Circular motion about a central point or axis

learn more… | top users | synonyms

2
votes
2answers
328 views

Rotation, cats landing on their feet, and conservation of angular momentum

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity. It is well-known that θ can change even when the body is not rotating, using the conservation of angular ...
2
votes
3answers
160 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
votes
2answers
961 views

3D: Get linear velocity from position and angular velocity

I want to find out the linear velocity of a point in 3D space, (Euclidean), given: Its position Its angular velocity The point it's rotating around (fulcrum) (This is a problem I need to solve ...
2
votes
2answers
964 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
votes
3answers
710 views

Does being suspended in air allow you to not be affected by Earth's rotation?

Let's assume that there was some mechanism by which we could remain suspended in air. By this I mean that our feet is not in contact with the ground. One possible way of doing this would be by means ...
2
votes
4answers
603 views

why does what get pushed away when centripetal acceleration is towards the center

If centripetal acceleration is towards the center, then why - when you spin a bucket of water (a classic demonstration) - does the water not get pushed out but rather stays in the bucket without ...
2
votes
1answer
167 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
votes
1answer
51 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
votes
1answer
93 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
votes
2answers
137 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
votes
1answer
71 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
votes
1answer
318 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
votes
1answer
571 views

What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
2
votes
2answers
195 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 ...
2
votes
1answer
237 views

What “I” should use in Rotational Energy formula $(I \omega^2)/2$

$\text{Rotational Energy} = \frac{1}{2} I \omega^2$. What $I$ should be used? $I$ as a inertia tensor matrix = stepRotation * inverse moment of inertia * inverse stepRotation; Or I as moment of ...
2
votes
2answers
136 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
75 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
votes
1answer
200 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
votes
1answer
638 views

Help understanding a Magnetic Levitation “Physics Toy”

I was shown a toy, yesterday, which I would like help understanding qualitatively. A fellow engineer showed me a kit which included three main parts: 1.) A base (black box), approximately 4 ...
2
votes
1answer
31 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
votes
1answer
113 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 ...
2
votes
0answers
49 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
votes
2answers
183 views

Would box on the floor rotate?

There is a floor that friction is proportional to its velocity (like $F=-kv$) and there is a box with its width as $l$ and its height as $h$. (you may assume that $l$ is longer than $h$). It is on the ...
2
votes
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 ...
2
votes
0answers
68 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 ...
1
vote
3answers
437 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 ...
1
vote
2answers
1k 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 ...
1
vote
2answers
262 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 ...
1
vote
1answer
143 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' ...
1
vote
2answers
1k 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 ...
1
vote
1answer
86 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?
1
vote
2answers
935 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 ...
1
vote
2answers
143 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 ...
1
vote
1answer
54 views

Is sun revolving around certain mass in space with reference to some other galaxy?

Every planet and satellite revolves around their mother planet and about their own axis as we know. So they are compacted as a system. Then why not sun?
1
vote
1answer
80 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 ...
1
vote
2answers
193 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 ...
1
vote
1answer
467 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 ...
1
vote
1answer
132 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 ...
1
vote
1answer
165 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 ...
1
vote
1answer
125 views

How can I name this 3D rotation

First I would like to be clear: this is a noob question, I need a simple answer if such an answer exists. In a three-dimentional space, how can I name this rotation? See an animation Let's assume X ...
1
vote
1answer
289 views

Finding stopping time when only given initial angular velocity and an expression for angular acceleration?

Question: A wheel starts is spinning at $27\text{ rad/s}$ but is slowing with an angular acceleration that has a magnitude given by $\alpha(t) = (3.0\;\mathrm{rad/s^4})t^2$. It stops in a time ...
1
vote
3answers
134 views

Derivation of the general Lorentz transformation

The standard Lorentz transformation or boost with velocity $u$ is given by $$\left(\begin{matrix} ct \\ x \\ y \\ z \end{matrix}\right) = \left(\begin{matrix} \gamma & \gamma u/c & 0 & 0 ...
1
vote
0answers
50 views

2d pool collision with rotational motion

I'm trying to calculate two 2d disks' collision with rotational motion. The collision is perfectly elastic: the sum of translational and rotational energy is conserved. In the instant of the collision ...
1
vote
0answers
41 views

Rotation motion like the number 8

I'm a college student majoring in culinology and I'm trying to find out the reason or method of the number 8 motion. Responses doesn't have to be in culinology examples, but that would be a great help ...
1
vote
0answers
59 views

Rotate the phase of a wavelet

Let's take a zero-phase Ricker wavelet which is given by: $$ \psi(t)=\frac{2}{\sqrt{3\sigma}\pi^{1/4}}\left(1-\frac{t^2}{\sigma^2}\right)e^{-t^2/2\sigma^2} $$ in the time domain which is often used ...
1
vote
1answer
41 views

Center of rotation and trajectory of a rigid body in a plane with applied *fixed* forces

This is my first question so please excuse me if my format is a bit off. Given a 2D rigid body with forces applied to it in such a way that the angle the force vector makes with the surface of the ...
1
vote
1answer
119 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 be ...
1
vote
1answer
99 views

Molecular rotation - Energy levels for an asymmetric molecule

For a molecule with spherical symmetry, the energy level of rotation for quantum number $J$ is: $$E(J)=\frac{J(J+1)\hbar^2}{8\pi^{2}I}$$ "$I$" is the Moment of inertia for the molecule ...
1
vote
0answers
31 views

Optics of a rotated spectacle lens [duplicate]

I have just discovered that if I rotate my left spectacle lens about the vertical axis by 10 degrees in one direction, the vision in that eye becomes much crisper. Note that the sphere and cylinder ...
1
vote
0answers
86 views

Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...