and the general solution is ## x(t)=A\sin\omega t+B\cos\omega t ## where ## \omega=1 ## is the angular frequency with the constants ## A ## and ## B ##. With the initial condition ## x(0)=0 ##, we have that ##...

I'm trying to understand if I'm making a mistake because the answer in the textbook is ##10.2~km/s##. Here's my attempt at a solution: The subscript A is intended to mean apogee and P is for perigee. ##v_A = 3~km/s## ##w_A = \frac{v_A}{r_A} = 7.5 \times 10^{-5}~rad/s## ##L_i=L_f## ##I_Aw_A...

Let the mass of the ball m₁ and the disk m₂ m₁vrsinθ = I₁ω + Ι₂ω I₁ = m₁r² and I₂ = ½m₂r², r=3m, rsinθ = 2m. Is this a correct approach? if not, what is? Can this be solved using energy conservation?

## a_t = r\alpha ## ## 9.8 \: m/s^2 = (.25 \: m)\alpha ## ## \alpha = 39.2 \: rad/s^2 ## Since the cylinder rotates through 20.01 radians after 5 m of cord has been removed: ## \omega_f^2 = \omega_0^2 + 2\alpha(\Delta\theta) ## ## \omega_f^2 = 2(39.2 \: rad/s^2)(20.01 \: rad) ## ## \omega_f...

Initially I thought a good strategy for solving the problem would be to find the torque on the pulley to get alpha (angular acceleration) and then use alpha to find the tangential acceleration of the pulley which is equal to the block's acceleration. I'm not sure if this is correct. Let ##...

In figure AO = OB = 4m. C is the midpoint of AO. The rod rotates with a velocity of 5 rad/s about the axis PQ. What will be the rotational velocity of the remaining rod if AC part is suddenly dropped from the rod? Assume that the mass of this uniform rod is M.

I started checking for angular momentum conservation. The initial state has ##J_{in}=S_{\phi}=1##. The pions in the final state all have 0 spin, so the total angular momentum in the final state comes only from orbital momentum. Call ##L_{\pm}## the orbital momentum of the charged pions orbiting...

Hello. I am reading Classical dynamics of particles and systems(Book by Stephen Thornton), I have problem in understanding the coordinate system they choose to define angular momentum for a rigid body. At the beginning of the chapter 11 they say: They use 2 coordinate systems to describe motion...

As someone who only knows elementary physics (so pardon me for maybe getting some things wrong), I have a question which troubles me and I'm having difficulties in finding an answer to: If a plane takes off at the equator and flies east to west, counter to earth's rotation, how it would be able...

I know that the speed of the centre of mass is ##v_{cm}=(mv_0+mv_0)/(2m)=v_0##. But I don't know how to proceed from here with the angular speed around the centre of mass of the system. Any help will be appreciated.

This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod. Is there a classical thought...

Hello, simplified the Angular momentum problem that comes up when i try to solve a mass moving inward or outwards and it does not conserver the angular momentum properly. I have tried this is many software by now, or by someone else and we all have found that there is no angular momentum...

How should I calculate the angular momentum carried by a current carrying circular wire? Is it correct to consider the angular momentum of the electrons moving with drift velocity? Like ##L = n m_e v_{drift} r## where ##r## is radius of the loop, and ##n## is total number of electrons moving in...

I don't understand the question. how am I supposed to find the magnitudes and directions of the velocity from the figure?

I've already solved the orbital speed by equating the kinetic and potential energy in the circle orbit case. $$\frac{1}{2}mv^2 = \frac{1}{2}ka^2.$$And so $$v^2 = \frac{k}{m}a^2$$Now when the impulse is added, the particle will obviously change course. If we set our reference point in time just...

Li = Lrf +Ltf Iωo = Iωf + mvRsinθ I = MR^2 (MR^2)ωo = (MR^2)ωf + mvRsinθ ωf = (MR^2ωo -mvRsinθ)/MR^2 = 3.99

The question is: A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming...

I can't find the answer anywhere here's my question. can a centrifuge exist outside a field of gravity. More specifically, in a theoretical void of nothing without stars in view or any point of reference for comparison how could motion like spinning or acceleration exist?

Hi all I am a little bit confused about the definition of angular frequency in the context of nuclear rotation, some times its defined in the regular way as $$ E=\hbar \omega $$ and other time from the rigid rotor formula $$ E=\frac{\hbar^{2}}{2I} J(J+1) $$ where ##I## is the moment of inertia...

The signal-to-noise ratio for angular power spectrum signal Cl under theoretical noise Nl, where Cl and Nl are functions of multipole l, is given as (S/N)^2= \sum (2l+1) (Cl/Nl)^2To increase the S/N we bin the power spectrum signal, if bin width \Delta l, this in principle decreases Nl by a...

