Circular motion about a central point or axis

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Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
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1answer
84 views

Deriving Rabi rotation matrix

I want to understand where the matrix: $$ \left|\psi(t)\right> = \binom{a(t)}{b(t)} = \begin{bmatrix} cos(\Omega t/2)&-ie^{i\phi_L t}sin(\Omega t/2) \\ -ie^{-i\phi_L t}sin(\Omega t/2) & ...
2
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1answer
143 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
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2answers
272 views

EM Fields in a Rotating Frame of Reference

I'm struggling on my approach to the problem of figuring out E and B fields in a non-relativistic way for a rotating frame of reference in the x-y plane around the z-axis. I am attempting to do this ...
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1answer
76 views

Schriffer Wolff Transformation - for first order change in eigenvalues

Step 1 Let me formulate the problem to convey my notation. I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation $$ U_A A\,\,U_A^{-1} = A_{diag}$$ Now the matrix is ...
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1answer
353 views

Transform torque from Euler angles to infinitesimal Cartesian rotations

For a certain pair of rigid bodies, I have the gradient of energy in terms of Euler angles. I want to transform this gradient to the gradient of energy in terms of rotations about the $x, y, z$ axes ...
2
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1answer
40 views

How can I set up an equation for distance traveled for a rubber band powered car?

I am to make a rubber band powered car, and I have to maximize it's distance traveled. The time taken to reach said distance, top speed of the car, acceleration of the car, is not relevant. I just ...
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0answers
59 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
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1answer
86 views

Symmetries of the action of the free classical Klein-Gordon field

I've read that the action for the free classical Klein-Gordon field $$S = \int \mathrm{d}^4x~ \mathcal{L} = \frac{1}{2} \int \mathrm{d}x^4 \left(\partial_\mu \phi(x) \, \partial^\mu \phi(x) - ...
2
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1answer
223 views

Increase in kinetic energy as some one walks to the centre of a merry-go-round?

When someone walks to the directly centre of a merry-go-round the total kinetic energy of the merry-go-round and person system increases. (assuming the kinetic energy due to the person walking to the ...
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0answers
114 views

Find the exact angle as a function of time for a rod that swings on a frictionless axle

This is a simple problem I thought of that I haven't been able to solve. Given a rod of uniform mass attached to a fixed axle, find the angle it makes with the horizontal if it is dropped from rest ...
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0answers
56 views

Stable planetary rotation states

In reading an article about theories as to how the slow retrograde rotation of Venus may have come into being, the article Why Venus Spins the Wrong Way (Franzen, 2001) stated that it is bound to ...
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0answers
2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
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0answers
73 views

Rotation in an 'empty' universe [duplicate]

Possible Duplicate: Is rotational motion relative to space? Assume a universe with the same physics as ours, but containing only one rotating (charge-free) body - let's say the size of the ...
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2answers
201 views

Does General Relativity correctly explain the ellipsoidal shape of the earth?

Does General Relativity theory correctly explain the ellipsoidal shape of the earth? It seems it does not because the Thirring expression¹ for the force of a spherical shell—of mass $M$, radius $R$, ...
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3answers
686 views

Maximum angular velocity to stop in one rotation with a known torque

I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that ...
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2answers
372 views

What point of application of force ensures more acceleration in a rod?

Suppose there is one rod and a force F is applied in two cases: Case 1: exactly at the middle on center of mass Case 2: at one end of rod In which case would the center of mass of rod be accelerated ...
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2answers
191 views

A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & ...
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3answers
2k views

Will a boiled egg or a raw egg stop rolling first?

If we roll a normal egg and a boiled egg at the same time on a floor 1) with friction 2) without friction which one will come to stop first (if they will stop at all) and why? Can anyone tell ...
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2answers
143 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
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2answers
285 views

Doubt concerning centripetal acceleration

What is the centripetal acceleration and angular velocity of a child located 8.2 m the center of a carousel? The speed (size of the tangential velocity) of the child is 2.1 m / s A train moves in a ...
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1answer
197 views

rotation matrix - why am I thinking this wrong?

The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix. $$ \begin{array}{lcl} x' &=& x \cos\theta - y \sin\theta \\ y' ...
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2answers
2k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
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1answer
36 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
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2answers
18 views

Stroboscope's unit

Can someone please tell me why does stroboscope's unit is rps or rpm. Revolution per minute/second. Although the stroboscope used was an electronic stroboscope. Is it has something to do with the ...
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1answer
36 views

Specific scenario involving rotation and inertial frames of reference?

