Angular Definition and 999 Threads

Homework Statement A 39.00 kg rod of length 2.8 m is hanging vertically by one of its ends that is free to swing in a complete circle about a frictionless axle/pivot. The rod has uniform mass density. Suddenly it is struck horizontally by a 5 kg putty that sticks to the center of...

If we define Si=(1/2)× (reduced Planck's const)×sigma Then what will be (sigma dot vect{A})multiplied by (Sigma dot vect{B}) Here (sigma)i is Pauli matrix. Next one is, what will we get from simplifying <Alpha|vect{S}|Alpha> where vect{S} is spin vector & |Apha>is equal to " exp[{i×(vect{S} dot...

Homework Statement A uniform disk of mass M = 3 kg and radius r = .22 meters is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1 n * m What is the time required for the disk to reach an angular speed of 800 rpm...

Homework Statement An 7.80-cm-diameter, 400 g solid sphere is released from rest at the top of a 1.70-m-long, 20.0 degree incline. It rolls, without slipping, to the bottom Homework Equations I=2/5 Mr^2 K = 1/2 m*v^2 Kroll = 1/2 Iw2 mgh=K+Kroll The Attempt at a Solution Using the above energy...

Hello everyone, I have some conceptual problems understanding the rotating frame transformation. Take the center of the Earth as inertial frame's origin and another point in Hawaii as rotating frame's origin. In many lecture notes from internet, or Marion chapter 10. The vector describing the...

Homework Statement [/B] A thin uniform bar 2.00 m long and weighing 90.0 N is hanging from the ceiling by a frictionless pivot. It is suddenly struck 1.50 m below the pivot by a small 3.00 kg ball initially travellimg horizontally at 10.0 m/s. The ball rebounds and moves in oppossite direction...

Homework Statement Consider an electron in a state described by angular wavefunction $$\psi(\theta,\phi)=\sqrt{\frac{3}{4 \pi}}\sin \theta \cos \phi$$ Here θ and φ are the polar and azimuthal angles, respectively, in the spherical coordinate system. i. Calculate the probability that a...

I am wondering, when solving rigid body exercises, how can I express the relationship between linear and angular acceleration for a general case? E.g. what would be the linear acceleration in function of the angular one of a 1m rod that is rotating through a fixed point 0.6 m away from its mass...

Homework Statement Homework Equations The Attempt at a Solution Is it correct?

Homework Statement Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed in his quest to improve communication between damsels and dragons (Fig. P12.20). Unfortunately his squire lowered the draw bridge too far and finally stopped it 20.0° below the horizontal...

Homework Statement The problem asks: The index of refraction for violet light in silica flint glass is 1.66, and the index of refraction for red light is 1.62. What is the angular spread of visible light passing through a prism of apex angle 60 degrees if the angle of incidence is 50.03...

Homework Statement Given the Schwarzschild metric generalisation for a mass M rotating with angular momentum J ##ds^2 = -(1-\frac{2 M}{r}) \; dt^2 +(1-\frac{2 M}{r})^{-1} \;(dr^2 +r^2 \;d\theta ^2 +r^2 \sin ^2 \theta \; d\phi ^2) -\frac{4J}{r} \sin ^2 \theta \; dt d\phi ## a) Write the...

Homework Statement We are given a passive RC low pass filter with an input voltage of 5 Vrms at a frequency of 1 kHz. The resistor has a value of 22 kΩ, the capacitor a value of 100 nF. There is a current i across the resistor. (see picture below) We are to calculate the magnitude and phase...

Homework Statement what is the angular acceleration of the arm when theta equals 45 degrees. v=2 m/s picture is attached Homework Equations law of sites law of cosinesThe Attempt at a Solution [/B] so I used the law of sines to resolve side r as being 579.555 mm now I now I need to take time...

1. A moving rough cylinder of radius a, and mass m collides with an identical cylinder, on a smooth horizontal surface. Its centre of mass moves with linear velocity v0, and its angular velocity is ω0. What is the motion of the cylinders after the collision? I have be told that the answer to...

