Angular Definition and 999 Threads

Homework Statement A gyroscope takes 3.8 s to precess 1.0 revolution about a vertical axis. Two minutes later, it takes only 1.9 s to precess 1.0 revolution. No one has touched the gyroscope. Explain Homework Equations ω = Δθ/Δt ω = ωo + at The Attempt at a Solution So is the gyroscope...

Homework Statement Kepler’s 2nd law of planetary motion says that the radius vector drawn from the Sun to any planet sweeps out equal areas in equal time intervals. By considering the small area swept out by the radius vector in time dt, show that \frac{dA}{dt} = \frac{L}{2m} , where L is...

Hi, I am reading about alpha-decay. I read that the decay 2- --> 2x requires lα = 1, 2, 3 or 4. Why does it have to be one of these numbers?

Are the results of the Angular Spectrum Method and the Fourier Transform of a Fresnel Diffraction be different, or the same? Given the same distance between the input and output plane, and the same aperture.

Hi All, Is the Angular momentum conserved at the singularity ? Thanks in advance

Homework Statement Solve: A*sin(ωt + Θ) = L*i''(t) + R*i'(t) + (1/C)*i(t). Where: A=2, L = 1, R=4, 1/C = 3 and Θ=45°. Homework Equations The system has to be solved by i(t) = ih + ip. I gave the values to A, L, R, 1/C and Θ. I can also give values to ω, but I've come to a doubt when solving...

Hi, I'd like to know how to calculate parity and total angular momentum of nuclei which have even Z and even N and also Z and N are magic numbers, such as 8O8 or 20Ca20 (the number before the element is Z and the after one is N). I don't know how to insert LaTeX formulas. Thank you in andvance

Hi. For the angular momentum l=2 case are the L2 and Lz matrices both 5 x 5 matrices with the following eigenvectors ? ## \begin{pmatrix} 1\\0\\0\\0\\0 \end{pmatrix} ## , ## \begin{pmatrix} 0\\1\\0\\0\\0 \end{pmatrix} ## , ## \begin{pmatrix} 0\\0\\1\\0\\0 \end{pmatrix}##,## \begin{pmatrix}...

While linear accelerating an electron, with direction of acceleration being the ##z+## axis of the spherical coordinates, its radiation in angular distribution form is(according to this tutorial: http://farside.ph.utexas.edu/teaching/em/lectures/node132.html) ##\frac{dP(t')}{d\Omega} =...

Homework Statement Homework Equations θ=1.22 (λ/D) The Attempt at a Solution Just want to know if I properly answered this question. Thanks in advance

A vector operator ##\mathbf{V}## is defined as one satisfying the following property: ## [V_i,J_j] = i\hbar \epsilon_{ijk}V_k## where ##\mathbf{J}## is an angular momentum operator. My question is what is the role of ##\mathbf{J}##, does it have to be the total angular momentum from all...

Hi, friends! Let the quantity ##I\boldsymbol{\omega}## be given, where ##I## is an inertia matrix and ##\boldsymbol{\omega}## a column vector representing angular velocity; ##I\boldsymbol{\omega}## can be the angular momentum of a rigid body rotating around a static point or around its -even...

Hello there! I was doing my Gravitation problems and I found this problem that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force produced by a proton and a neutron is: U(r) = \frac{k}{r}e^{-\alpha r},\ k<0,\ \alpha > 0...

Hi I read that for Dirac equation, [ L , H ] =/ 0 , so Dirac found a operator S such that 1. [ S , H ] = - [L, H] ---> [ J, H ] = 0 where J = L + S , the total angular momentum. 2. S gives an eigenvalue of spin 1/2 ---> solutions of Dirac equation describe fermions. The total...

1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed? 2. Homework Equations : I = mR^2 Ia = -k(theta) x(t) = Xm Cos(wt + @) (just using @...

Hi, I have a very simple question. What is meant by "angular spread"? I'm not too sure what is meant by that. I have tried looking on this forum as well as on google have not found any sort of definition or description. For example, the spread of light when diffracting? Or the spread of light...