I understand how a massive, electrically charged spinning ball would have both angular momentum and a magnetic dipole, and i can see how the Stern–Gerlach experiment shows that the magnetic dipole of an electron is quantized. What kind of experiment demonstrates a connection between electron...

I tried to multiply 1/8 g (1.22625) by the radius (1.25 m) and got 1.53 rad/s^2. This is actually the linear acceleration of the elevator. How do I get the angular acceleration of the disk? Thanks!

Hi, I have a question. Let us say we have the wave function as with eigen value and base eigen value of: ##!\psi >\:=\:\frac{1}{6}\left(4!1,0,0>\:+\:3!2,1,1>\:-1!2,1,0\:+\:\sqrt{10}!2,1,-1>\right)## I need to find <Ly^2> the solution of the problem according to answers, is demanding that...

v=1.00*8=>v=8 rad/s ar=>100*8^2=>ar=64 rad/s^2 at=1.00*4=>at=4 rad/s^2 The only question I have is ar=-64 rad/s^2, not 64 rad/s^2 as I calculated. I believe this is because the wheel is accelerating in a clockwise direction. However this is not indicated by the mathematical equation. How do I...

wfinal=98.0 rad/s, dt=3.00s w=(37 revs/3)=>w=(37 revs*(2*pi/1))/3=>w=77.493 a=(98-77.493)/3=>a=6.8357 My answer is exactly half of the correct answer. Where did I go wrong?

Cohen tannoudji. Vol 1.pg 702"Now, let us consider an infinitesimal rotation ##\mathscr{R}_{\mathbf{e}_z}(\mathrm{~d} \alpha)## about the ##O z## axis. Since the group law is conserved for infinitesimal rotations, the operator ##R_{\mathbf{e}_z}(\mathrm{~d} \alpha)## is necessarily of the form...

I read that quantum spin is the measure of the angular momentum of a quantum object. Suppose you have a rotating Thing 1. Quantum objects bounce off of it then collide with Thing 2. Will this transfer angular momentum from Thing 1 to 2, causing it to rotate?

For this problem, Why for part (a) the solution is, Is the bit circled in red zero because since the putty is released at a very small distance above the rod it velocity is negligible? Also for part (d) the solution is I did a computation of the initial and finial kinetic energies of the...

how do I know that both angular accelerations are the same for both wheels here? should I apply relative motion analysis for the acceleration at A(with ##a_x,A and a_y,A##) and B(with ##a_{x,B} and a_{y,B}##) here, or is just a_A=r*alpha_C and a_B = r*alpha_D enough from which a_A=a_B and thus...

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.

I tried the formula I showed up there but got 0.399 instead of 7.88rad/s^2.

The planet is faster when it is closer to the planet because when it is closer to the planet it has less rotational inertia, and rotational momentum is conserved in this system, so less rotational inertia means a greater angular velocity. This explains why it is slower when it is farther away...

I am not understanding how to even start the question

The section Kepler’s Second Law here describes the above equation. In this problem, ##\text{r = D, m = M and v = V}## What is the way to go about finding out ##\theta## as shown in Figure 13.21?

365 rotations - 365 days 365 days - 31536000 s apart from that I do not know how to continue the question

6.0 rev - 1 s 1 rev - 1/6 5.0 rev - (1/6) x 5 = (5/6) s = 0.833 s I do not know how to calculate the angular acceleration

I am not understanding the 2nd part of the question where it is asked about how many revolutions will the blade make when it reaches full speed. Please help

Speed = 900km/hour tan(α)=900t/10000 α=arctan(900t/10000) Derivative is 900/(10000+81 t^2)

So i was able to solve the angular velocity part but i don't know how to find the velocity of centre of mass . For the first part i simply conserved momentum about COM because if i consider the particles as a part of the same system as rod the collision are internal forces . I am mainly...

Specifically given a purely magnetic hamiltonian with some associated vector potential : $$ H = \dfrac{1}{2m} (\vec{p} - q\vec{A}) $$ How can I deduce if $$ \vec{L} = \vec{r} \times \vec{p}$$ is conserved? ( $$\vec{p} = \dfrac{\partial L}{\partial x'}$$, i.e. the momentum is canonical)

Suppose two satellites are in a circular heliocentric orbit with radius R and with angular velocity O'. Satellite 2 then undergoes a low continuous thrust. Can Satellite 2 (the one that undergoes the continuous low thrust) maintain the same angular velocity O' about the sun? It seems that...

i,j,k arevector I know L=P*r=m*v*r=m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k=mabωk. but why m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k.I need some detail. please help me.

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...

So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall...

I think that the quantum numbers are l=1 and ml=0, so I write the spherical harmonic Y=Squareroot(3/4pi)*cos(theta). I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.

I tried using the equation w^2 = (4*K)/(mr^2) but I don't think this is right... I got my answer to be 3.2243 and that's not correct