Rotation Definition and 1000 Threads

Homework Statement How to prove that for any representation of the spin, the state e^{-i{\pi}J_x/\hbar}|j,m\rangle is proportional to |j,-m\rangle The exponential term is the rotation operator where J_x is the x-component of the total angular momentum operator, and |j,m\rangle is an...

Homework Statement Say we have a 2D rigid body transform, with parameters p = [ p_1,p_2,p_3] for rotation, x translation and y translation respectively. I'm using the transform to .. transform an image. Is there a way to have: For a point x , y : x',y' = transform(x,y,p) <=> x,y =...

Hey, I have Wick's rotated a contour integration of the form \frac{i\lambda}{2}\int d^{3}p\int \frac{dE}{(2\pi)^{4}}\frac{1}{E^{2}-p^{2}-m^{2}} this is the form where we integrate along the real line, we rotate this to 'Euclidean' Space such that we make the changes E\rightarrow iE\...

Homework Statement Find the volume of the solid generated by revolving the region between the parabola x = y^2 + 1 and the line x = 3 about the line x = 3. Homework Equations The answer is found by integrating with respect to y with disk method, but I don't understand why my answer is...

This has been a contradiction in my brain for some time. If I want to rotate one nuclei (spin 1/2), with say an applied magnetic field B and RF pulse (at the appropriate larmor frequency), how does the spin actually rotate? I thought it can only take on discrete values of 1/2 or -1/2...

If I have a point (x,y) and I rotate the axises by some amount. Why is x' = xcosθ+ysinθ and y'=-xsinθ+ycosθ?

First, while this is "homework" related I'm not seeking any direct answers. I'm stuck on a concept that I'm not sure even exists. In short I've got a rotating disk with a weight at the edge with "an initial" ω. If that object was to decrease the distance towards the center, would the ω...

Questions -- solving pendulum period of rotation Physical pendulum has a period of rotation that changes by Changing the temperature. According to the above show that the frequency shift of the pendulum would be: I have 2 questions,first solving the above question and the second how...

If i have a point at (0,0,5) in x,y,z system, then i make 2 rotation on the point with center at origin. i)the first rotation is on y-axis with angle P in clockwise direction. ii) the second rotation is on the point's new x-axis rotate in angle Q in clockwise direction. How can i find the...

Homework Statement I attached the problem as a word file. Homework Equations The Attempt at a Solution I think I will be able to solve this problem; my only questions is, can I treat the two disks as one, by summing their rotational inertias together?

Hello, If a rotation of a 2-d disk about a 1-d line can produce centrifugal gravity, is it right to infer that rotation of a 3-d volume about a 2-d plane would create gravity, observable in the 3-d volume? It is confusing to think about the direction of this gravity, if it exists...

I have a question about the concepts of rotation and revolution - on how they are treated in relativity. Since all motion is relative, a revolution of a planetary body around a central body could also be seen instead as a rotation of the central body w.r.t. a fixed (non-revolving) planetary...

Homework Statement So the problem states that we have a (+) enantiomer of a coumpund with an optical rotation of 50*. If a pure sample containes 42% of the (+) enantiomer and 58% of the (-) enantioimer, what is the optical rotation value. (By * i mean degrees) Homework Equations I'm not...

I have two 3d applications and when an object(a cube for example) is transferred between them, the rotation values of the cube change(the object stay at the same location. translation and scale values stay the same) and I can't find why that occurs and it's driving me crazy. app 1 rotation...

This has been brought up numerous times but I don't really understand it. Consider a rod in freefall. If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on...

Hi, A liquid in rotation give two kind of forces: 1/ centripetal 2/ pressure forces (Fa, Fb in the drawing) I'm ok that centripetal forces can't give energy (we lost kinetics energy) but Fa/Fb seems in direction to external circle, why it's not possible to recover energy from these...

Homework Statement A 0.9 kg mass at (x, y) = (20 cm,20 cm) and a 2.0 kg mass at (20 cm,100 cm) are connected by a massless, rigid rod. They rotate about the center of mass. Homework Equations x=(m1*x1+m2*x2)/(m1+m2) y=(m1*y1+m2*y2)/(m1+m2) I=1/12*ML^(2) The Attempt at a...