Homework Statement A child (mc = 36 kg) is playing on a merry-go-round (mm = 225 kg, R = 2.9m) that is initially at rest. The child then jumps off in a direction tangent to the edge of the merry-go-round. The child has a speed of 5.0 m/s just before she lands on the ground. What is the...

Homework Statement A solid sphere of mass m and radius a can rotate freely about a point A on its surface. The sphere is held initially at rest with the line OA through A and the centre of the sphere O horizontal and is released under gravity. Find the angular velocity of the system when OA...

Homework Statement Homework Equations The Attempt at a Solution For a angular momentum ##J##, there exists the eigenvalue problems $$J^{2} \mid j \hspace{0.02 in} m \rangle = j(j +1)\hbar^{2} \mid j \hspace{0.02 in} m \rangle $$ $$ J_{z} \mid j \hspace{0.02 in} m \rangle = m \hbar \mid j...

Torque is defined as the cross product of position vector and force, i.e. \vec \tau = \vec r \times \vec F . However the force vector \vec F is fixed, but the choice of origin is arbitrary, making \vec r also arbitrary. Does it make the torque vector also arbitrary, which apparently shouldn't...

In case of simple microscope .we take angular magnification I know The angular magnification of an instrument is the ratio of the angle subtended at the eye when using the instrument divided by the angular size without the instrument But what I am not getting is how this subtended angle is...

Homework Statement A bicycle rider is moving with a velocity of 13.0 m/s. What is the angular velocity of his wheels if they have a diameter of 0.660m? Assume the wheels are rolling without slipping. a) 39.4 m/s b) 19.7 m/s c) 39.4 s-1 d) 4.29 s-1 e) none of the above Homework Equations v =...

How the relative angular momentum of two particles can be detect by detector in two particle decay (center of mass frame)? I am curious about the signatures/differentiation between different relative momenta, means how one can decide that it is L=0, L=1,2,3,...? Of course the distribution would...

Homework Statement Finding angular velocity after impact Homework Equations Moment of inertia x angular velocity = constant The Attempt at a Solution Hi, I believe that angular momentum is conserved in this case? If that's the case, how do I use the formula to calculate angular velocity if...

Homework Statement In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 3.50m in diameter (the figure (Figure 1) ). The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of...

It seems to be implied, but I can't find it explicitly - the order in which linear operators are applied makes a difference. IE given linear operators A,B then AB is NOT necessarily the same as BA ? I thought it was only with rotation operators that the order made a difference? I noticed this...

Hello, For the spin angular momentum operator, the eigenvalue problem can be formed into matrix form. I will use ##S_{z}## as my example $$S_{z} | \uparrow \rangle = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \frac {\hbar}{2} \begin{pmatrix} 1 \\ 0...

Please help I am not sure of how to work this out The angular separation between Styx and Nix 28 days after they are in line with each other on the same side of Pluto. Mass of Nix = 5*10^16 Kg Orbital Radius of Nix = 48675 Km Orbital period of Styx = 20 Earth days

Homework Statement A bird m_b=0.470kg, is flying horizontally at v_b=2.50 m/s, not paying much attention, when it suddenly flies into a stationary vertical rod, hitting it d=25cm below the top. The rod is uniform, L=0.740m long, has a mass of m_r =1.60kg and is hinged at its base. This time the...

Homework Statement A star with mass 2.4x1030 kg and diameter 1.7x109 m rotates once every 34 Earth days. It eventually dies and becomes a white dwarf, shedding about half of its mass and contracting to a diameter of 1.9x108 m. If we approximate the star as a perfect sphere, what is its...

The direction of the torques in the following working will be found using: \vec{\tau} = \vec{r} \times \vec{F}. When viewed from above, the counterclockwise rotation of the blades produces a torque out of the page: As the angular momentum (right-hand corkscrew rule) is also out of the page...

Homework Statement We model a dirt bike as a rod of mass (M) 100 kg, and length (L) 2 m to which are attached two wheels of mass (m)=40 kg kg, and radius R=0.5 m. The bike goes off a spine ramp with angle ##\phi=1deg.## to the vertical on either side (see diagram below). Our question is, at...