Homework Statement Determine the angular frequency of the system in the image. The cable is ideal but the pulley is not. I will present the same solution but with different coordinate axes. For some reason they arent the same and neither of them are correct. Given data: R is the radius of...

I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953 They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...

Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...

I have a couple of questions that i thougth this group could help me with. 1. A plane (SR71) takes off from the equator, with a lateral speed, relative to space of 1000mph. (earth rotational speed) say it takes an hour to get there so, its going 10,000mph or something. . Tt flys over the...

Homework Statement The figure shows an overhead view of a 2.50-kg plastic rod of length 1.20 m on a table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 39.0 g slides toward the opposite end of the rod with an initial...

Consider a circle rotating about a point X on its circumference at ##\omega = 2## rad/s. That means all points on and in the circle rotate at the same ##\omega = 2## rad/s. What are the angular velocities of various different points, say points A, B and C, with respect to the centre O of the...

Homework Statement Basically, I'm dealing with part d) in this document: https://s3.amazonaws.com/iedu-attachments-message/b663095a5021cb6aee55657de728a8d7_bfbe0ba9d2f10f8ac9ef9d049934c1da.jpg. I have found that the angular momentum only depends on spatial coordinate and it doesn't on time. Is...

Homework Statement "A drum of 60-mm radius is attached to a disk of 120-mm radius. The disk and drum have a total mass of 6 kg and a combined radius of gyration of 90 mm. A cord is attached as shown and pulled with a force P of magnitude 20 N. The disk rolls without sliding. Determine the...

Hi. I have come across the following statement - the eigenvalue equation for J+ is given by J+ | j m > = ħ √{(j+1)-m(m+1)} | j , m+1> My question is this - how can this be an eigenvalue equaton as the ket | j, m> has changed to | j , m+1> ? Surely the raising/lowering operators don't have...

My general question is: What is the angular power spectrum C_{l,N,ω} of N weighted (weight ω_i for event i) events from a full sky map with distribution C_l? I'm interested in: Mean of C_{l,N,ω}: <C_{l,N,ω}> Variance of C_{l,N,ω}: Var(C_{l,N,ω}) The question is important, since we observe in...

Homework Statement Homework Equations ... The Attempt at a Solution I've been searching for the relation between the spinning speed and inertia in equation form. I do know that since the skater inertia is smaller the spinning speed is faster but that about it. Any hint would be helpful. One...

Homework Statement An Atwood machine is a rope that passes over a pulley with a block attached to each end of the rope so that the blocks are not in contact with the floor. The frictionless axle of the pulley is oriented horizontally, and the rope is vertical save where it makes contact with...

Does a rotating magnetic field possesses angular momentum in the direction of rotation? I suppose this comes down to a broad question about the physical nature of fields in general. I love the Einstein-de Haas effect, where an iron core spins in the opposite direction of the induced spin...

Suppose that angular momentum of mass M is equivalent to the angular momentum of the background universe spinning in the opposite direction from center of mass M. Suppose that the background's true rotation is un-observable. What would be the implications of such a supposition?

Hi. To show that [ L2 , L+ ] uses the following commutators [ L2 , Lx ] = 0 and [ L2 , Ly ] = 0 . But if [ L2 , Lx ] = 0 this shows that L2 and Lx have simultaneous eigenstates ; but then should L2 and Ly not commute ? Thanks

1. Homework Statement Light of wavelength 6000Å illuminates a single slit of width 10-4m. Calculate the angular spread of first diffraction minima.Homework Equations d*y/D = nλ Y = nλ/a for minima Y = (2n±1)λ/a for maxima Y stands for the position on screen, d is slit width and D is separation...

A friend of mine posed a question to me the other day and I can't seem to wrap my head around it. He's working with an electric stepper motor to turn a large thin disk, but he can't be sure of the torque required because to find the torque he needs the moment of inertia and the angular...

When analyzing the conservation of angular momentum of a particular system, should we use the same p.o.r. before and after or can we use different p.o.r.'s? As far as I know, we should always use the same reference, but sometimes I see several solutions that use different references in my...

