Angular Definition and 999 Threads

Homework Statement Homework Equations Langevin equation (I included all the equations in the next section.[/B]The Attempt at a Solution I do not know how I can proceed from this point. I'm stuck since I have no information on the drag coefficient. Maybe my approach is wrong, and there may...

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...

Consider a tiny planet orbiting a massive star. If the value of the planet's angular momentum (w.r.t. to star) is fixed, does the action of the planet's orbit depend on the eccentricity of the orbit?

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...

I do not get some points of this proof about the time derivative of a unit vector $\hat{u}$ (costant magnitude) which is following a precession motion. The picture is the following. I want to prove that $$\frac{d\hat{u}}{dt}=\vec{\Omega}\wedge \hat{u}.$$ I'm ok with almost all the proof except...

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 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...

1. Homework Statement Homework Equations KE=½m(ωa)2 The Attempt at a Solution So first I did this: 2.4x10-3= ½ mω2(1.5x10-2)2 To find mω2=21.33 And substitute that into the KE eqn to find the new amplitude, which is 1.30x10-2 But I only did that because that was the only way I could think...

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 The Hubble space telescope has a maximum diameter (cylinder) of 4.20 m and a moment of inertia of 77,217 kg-m2 about its axis. A reaction motor applies a force of 18.0 N tangentially to the edge of the cylinder for 5.00 seconds. (a) What is the angular speed of the telescope...

Homework Statement Block D of the mechanism is confined to move within the slot of member CB . Link AD is rotating at a constant rate of ωAD = 4 rad/s measured counterclockwise. Suppose that a = 350 mm , b = 200 mm. Find wCB and αCD Homework EquationsThe Attempt at a Solution [/B] I hope its...

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 1) Calculate the angular diameter distance to the last scattering surface in the following cosmological models: i) Open universe, ΩΛ= 0.65, Ωm = 0.30 ii) Closed universe, ΩΛ = 0.75, Ωm = 0.30 ii) Flat universe, ΩΛ = 0.75, Ωm = 0.25 Describe how the CMB power spectrum...

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...

Homework Statement Hi Everyone would somebody please be able to give some advice on the following questions: Part (a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its...

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 =...

In the spring 2016 issue of the Johns Hopkins Magazine, there is a non-technical article (in graphic novel format) about a new instrument, dubbed CLASS, which is intended to detect "pinwheel patterns" caused by gravitational waves originating in the inflation era acting on the CBR. If these...

Homework Statement [A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v , then its escape velocity on Planet X is a) 2 v b) (√2)v c) v...

Hello everybody. I would really appreciate some help Homework Statement I have some problem where I have measured angular velocity data. This measurements are not equally spaced, meaning there were taken after some (variable) delay passed. I need to find what is the angular acceleration at...

I'm learning about beta decay and as I understand in beta decay we get: neutron → proton + electron And since all these have spin 1/2 we have that the conservation of angular momentum is not conserved. The neutrino with spin 1/2 is proposed to also exist in the process to solve this so that...

Homework Statement At the instant illustrated, which best describes the angular momentum of the ball and net torque on the ball, as measured around the origin? L⃗ is in the kˆ direction, ⃗τ is 0. Homework Equations torque= (F)x(r) Tension in rope= (mv^2/r)+qvbThe Attempt at a Solution I am...

Hi, I'm preparing a computer software to simulate the fall of an object for an academic project. The object is rotating (not rolling) over the circular bottom point. I know that the angular velocity at the horizontal point is ω = √(3g/L). I would like to calculate the angular velocity at every...

Homework Statement A 60.0 kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 500 and radius 0f 2.00 m. Turntable is initially at rest and is free to rotate around frictionless vertical axle through its center. Woman then starts walking around the rim at...

Hello, I have a question about using the properties of conservation of angular momentum to provide mechanical resistance. Basically, I'd like to create a device that spins a disk similar to a gyroscope. The device has an external input that, depending on the configured orientation of the disk...

Homework Statement A horizontal plank (mass 2kg, length 1m) is pivoted at one end. A spring (k=1000N/m) is attached at the other end. Find the angular frequency for small oscillations. Answer: ω=39rad/s Homework Equations ω = √(mgd + kΔxd/I) I think I would be treating the plank as a long...

http://www.tech.plym.ac.uk/sme/mech226/gearsys/gearaccel.htm Hello, I tried to derive n=N1/N2=omega2/omega1 with using T1=T2 but it is a wrong assumption. I thought they should balance to satisfy Newton's 3rd law, but it is not. Could you explain me why.

Imagine a motor, spinning a rotor blade around and around and around and around and around... How does the angular velocity of the rotor blade, and the torque affect the thrust produced?

Homework Statement Hi, I am trying to use the angular velocity and angular position to find the age of the Crab Nebula but my calculations seem to be erroneous. I am supposed to get a number around 800 but I keep getting 5000+ years of age. I'm going to try to be very specific in what I'm...

Homework Statement The following problem is part of a physics lab with unclear directions. The lab prompt says: Find the angular acceleration of a meterstick as it slips down a wall. Here is my interpretation of the lab: A meterstick of mass 0.15kg is leaning against the wall. At an angle of...

Homework Statement Two go-karts race around a course that has concentric circular tracks. The radius of the inner track is 15.0 m, and the radius of the outer track is 19.0 m. The go-karts start from rest at the same angular position and time, and move at the same constant angular acceleration...

1. The problem statement, all variables and given/known A hamster runs in its wheel for 2.7 hours every night. If the wheel has a 6.8 cm radius and its average angular velocity is 3.0 radians per second, how far does the hamster run in one night? Homework Equations w= delta theta/change in...

Homework Statement Show that ##<L_x^2> = <L_y^2>## using the commutation relations. The system is in the eigenstate |l,m> of ##L^2## and ##L_z##. Homework Equations ##[L_x, L_y] = i \hbar L_z## ##[L_y, L_z] = i \hbar L_x## ##[L_z, L_x] = i \hbar L_y## ##[L_x, L^2] = 0## ##[L_y, L^2] = 0##...

Homework Statement Initially collar is at rest with theta = 0. Find \dot\theta=f(\theta). And find maximum theta reached. Homework Equations I don't know if i allowed to use angular momentum about top-right frame corner as it's accelerating. But i definitely will need second Newton law:)...

Ok, so here's the deal. I'm working on something that I SHOULD know the equations for after 5 years of school and a degree in mechanical engineering, but then again I can't remember why I walked into a room most times. So if ya'll could give me some guidance and at least a starting point I...

Two free electrons approach each other, so they start to emit photons due to bremsstrahlung. Where does the angular momentum carried away by the emitted photons come from?

Recently I've been studying Angular Momentum in Quantum Mechanics and I have a doubt about the eigenstates of orbital angular momentum in the position representation and the relation to the spherical harmonics. First of all, we consider the angular momentum operators L^2 and L_z. We know that...

I am trying to work out the angular acceleration of a small flywheel (with axle running through) when an attached piston (by means of a pin) with an outstroke force acts on it. I assumed I would need to work out the torque using the formula torque = force x radius, and find out the flywheel’s...

Two things I'd like to discuss: 1. The conservation of angular momentum. If you have two discs rotating on the same fixed rigid axis, will these nullify each other? I.e. Create no net angular momentum? 2. How / is it possible to convert angular momentum to linear momentum in the sense to be...