Angular Definition and 999 Threads

I'm trying to get the Electric Field of a Thin spherical shell along $$ \hat z $$ axis. In this problem I've got a charge/area density: σ(θ)=σ0⋅cos(θ)σ(θ)=σ0⋅cos(θ). θ∈[0,π]θ∈[0,π] (theta is the polar angle)Can you please help me with how can I know the area element? thanks.

I am strugglin with this step in my assignment. I am dealing with a centrifuge with a known moment of inertia. I should write the expression for a torque of the motor and express it as a function of angular velocity. Can you help me please?

When do we use L=r x P and L=I x Omega (angular velocity)? in old 8.01x - Lect 24, I pasted here link of the lecture, which will take you at exact time (at 27:02)he says "spin angular momentum" in classical physics lecture and why? I expected to hear "angular momentum" vector. Normally...

Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...

Homework Statement Finding the general formula for max angular velocity ( answers say 0.839*(g/b)) but I do not understand how Homework Equations 0.839*(g/b) The Attempt at a Solution

Homework Statement :[/B] The following expression stands for the two angular bisectors for two lines :\frac{a_{1}x+b_{1}y+c_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}=\pm \frac{a_{2}x+b_{2}y+c_{2}}{\sqrt{a_{2}^{2}+b_{2}^{2}}}\qquad Homework Equations The equations for the two lines are : ##a_1x + b_1y +...

1. A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it as shown above. Outside edge of the disk is moving at a linear speed of V and the clay is moving at speed v/2. How does angular momentum of system after the clay sticks compare to the angular...

think of a engine. it has a flywheel and a rod connected to it. a string had been totally wrapped around the rod and a mass is hanged from the very end of the rod. the system is in equilibrium. but as the engine starts to rotate, the rod with rotate as well and cause the hanged object to go...

Given the figure, how can i arrive to this formula knowing that angular momentum is conserved? I know that p = mv and L = p x r. So the initial momentum will be L1 = mV x R and the final momentum will be L2 = mv x r. I am not sure how R will equal to b since the distance between the...

I understand that in a system composed of two articles, the total angular momentum is: J = J1 + J2 From the operators: J^2, Jz, J1z, J2z，J^21z，J^22z, I get two possible sets of operators that commute: {J^2, Jz, J^21z, J^22z} and {J^21z, J^22z, J1z, J2z} What I don't understand is why the...

Homework Statement Question: A 600 g steel block rotates on a steel table while attached to a 1.20 m-long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 5.01 N perpendicular to the tube. The maximum tension the tube...

Homework Statement A solid body begins to rotate around a fixed axis with angular acceleration ##\beta=\beta_0\cosφ##, where ##\beta_0## is a constant vector, ##φ##, is the angle of rotation of the body from initial position. Determine the angular velocity of this body as a function of the...

So,this is problem from David Morin's Classical Mechanics(Screenshot 1). I solved the problem. Then I went to see the solution in manual hoping for out of box thinking. As in screenshot 2 is solution by Morin. My question is why he conserves angular momentum about the point (R-h) below C.M...

Statement of the problem : "Using the definition L = r ##\times## p, prove that the direction of L is constant for an alpha (##\alpha##) particle whose scattering is shown in the diagram below. " Relevant equations : We are aware that the scattering takes place via a central force F = F(r)...

Homework Statement I am solving a kinematic problem, where I have a link that is attached to a rotational joint. I need to find the position of the joint for t=0..8, and I need to do it for every 0.01s. The problem comes from the fact that I have three stages for the velocity, during t = 0..0.1...

Good day dear forum, greetings from Argentina. I am studying the Lamb Shift, which says that in the atomic orbitals, an upward energy shift occurs due to an interaction of the electron with itself. This means that a level s can have an energy slightly greater than a level p. So far so good, but...

Homework Statement A system has a ball and a uniform rod. The rod is rotating about point X on a frictionless table until it strikes the ball. The rod stops and the ball moves away. Variables: Rod's mass: m1 Ball's mass: m2 Rod's original angular velocity: ω Ball's final velocity: v Rod's...

Homework Statement A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ2/3)rad/s2 , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s. Homework Equations α =...

Hello there, I'm new here and i need some help on my home work. A DVD drive rotates at an angular frequency of 4800 rpm. a) what is it's angular speed in rpm? b) at 4800 rpm, what is the linear speed (in knm/hr) of (i) the center point and points (ii) 5 cm and (iii) 6 cm from the center? Thanks!

Statement of the problem : A ball shown in the figure is allowed to swing in a vertical plane like a simple pendulum. Answer the following : (a) Is the angular momentum of the ball conserved? No, the angular momentum ##L = mvl##, where m is the mass of the ball and v is its speed at an...

Can someone explain to me how we find it? Examples Y10X-= = |1,0>|1/2,-1/2> = √2/3 |3/2,-1/2> + √1/3|1/2,-1/2> Y11X-= = |1,1>|1/2,-1/2> = √1/3|3/2,1/2> + √2/3|1/2,1/2> Y2-1X- = = √4/5 | 5/2, -3/2> + √1/5 | 3/2, -3/2> I understand it goes like YlmX± = |l,m>|s,ms> = a |jmax, ?> + b |jmin, ?>...

Homework Statement Homework Equations For this problem I got the angular momentum conservation equations, mv(l+h)=mv'(l+h)+Ml2ω and momentum conservation equation as mv(l+h)=mv'(l+h) m=colliding mass,v and v' velocity before and after collision. M=mass of the rod. 2l=length of the rod...

1. Homework Statement A spherical billiard ball of uniform density has mass m and radius R and moment of inertia about the center of mass ( ) 2 cm I = 2/ 5 mR^2 . The ball, initially at rest on a table, is given a sharp horizontal impulse by a cue stick that is held an unknown distance h above...

