2. ### I C-G coefficients and Angular momentum

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, ?>...
3. ### Definition of work done by torque

I' m trying to derive the work done by a torque from W = ∫ F ⋅ ds and I' ve looked up the internet, it said: W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 ) it can be written as W = ∫ F ⋅ dθ x r this is a vector triple product , thus can also...
4. ### B When a particle is rotating about an axis "r" away, is its linear velocity constant?

If talking about a particle rotating around an axis away from it by r. if the particle is moving with constant angular velocity ω. is the linear velocity constant or no? Now what I know is that since we have Vt= ωr, so r doesn't change, as well as ω, so Vt is said to be constant. but I think...
5. ### Conservation of angular momentum

Homework Statement A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I Homework...
6. ### Kepler's Second Law with Angular Momentum

Homework Statement I am working on the derivation of Kepler's Second Law based on torque and angular momentum. I understand that the vector "L" is equal to the mass (m) times the cross product of the vector "r" and the vector "v." The source I am following then states that L = mrvtheta. I do...
7. ### I Spin confusion: Stern-Gerlach experiment

I have some serious issues trying to understand the idea of the spin in the context of the Stern-Gerlach experiment and would appreciate some assistance! Assuming that a homogenous magnetic field ##B## in the "North-wards" ##z##-direction, assume that there is a magnetic dipole moment ##\mu##...
8. ### I Translational + Angular Acceleration of Free Body (not fixed)

Imagine a long brick in outer space. You apply a force tangential to the center of mass. The brick accelerates in a transitional and angular fashion. There are no constraints or fixed axis. How would I calculate the translational and angular acceleration? I would like to run some simulations...
9. ### Find the angular speed of the smaller gear

1.Why does the angular speed of small gear depend only on larger gear only? 2.Why does the length of linkage connecting two gears does not have any influence on the angular speed of smaller gear? The first question can be answered by looking at slack and tightening of chain caused by rotation...
10. ### Elliptical Orbits and Angular Momentum

Homework Statement Why is the magnitude of Angular Momentum for an elliptical orbit as such? $$l = mr^2\dot{\phi}$$ where ##\dot{\phi}## represents angular momentum. I have always assumed that angular momentum was $$l = r \times P = mr \times V = mrVsin(\theta) = mr^2\dot{\phi} sin(\theta)$$...
11. ### I Rotational excitation of quantum particle

I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I$$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$n^2 * ħ^2$$ was...
12. ### Orthonormality of Spherical Harmonics Y_1,1 and Y_2,1

Homework Statement Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} [Broken] the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1. Homework Equations Y_1,1 =...
13. ### Rotational Motion of a thin rod about a pivot

Homework Statement A uniform thin rod of Length L and mass M is pivoted at one end is held horizontally and then released from rest. Assuming the pivot to be frictionless, find a) Angular velocity of the rod when it reaches its vertical position b) The force exerted by the pivot at this time...
14. ### Masses Over a Uniform Cylindrical Pulley

ηϖ1. Homework Statement Homework Equations I=½MR2 PE=mgh The Attempt at a Solution The first thing that jumped out at me was "uniform cylinder" so I went ahead and calculated the moment of inertia for the cylinder and got I=½(4.4)(.4)2 = .352 and held onto that. Then, I calculated the...
15. ### Masses over a Pulley (w/ angular kinematics)

Homework Statement http://imgur.com/koz4PpI Homework Equations The Attempt at a Solution I was able to calculate the net torque on the pulley as 55.88 and the Inertia as .352. Those could be wrong, but that's as far as I could get. I really have no idea. Any kind of help/explanation would be...
16. ### B Angular Velocity in Linear Momentum Equation

m1v1 = m2v2 v = rω m1(rω)1 = m2(rω)2 m1ω1 = m2ω2 Does this make sense?
17. ### B Angular acceleration of Pendulum equation

Is this a legitimate equation? θ'' = − g⁄R sin θ Source: ftp://www.myphysicslab.com/pendulum1.html ftp://www.myphysicslab.com/images/pendulum_2.gif [Broken] The pendulum is modeled as a point mass at the end of a massless rod. We define the following variables: θ = angle of pendulum...
18. ### B Average Angular Momentum Conservation? mω

My textbook talks about the average angular speed that ω = angular displacement / time for the angular displacement to take place. So the question is like there is m1v1 = m2v2, can the velocity be instead average angular speed to have the conservation of momentum equation like this? m1ω1 = m2ω2
19. ### I How to derive linear velocity from position and angular vel.ocity

Hello! I'm trying to derive the linear velocity vector from the position vector and the angular momentum vector. I've seen on the internet that V = W x R (V,W and R are all vectors and x is the cross product) but I cannot for the life of me derive it! I've tried doing it by writing out the...
20. ### I Proof derivative of a vector following precession motion

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...
21. ### Angular Momentum and Conservation of Angular Motion

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 cant get a crack at...
22. ### Using conservation of angular momentum as a braking system

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...
23. ### Construct States from Clebsch-Gordon Coefficients

Homework Statement Hello all, Im asked to construct the state | \frac{5}{2} , \frac{3}{2} \rangle from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle . Homework Equations Clebsch Gordon Coefficient's table The Attempt at a...
24. ### Linear momentum and Angular momentum

Homework Statement Two objects with mass of m are connected with a rod with length 2l and with no mass. The center of the rod is pinned so that it can spin. Object with mass M comes with speed v and sticks to m. There is no friction. 1) What is the angular speed w after collision? 2) FInd the...
25. ### Find the average angular acceleration of the sprinter

Homework Statement A sprinter runs the curve of this 200 m in 11.61 s. Assume he ran in a lane which makes a semicircle (r = 32.4 m) for the first part of the race. At 3.59 s into the race his speed is 5.9 m/s. At 7.9 s into the race his speed is 8.4 m/s. His speed after the curve was 12.4 m/s...
26. ### How to convert orbital momentum into spin momentum?

orbital movement occupy more space than spin movement. If an object are running in both orbit and spin, how to stop orbit and transfer orbit energy to spin energy? Of course the total angular momentum conserves. I know new optical technology can convert spin energy into orbital energy, but it...
27. ### Falling chain on a cylinder

Hi! I am struggling with this problem the last two days and I cannot decide which solution is correct. Homework Statement A cylinder of radius R is fixed horizontally on the floor. A uniform chain of mass M and length L (L<πR/2) is placed on the cylinder in such a way that one end of the...
28. ### Collision of two rolling bodies

Homework Statement A solid sphere is rolling without slipping on rough ground with an angular velocity w and linear velocity v. It collides elastically with an another identical sphere at rest. Radius of each sphere is R and mass m. What is the linear velocity of the first sphere after it...
29. ### Rotational Kinematics - angle between force and velocity

Here is the problem I am working on. I have found answers for all of them except part (f), which is the one I need help with. I will report the answers I have so far: A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00...
30. ### Setting up the double integral

A sheet of metal in the shape of a triangle massing 10 kg per square meter is to be spun at an angular velocity of 4 radians per second about some axis perpendicular to the plane of the sheet. The triangle is a right triangle with both short sides of length 1 meter. (a) The axis of rotation is...