We recently went over some rotational motion in my freshman physics class, I had a question for the professor on your frame of reference, and how that would effect the rotation of the object. Say you ...
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1answer
52 views

Motion of a rigrid body: Why is motion only a compostition of two forms: rotation and Translation?

If you are in a 2-D space the motion of any rigrid body is composed of 2 different things, namely rotation and translation. If you are in 3-D space the motion of any rigrid body is also composed of 2 ...
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1answer
50 views

Rotational Speeds

I was driving the other day and couldn't help but look at all the wind mills in the wind farms. I know I am not doing the math correctly, but I want to know what is "really" happening when a windmill ...
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4answers
228 views

Gravity doesn't seem to work the way it is supposed to [duplicate]

This has been a bit of an awkward question that's been plaguing me ever since I started watching space documentaries on discovery about 10 years ago. I was saving this for the day I would ever meet ...
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3answers
638 views

Is there a difference between “average acceleration” and centripetal acceleration?

Question adapted from Examkrackers MCAT prep book: A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the ...
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2answers
188 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
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2answers
232 views

What happens if the earth stops rotating? [duplicate]

I was wondering what would happen to all the components on the surface of the Earth if the Earth suddenly stops rotating but does not stop revolving.
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1answer
58 views

A pretty dumb question on observation

Very often I have seen, that a bicyclist can balance himself better, while in motion, than he can while at rest(with his legs on the paddles of the bicycle). Now, I know that objects, say, a disc ...
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2answers
63 views

Kinetic energy of a mass rotating about two axes

I'm working on a question where I have to find an equation for the kinetic energy of a mass being rotated by a fold-able arm. The equation for $m_1$ is obvious, however, the equation I derived for ...
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1answer
132 views

Can we calculate the frame dragging force of the Earth?

Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?
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1answer
3k views

How do I calculate the experimental and theoretical rotational inertia of a point mass?

I'm getting some weird results from a calculation I'm doing and quite honestly, I'm pretty sure it's my fault. I do have an apparatus involved for the experimental process for my lab but I don't think ...
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2answers
3k views

Slowdown rate of rotating body due to friction force [closed]

This isn't a homework question, but it might as well be. The problem I have been pondering is: If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
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2answers
200 views

Relativistic Lagrangian transformations

I need to study the relativistic lagrangian of a free particle. It's $\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
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1answer
45 views

Angular velocity and instantaneous rotation axis

Let's suppose that we have a cylinder of moment of inertia $I$ rolling on the floor without sliding, moving with linear velocity $v$ and rotating around an axis passing through the center of mass with ...
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1answer
70 views

Euler angle rotation - active/passive

I have a very simple problem, that I cannot wrap my head around and is hurting my brain. I have a very simple example of the problem, please consider the the figure below: In the first picture, you ...
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1answer
72 views

Physical interpretation of diffeomorphism from $SO(3)$ to $\mathbb R \mathbb P^3$

I am not good at picturing either $SO(3)$ or $\mathbb R \mathbb P^3$, the latter denoting the real projective space. Can someone give me a rough physical understanding of the geometry and implication ...
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1answer
107 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
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1answer
149 views

How to model a very simple spinning wheel

First off, I'm not a physics person, just a lowly software engineer with below average math skills. What I've written is a simple animation of a spinning wheel using C++/GTK/Cairo. It allows the user ...
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1answer
85 views

Rotating metal sphere

My knowledge of physics is not that great, but I am always willing to learn. I have the following question: If we have a sphere made out of metal with a radius of 1 meter, and it rotates in an ...
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1answer
1k views

Explaining the restorative force in a bifilar pendulum

Ok so I am an A2 physics student, and for one of my pieces of coursework I conducted a practical investigation, my topic being the factors affecting the period and swing of a bifilar pendulum. The ...
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2answers
265 views

Rotating a reference system on a vector

Assume you have a vector $\vec{x}=(\sin(\vartheta)\cos(\varphi),\sin(\vartheta)\sin(\varphi),\cos(\vartheta))$ given in spherical coordinates in a reference System "R". I want to rotate the reference ...
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1answer
763 views

Non-commutative property of rotation

Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
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3answers
1k views

Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram. Would an ...
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1answer
164 views

Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$

If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this: $$[J^2,R]~=~0?$$ This is stated in ...
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1answer
211 views

Earth is rotating [duplicate]

Possible Duplicate: Why does the atmosphere rotate along with the earth? If i take off from land on a helicopter straight above the earth surface to a certain height and stay there for few ...