Homework Statement One silly thing may be I am missing for small oscillations of a pendulum the potential energy is -mglcosθ ,for θ=0 is the point of stable equilibrium (e.g minimum potential energy) .Homework Equations Small oscillations angular frequency ω=√(d2Veffect./mdθ2) about stable...

Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...

This question is about the conservation of angular momentum: So far, I have understood the reason as to why an object with a high moment of inertia has a small angular acceleration whereas an object with a low moment of inertia has a larger angular acceleration. The reason for this is that if...

Greetings. So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is \mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r} where \mu is the reduced...

Homework Statement 4 masses attached by a cross with no mass are spinning on a smooth table around the center of the cross. The distance between any mass to the center is L. The angular velocity is ω0. m1=m3,m2=m4 Suddenly, at t=0 (the time described in the picture), m4 disconnects from the...

Homework Statement Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic...

How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)? I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) ...

Hi. The angular resolution is calculated through $$\theta=1.22\frac{\lambda}{D}\enspace.$$ It's the first zero of the intensity function (in small-angle approximation) of the Airy disk...

Hi everyone, I have a question that can't solve. Does exist a lagrangian for the relativistic angular momentum (AM)? I can't even understand the question because it has no sense for me... I mean, the lagrangian is a scalar function of the system(particle,field,...), it isn't a function FOR the...

Homework Statement Homework Equations ##v=\omega r## The Attempt at a Solution So, using the equation, one can work out the velocity at point ##B##. ##v_B=\omega_{AB} \cdot r_B## ##v_B=6(0.4)=2.4~ ms^{-1}##I then tried working out the angular velocity at point ##C## using the instantaneous...

For a question involving a ball hitting orthogonally the bottom corner of a board held by wires, I need to calculate the angular velocity of the board and ball (collision is inelastic) right after the collision, before there's any external torque. I can easily calculate the angular momentum L...

Last week I posted in General Physics some questions about what happens in a collapsing gas cloud, and I was advised that total angular momentum is conserved. I thought of asking for extra clarification here, as that seems really amazing -- I apologize for asking the same thing twice. I use a...

Hi, I'm having trouble understanding angular moment of the one electron hydrogen atom. Solving Schrodinger equation on a referece system (say S) I get the energy eigenstates. They depend on three quantum numbers, n, l, m \frac{-ħ}{2 m}\nabla^{2} \Psi - \frac{e^{2}}{4 \pi \epsilon r} \Psi =...

Homework Statement A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30 degrees with the horizontal...

I find conservation of energy and linear momentum to be quite natural to understand, but I find conservation of angular momentum really, really tricky. Let me give two examples: (a) I call my system as a stick with identical springs at its ends, facing opposite directions, each spring is coiled...

This took a lot of time and effort and I understand if you wish to skip past everything and just read my questions about it in the The too long didn't read summary (TL;DR) at the bottom. Homework Statement The 10-g bullet having a velocity of v = 750 m/s is fired into the edge of the 6-kg...

Homework Statement Consider a 2-particle system where the two particles have angular momentum operators ##\vec{L}_1## and ##\vec{L}_2## respectively. The Hamiltonian is given by $$H = \mu\vec{B}\cdot (\vec{L}_1+\vec{L}_2)+\gamma \vec{L}_1\cdot \vec{L}_2.$$ Determine explicitly the eigenvalues...

I know that spin is a type of intrinsic angular momentum. For electron spin is (1/2)ħ . But unit of (1/2)ħ is J.s, which is not the unit of angular momentum. Can you please explain this discrepancy?

Homework Statement I have been set this question and I am struggling with parts b and c. I think I am nearly there but can't quite get over the line. Please could someone give me a nudge in the right direction. [/B] 1. (a) For the mechanism shown in FIGURE 1 determine for the angle θ = 45°: (i)...

Homework Statement λ = 240 nm D = 2.40 m We are supposed to find the angle resolution (minimum angular distance between two objects so we still see them as two separate objects) to the telescope for ultraviolet light with wavelength 240 nm Homework Equations The equation that I used is θ =...

Taking the Earth orbiting the sun as an example, when I consider the angular momentum of the Earth about the sun, should the spin angular momentum be counted? I'm confused that if it's counted, the spin angular momentum, Lcm=Icm×ωspin, is different from other angular momentum regarding the...

Hello, I'm trying to calculate the measurement of the orbital angular momentum of the state l=1 and m = -1. The operator for the angular momentum squared is ## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial}{\partial \theta}(sin\theta\frac{\partial}{\partial \theta}))...

Homework Statement (Problems/diagrams referenced are attached as images.) Homework Equations Net torque about an origin = time derivative of the angular momentum vector about the same origin. The Attempt at a Solution I've solved these problems before, but I'm now looking back at them and...

Homework Statement A point particle travels in a straight line at constant speed, and the closest distance it comes to the origin of coordinates is a distance l. With respect to this origin, does the particle have nonzero angular momentum? As the particle moves along its straight-line path...

Good afternoon I just have this little doubt: imagine the osculating orbit of Mars changing slowly in its elements along the centuries. The semi major axis changes, the period, etc. Is the specific angular momentum allways equal in all the osculating orbits Mars has in those centuries? Or does...

Homework Statement Two pucks are lying on ice where they can slide and rotate with almost no friction. A string is tied to both pucks but it is tied to the middle of the first puck and wrapped around the second puck. You pull on both strings with the same force, F. The first puck moves without...

I have a 5.0 m tractrix and am trying to work out angular momentum and total angular momentum for two hitchpoint speeds 60 & 70 km/h. My result shows a higher total angular momentum for the lower speed. This is not what I expected. Here are my equations Positions: Derivatives Angular velocity...