Homework Statement An object undergoes simple harmonic motion along an x-axis with a period of 0.50s and amplitude of 29mm. Its position is x = 12mm when t = 0s. Determine the value of ω in the equation of motion. Suppose that ω > 0. Homework Equations $$ω = \frac {2π} {T}$$ The Attempt at...

I need websites or books that has quantum mechanical exercises in particular that finds the total angular momentum eigenvalues (for example two spin 1/2 systems). Do you know where I can train?

Homework Statement An "ideal" spring with spring constant 0.45 N/m is attached to a block with mass 0.9 kg on one end and a vertical wall on the other. The floor has negligible friction, and you give the block a push and then let go. You observe that the block undergoes simple harmonic motion...

I'm working on finding the equation for the horizontal speed of a drone given the roll/pitch angle, mass, the angular velocity, and possibly other variables. Though to calculate, I need a way to calculate the thrust that a propeller creates. What is the relation between angular velocity and...

Homework Statement If the Earth, with a radius of 6400 km, were collapsed into a sphere of the same mass, having a radius of 10 km, what would be its rotational period? Homework Equations L = Iw The Attempt at a Solution I can solve this if the moment of inertia is given but since it isn't I...

Hi there, I've been trying to solve the following problem, which I found looks pretty basic, but actually got me really confused about the definition of angular momentum. Problem The trajectory of a point mass m is described by the following equations, in spherical coordinates: r(t) = r_0 +...

Homework Statement A door ( a rod of length ##L##, mass ##M##) rotates with angular velocity ##\omega## about a point ## H ##, and approaches a stop at ##S##. ##H## and ##S## are along the same line, and separated by a distance ## s ##. Show that the angular momentum of the door about the point...

Homework Statement If the steel disk has mass of 200 kg and a radius of 2 meters you can make it spin by applying a force to the rim. This torque increases the angular momentum of the disk. Suppose the force is 20 Newtons. How long would you have to apply it to get the wheel spinning 5...

I have two balls spinning with v1, omega1 and v2, omega2. They collide elastically with no tangential slip, resulting in new values for v1, omega1 and v2, omega2. I have the two components v1 & v2 figured out in the plane of contact, where angular momentum does not come into play. But I am still...

Is the wavefront velocity if an OAM mode 1 light beam proportional to its wavelength? I understand that the helical structure step length gives the wavelength of the beam. In this case, a small wavelength beam would travel much slower. The problem is, f=v/λ, but now v<c and if λ is shorter then...

It is known that particles with rest mass cannot travel at the speed of light. Can we also say that particles that travel at subliminal velocity, like these OAM photons do, have mass? It has been demonstrated [1] that these beams can be thought as made of photons that posses intrinsic OAM, and...

Homework Statement Starting from rest, a wheel has constant α = 3.0 rad/s2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval? ω0 = 0 α = 3.0 rad/s2 θf = 120 rad Homework Equations Δθ = ω0⋅t + ½αt2 The Attempt at a Solution 120...

1. The problem statement, all variables, and given/known data Joe is painting the floor of his basement using a paint roller. A roller has a mass of 2.4kg and a radius of 3.8cm. In rolling the roller across the floor, Joe applies a force F= 16N at an angle of 35 degrees. What is the magnitude if...

Homework Statement an object starts from rest and has a final angular velocity of 6 rad/s. the object makes 2 complete revolutions. find the object's angular acceleration. Homework Equations wf^2=wi^2+2αd The Attempt at a Solution Not sure what to do with the revolutions, would it take act as...

In my textbook.In some question gives me angular speed as ( )rev/s.I know that its the frequency (f).But some questions It says angular velocity and says rad/s. Interesting thing happens when the textbook says in angular speed and I use f and then using w=2πf and then continue I get wrong...

Homework Statement A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s. Mass of wheel: 3kg Outside rad. of gyration of wheel: 300mm Radius of gyration: 212mm calculate: (a) The linear acceleration of the...

Homework Statement “A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of 6.55 kg, a radius of R = 38.0 cm, and is in the shape of a ring. A mass M = 1.85 kg is attached to the end of a string which is wrapped around an inner hub which has a radius r =...