Homework Statement (see attachment) Homework Equations The Attempt at a Solution I am not able to understand the question and build a scenario in my mind. The question asks the distance traveled when the cylinder starts slipping. I can't think of the situation when the cylinder...

Object rotation about a fixed axis?? question about derivatives in this problem?? An object rotates about a fixed axis, and the angular position of a reference line on the object is given by θ=0.40e^(2t), where θ is in radians and t is in seconds. Consider a point on the object that is 4.0 cm...

Homework Statement a small solid sphere of mass m and radius r starts from rest and rolls down a hill without slipping. the sphere encounters a loop of radius R where R >> r. Given R determine the min height h such that the ball remains on the track throughout the loop Homework...

Homework Statement I need to express the rotation operator as follows R(uj) = cos(u/2) + 2i(\hbar) S_y sin(u/2) given the fact that R(uj)= e^(iuS_y/(\hbar)) using |+-z> as a basis, expanding R in a taylor series express S_y^2 as a matrix Homework Equations I know...

Homework Statement In a particular coordinate frame, the moment of inertia tensor of a rigid body is given by I = {{3,40},{4,9,0},{0,0,12}} in some units. The instantaneous angular velocity is given by ω = (2,3,4) in some units. Find a rotation matrix a that transforms to a new coordinate...

Homework Statement Equate the expression for centripetal acceleration with the gravitational acceleration to show that the central parts of the galactic rotation curve are consistent with rigid body rotation. The attempt at a solution Say a star near the galactic center has mass m and the...

Hello everybody :smile:, I'm new here and hope you can help me with this problem. I have to simulate the Earth rotation with eulers equations of motion (without external torques at first). I have given: Solution of eulers equation without external torques: \omega = (x, y, z)'...

Weird!? About the direction of rotation of wheels Suppose we consider a car moving on rough road in forward direction, wheels rotating clockwise. Since wheels rotate clockwisely they will push road backwards so friction acts forwards i.e. in direction of motion of car.The car will move...

I'm working with 3D applications, and I'm trying to figure out how to calculate the rotation of x number of points between two points. I've made a video to illustrate what I mean: https://www.youtube.com/watch?v=CmIk8I8itrQ So the thing is, I need to find some kind of formula that...

Hey, I have a question regarding the invariance of a 'mixed' Casimir operator under rotation, By 'mixed' Casimir operator I refer to: \vec{J}_1\cdot \vec{J}_2 Where J1 and J2 are two independent angular momenta. I want to show that this 'mixed' Casimir operator is invariant under...

Homework Statement m=55kg r=6400km The Earth's rotation increases so on a bathroom scale, it now reads that you weight 0. how long is 1 "day" on Earth? Homework Equations I keep trying to figure this one out, but with different ways I've tried, I put Fg as 0 and it basically...

the pressure of air inside a car tyre increases when the car is traveled at HIGH SPEEDS?why is this so?my guess is that at high speeds,the friction between the tyre and road surface increases..so kinetic energy is dissipated as heat energy due to friction.this heat is transfers to the inside of...

Homework Statement Hi I have a coordinate system as attached, and I want to rotate it along the y-axis in the clockwise direction as shown. For this purpose I use R = \left( {\begin{array}{*{20}c} {\cos \theta } & 0 & {\sin \theta } \\ 0 & 1 & 0 \\ { - \sin \theta } & 0 & {\cos...

Hi, I am interested in the issue of frame dragging used in a number of galactic rotation models. However, I wanted to first make sure that I have a better understanding the relativistic implications of frame dragging. While the issue of galactic rotation is not the subject of this thread, it is...

I recently saw a documentary, which claimed that if the Earth rotation slows down the water of the oceans will flood to the north and south because the centripetal force at the equator diminishes. In fact, earth’s radius is about 20 km longer at the equator than at the poles. However, I doubt...

Hello all. I'm a newer engineer in rotor dynamics trying to better understand some things, so perhaps someone can provide some insight... First, I'm trying to better understand the physics of forced, non-centroidal rotation (for a spinning cylinder in particular). Non-centroidal rotation...

