Circular motion about a central point or axis

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1answer
133 views

Why does this model fall apart when angular velocity is small?

I'm doing a physics problem in which a marble spins around a spinning bowl and both have angular velocity $\omega$. It rotates with radius $r$ around the central axis and the hemispherical bowl has ...
2
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3answers
220 views

Could we use the coriolis effect to travel

Given a platform that is floating independent of Earth's gravity, would it be possible to put a platform over the equator and over the day, would the Earth rotate from under it allowing you to travel ...
2
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1answer
28 views

Can a tidally locked planet have a horizontal rotational axis?

Is it hypothetically possible for a planet to be both tidally locked, and still have a rotation "horizontally"? Where the substellar point would in effect be like the point of a top, spinning and yet ...
2
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2answers
61 views

What happens to a body if it rotates extremely fast?

I am thinking on a object, e.g. ball or planet that starts rotating with increasing speed. Let's assume that his speed get's closer to the speed of light, what happens to this object? There are ...
2
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1answer
3k views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
2
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4answers
109 views

Do these cars rotate on themselves?

I was reading about the moon rotation around earth and the tidal lock related. I found some interesting information already here and on astronomy.stackexchange.com as well. The moon is known to have a ...
2
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2answers
3k views

Why do most of the motor with blades rotate anti-clockwise when viewed from the front facing the blade?

I have noticed that most of the motor with blades and engines rotate anti-clockwise direction when viewed from front facing blade. Is there any specific reason for this? Is it because of any kind of ...
2
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1answer
615 views

Eigenvectors of a 4D rotation, and their interpretation

Let us define a 4D rotation by using two unit quaternions: $$\mathring{q}_l=\frac{a+ib+jc+kd}{\left|a+ib+jc+kd\right|}$$ and $$\mathring{q}_r=\frac{e+ib+jc+kd}{\left|e+ib+jc+kd\right|}.$$ They differ ...
2
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1answer
286 views

Does the Earth rotate the same encased in ice during the height of an Ice Age as it does when the bulk of it's water is liquid and always in motion?

Ice Age vs. Now. Does the Earth rotate at the same rate when encased in ice during the height of an Ice Age as it does when the bulk of it's water is liquid and always in motion?
2
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2answers
3k views

Formula for Rotation curves of Galaxies

To ask a more specific one for the rotation curves of elliptical galaxies, and hope from there to later understand the dynamics of spiral galaxies. Treating the galaxy as an isothermal ...
2
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1answer
62 views

Who has succeeded in demonstrating the Lense-Thirring effect?

Who has succeeded in demonstrating the Lense-Thirring effect? This effect is one that describes the rotational motion of the Earth from a space-time structure. This effect is the "drag" of the ...
2
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1answer
104 views

Synchronising the Earth's rotation via mass redistribution

How much material would have to be moved per year from mountain-tops to valleys in order to keep the Earth's rotation synchronised with UTC, thus removing the need for leap seconds to be periodically ...
2
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1answer
51 views

Contraction of a rotating system

Consider a system of two masses that rotates with constant angular velocity. When a force contracts the system the velocitie of the two masses increase. I understand this in terms of conservation of ...
2
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1answer
105 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
2
votes
3answers
328 views

Sign of torque when rolling an object down an incline

Suppose you have an object rolling down the incline at 30 degrees. Given the point of contact is instantaneously at rest, I decided to analyse torques at that point. Therefore, the only force ...
2
votes
1answer
394 views

Why do Uranus and Venus rotate from East to west?

Why do only Uranus and Venus rotate from East to west, while others rotate in opposite direction? Is it because of the angle of their tiltness? Or due to the process of their formation?
2
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1answer
560 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
2
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2answers
86 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
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3answers
133 views

Is it possible to extract energy from mass rotating in space?

Consider a single isolated rotating mass (for example planet), is it possible to extract energy out of its rotation? If yes, how could that theoretically be achieved?
2
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1answer
220 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
2
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2answers
442 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
2
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2answers
335 views

Exchange operator in terms of rotation operator

I have studied about exchange operators and rotation operators and I know that an exchange between 2 particles in a combined state is the same as rotating each particle 180 degrees (according to http:/...
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3answers
52 views

Force at axis of spinning wheel

This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis ...
2
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3answers
64 views

Kinetic energy of a rotating object

in an exercise, a linear molecule is being subject to a force applied on the edge in its axis. Then $K_1=\frac{1}{2}mv^2$, all is well. Then in the second point of the exercise, the force is applied ...
2
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1answer
632 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 ...
2
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2answers
140 views

Half-integer spin and infinitesimal rotations

On p. 692 of 'Quantum Mechanics' by Cohen-Tannoudji, he states that: Every finite rotation can be decomposed into an infinite number of infinitesimal rotations, since the angle of rotation can ...
2
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1answer
192 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
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2answers
77 views

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 ...
2
votes
1answer
120 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
150 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 $R(n,...
2
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2answers
504 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 ...
2
votes
1answer
79 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 ...
2
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1answer
543 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 (...
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0answers
14 views

What force is needed to turn the Earth Pole-over Pole. Eg. UK now on Equator? [closed]

Specifically, if someone could specify the Joules energy required to force the Earth to slowly rotate the poles end-to-end by say 1 degrees rotation, and by 5 degrees. To be clear I mean to literally ...
2
votes
1answer
207 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
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0answers
48 views

Euler angles and curvilinear coordinate systems

If I have a curvilinear coordinate system and supposing I impose the condition that back transformations to Cartesian coordinate system are not permitted. I perform a rotation of the three axes( say ...
2
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2answers
117 views

Prove that a translation operator times a reflection operator is unitary and Hermitian [closed]

I am trying to prove some properties of the product of the (unitary) translation operator $\hat{T}(a)\psi(x) = \psi(x-a)$ and the (Hermitian) reflection operator $\hat{R} \psi(x) = \psi(-x)$. In ...
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2answers
98 views

A Confusion in Rotational Dynamics

I am trying to analyse the following situation using classical mechanical concepts. Consider a a straight rod $AB$ of mass $M$ and length $L$ placed on a frictionless horizontal surface. A force $F$ ...
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0answers
86 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 $\omega~\text{rad/s}...
2
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0answers
162 views

What is the relativistic mass of this spinning ball? [closed]

Relativistic Mass is: $$ m_r = \frac{m}{\sqrt{1 - v^2/c^2}} $$ So Einstein says that the faster an object moves, the more mass it gains (relativistic mass). So suppose you have a spherical ball ...
2
votes
1answer
511 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 ...
2
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0answers
205 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
70 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 ...
2
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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 http://en.wikipedia.org/...
2
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0answers
76 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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5answers
108 views

Rolling without slipping taking the contact point as pivot

I'm confused about this "rolling without slipping" kind of situation. Or better in this case the object is rolling and slipping, just use the label "rolling without slipping" to identify the kind of ...
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2answers
290 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
4k 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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3answers
963 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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3answers
83 views

Rolling without slipping in absence of friction force

I'm confused about a rolling without slipping situation. Suppose to have a disk of radius $R$ on a floor, and exert a horizontal force at a certain distance $r$ from the center of mass. I would like ...