Homework Statement The cosmoclock 21 Ferris Wheel in Yokohama City, Japan, has a diameter of 100m. Its name comes from its 60 arms, each of which can function as a second hand (so it makes one revolution every 60.0s). a) Find the speed of the passengers when the Ferris wheel is rotating at...

Homework Statement Homework Equations Torque = r X F The Attempt at a Solution r is 2.5m since that's the length of the red (minus 0.5), and F should be the weight, so ma? That gives something like (5 * 2.5/3) * 9.8 * 2.5, which doesn't give me an answer at all :(

Homework Statement http://tinypic.com/r/vsew5k/8 Homework Equations Angular momentum for rigid bodies Kinetic energy of rigid bodies The Attempt at a Solution I tried to start by using conservation of energy, but I can't find the center of mass of the rod. I'm also not sure where to put the...

Homework Statement What is the direction of the red ball's angular momentum about the point A? (see figure) Same as the momentum. Out of the page. Zero magnitude. Opposite to the momentum. Same as rA. Into the page. [/B] Homework Equations Angular Momentum[/B] The Attempt at a...

Homework Statement See the attached image. Homework Equations ##T = 1/2 \omega^2 I## The Attempt at a Solution So ##I_1,I_2,I_3## are just the moments of inertia of the object with regards to the 3 axes. Right? OK, then I intuitively assume that the total kinetic energy must simply be...

Homework Statement I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - http://www.kwon3d.com/theory/moi/iten.html I follow clearly to the...

Homework Statement Homework EquationsThe Attempt at a Solution This whole thing about angular momentum has me totally confused and stumped, but I am trying this problem given in a youtube video lecture I watched. I know of this equation ##L^{2} = L_{\pm}L_{\mp} + L_{z}^{2} \mp \hbar L_{z}##...

Homework Statement A circular turntable of mass 2.0 kg and radius 6.0 inches is rotating freely at 66 2/3 rpm. If a 500 gram blob of clay is dropped on the disk at a distance of 4.0 inches from the center, what is the resulting angular speed of the system? Treat the clay as a point mass (I =...

Hey all, I'm not understanding why the bits highlighted in red are equal? Any help appreciated, thanks.

Homework Statement : A centrifuge starts from rest and speeds up at 3400rpm after 50 seconds. a sample is at a distance of 37.5mm from the centre 1) find the angular acceleration 2) calculate the centripetal acceleration [/B] Homework Equations : v2 / r v = rω a = rω2 a=Λω/Λt 3. The...

Homework Statement If the angular momentum of Earth in its motion around the Sun were quantized like a hydrogen electron, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? Would that energy release be detectable? What would be the...

(Based on a problem from the 59th Polish Olympiad in Physics, 2009) Let's consider a ball of mass ##m##, radius ##r## and moment of inertia ##I = 2/5mr^2## approaching a wall with linear velocity ##v_0##, rolling without sliding with angular velocity ##\omega_0##. It collides with a wall. Its...

Essentially just a consequence of inertia and gravity?

Homework Statement I play swing a yo yo above my head in a circular horizontal motion. The yoyo travels around 370 degrees. what is the angular displacement? Homework EquationsThe Attempt at a Solution would I say the angular displacement is 10 degrees? or still 370 degrees? or would both...

I walk around a circular track. My displacement is 0 because I'm back at my starting point. How about my angular displacement? Is it 2 pi radians, or is it also 0? The definitions I've been reading online seem to indicate that 2 pi radians is the answer.

Homework Statement Prove that ## e^{2\pi i \mathbf{n\cdot J}/\hbar} |j,m\rangle = (-1)^{2j}|j,m\rangle ##. This equation is from Ballentine's QM book. The term in front of the ket state in the LHS is a rotation operator through ##2\pi## angle about an arbitrary direction ##\mathbf{n}##...

Homework Statement A uniform plate of mass m is suspended as shown.What will be the angular acceleration immediately after connection at B has been released? http://i.stack.imgur.com/1hMuk.png 2. My attempt- I used torque=M.I*angular acceleration I chose the axis to be perpendicular to the...