Hello, I make the calculation of the curve rotation. Casertano(1982г.) [SIZE="3"]V^{2}=-8GR \int_{0}^{\infty}{r} \int_{0}^{\infty}{ [\frac {\partial p(r,z)} {\partial r}] \frac {K(p)-E(p)} {\sqrt{R r p}}}dzdr [SIZE="2"]p = x - \sqrt{x^{2}-1} x=(R^{2}+u^{2}+z^{2})/(2Rr) Density...

I'm just learning this Latex(sic) formatting, so it's not ideal. I was trying to explore the geometrical significance of the cross product when I happened upon an interesting observation. I've seen things like this before, but never had time to really examine them. I define two vectors...

Homework Statement if a disc of mas m is pure rolling , with velocity v . the instantaneous axis of rotation would be the point of contact with the ground . As shown in the diagram this could be considered as a disc rotating about one of the point on circumference for an instant of time ...

Homework Statement https://dl.dropbox.com/u/66988308/Capture.JPG Homework Equations V=rWThe Attempt at a Solution I tried to plug in the forumla , and algebras but I keep getting rc/rf as answer instead of rf/rc as the book says. Work: Vf=(rf)W W=Vf/rf W=Vc/rc Vc/rc = Vf/rf (Vc)(rf) = (Vf)...

was watching a documentary about Kurt godel and his idea about going back in time if you looped time, and the only real world way they said that this could be done was to loop time everywhere. The they said that the universe however does not rotate. Which interested me because i couldn't think...

If I rotate an object about an arbitrary axis, I can draw an arrow along that axis, and assign it a length proportional to the amount of rotation. I can project that arrow onto the basis of a rectangular coordinate system. The question arises, is it a vector? I can certainly transform it...

The matrix is | 1/2 -1/2 | | 1/2 1/2 | Why is this matrix not representing a rotation? The form of rotation is | cos x -sin x | |sin x cos x | So in this case tan x = 1 and so x = 45...isn't this rotation of 45 degrees?On similar note, for the matrix | 5 6 | | -6 5 | it...

Hi all, Q. A function takes (x,y) and gives (y,x). Is this function injective? For any function to be injective, f(x,y)=f(x',y')=>(x,y)=(x',y'). But here, I get, (y,x)=(y',x') How can I show the function is injective? It appears to be one. Thank You.

Let's say I had an object in space, a ring in this particular case, who was using light energy to spin itself up. The ring was built with a reactor inside of it along with a passenger/observer (we'll call the inside observer Bob for now). Bob, the ring, and the reactor are pretty much...

Homework Statement Determine the matrix representation of the rotation operator R(\phi k) using the states |+z> and |-z> as a basis. Using your matrix representation verify that R^{\dagger}R=1 The Attempt at a Solution Do I need to write R| \psi> in terms of a matrix. If I...

I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0). To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0) I rotated around the z...

Greetings, this is my first post, though I have been reading these forums for a while. I understand that the average energy of each degree of freedom in a thermodynamic system in equilibrium is kT/2. My textbook says that for a monatomic gas particle, the only degrees of freedom that count...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=1+sec x y=3 about y=1 Homework Equations The Attempt at a Solution I don't understand how to do...

Homework Statement Please see the rotation formula in the attachment. Homework Equations The Attempt at a Solution I understand this formula rotates x,y into x',y' by some angle theta. Problem is, how is this formula derived? I cannot for the life of me visualize the cosine and...

imagine we rotate a vector centered at the origin with euler angles alpha,beta,gamma. now the question is, can we do this rotation by the means of defining a vector N(which its length is 1).and rotating the vector zeta radians counter clockwise around N? I think it must be possible and I want...

Hey, I am trying to solve the following problem: va=vr+ ω × rra vb=vr+ ω ×(rra+rab) vc=vr+ ω × (rra+rac) I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid...

I heard an interesting proposal - it sounds plausible but I'm here to see what you guys think. It is a way of explaining a diverse set of natural phenomena on Earth with one mechanism - rotation. The proposal is this: The core of the Earth rotates in the opposite direction to the Earth's...