Circular motion about a central point or axis

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980 views

Does the Earth rotate vertically too?

We know that the earth has seen several Ice Ages. And we know the Earth's magnetic poles seem to flip once in a while. Could all of this be explained by a once every 250 Million Years or so the ...
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1answer
768 views

How do you rotate spin of an electron?

I can't seem to connect these two stories. Can you please help? I have heard that you have to turn electron by 720 degrees in order to get the same spin state. Has this been seen experimentally? How ...
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What is the formal definition of a stellar day?

I'm having trouble understanding precisely what a stellar day is. Neither the USNO nor the IERS sites provide a definition. And Wikipedia's description as the "rotation period relative to the fixed ...
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2answers
176 views

Would the arms of a rotating ice skater still move outwards if there was no other object in the universe?

If there is no other object in the universe apart from a rotating ice skater, then nothing can be used as a reference frame. Would it make any sense to say that the skater is rotating? If so, rotating ...
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1answer
447 views

Does total angular momentum of the Earth-Moon system include individual rotational angular momenta?

To calculate the angular momentum of a body we need to specify a point (or an axis?) from which to define the displacement vector $\vec{r}$, so that $\vec{L} = \vec{r} \times \vec{p}$. For a rigid ...
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273 views

Bicycle counter-intuitive: in which direction it will move? [duplicate]

I saw this puzzle in a local newspaper: Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the ...
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2k views

Angular Displacement

If something is rotating about a point and it covers a complete circle, should we take its angular displacement as 360 degree or 0? Please give link to some established material on this subject ...
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922 views

Why do gyroscopes not maintain their stability as seen in this video

What exactly causes gyroscopes to oscillate as seen in this video. http://www.youtube.com/watch?v=gdAmEEAiJWo Even when my toy gyroscope spins on Earth, I get oscillations. Is this a result of ...
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How can I cause a levitating magnet to rotate?

I have a device like this one: http://www.youtube.com/watch?v=kA_hw_lY-OY (All of them work the same) Here's an image: I want to make it spin without touching it with hands. I tried using magnets ...
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1answer
162 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
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1answer
194 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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302 views

Can a minimum ultimate tensile strength (UTS) for an asteroid be established based on its diameter and rotation?

I found it fascinating that many asteroids rotate with a period of just seconds. For this fast of a rotation on this size of object, I thought that would actually cause significant acceleration on the ...
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Why rotating reference frames are not inertial? [duplicate]

Let's say I'm standing on the equator, and that there is no other reference point in the sky. If the planet is rotating, then I measure my weight to be lower than if it is not. But given that I have ...
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1answer
552 views

Angular velocity relative to different frames

In Goldstein it is said "It is intuitively obvious that the rotation angle of a rigid body displacement, as also the instantaneous angular velocity vector, is independent of the choice of origin of ...
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2answers
77 views

Tensors of rotations about an arbitrary vector in C^2

I'm trying to solve the following equation: $$e^{-i\theta/2 \sigma_{\vec{i}}^A} \otimes e^{-i\theta/2 \sigma_{\vec{i}}^B} |\Psi\rangle_{AB} = e^{i\phi} |\Psi\rangle_{AB} $$ where $e^{i\phi}$ should ...
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Puzzling : Relative motion of two points on a rotating disc

Consider two points on a radial line for a rotating disc. One point, $A$, is at the circumference and the other, $B$, is at distance $R/2$ from disc's centre. Relative velocity of $B$ w.r.t. $A$ ...
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Why does a pot start rotating when coffee is stirred inside?

I usually make Turkish coffee as my morning coffee. I have a small somewhat rounded pot with handle on one side. I noticed that when I pour water in and start stirring, pot has a tendency to start ...
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2answers
710 views

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

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 ...
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4answers
30k views

Relationship between torque and angular momentum

I want to know how to deduce the equation $\vec{\tau}=\vec{\omega} \times \vec{L}$, where $\vec{\tau}$ is the moment of force (also known as torque), $\vec{L}$ is the angular momentum, $...
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2answers
199 views

Confusion with rotation operator definition in Shankar

In Shankar quantum mechanics on page 306-307 it has the following: 12.2. Rotations in Two Dimensions Classically, the effect of a rotation $\phi_0\mathbf{k}$, i.e., by an angle $\phi_0$ about ...
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2answers
282 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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2answers
3k 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 ...
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3answers
679 views

Rotational speed of a discus

I was wondering whether the rotational speed of a discus has any influence on the flight of the discus. Would slowing the rotation or speeding it up change the trajectory in any way or would the ...
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3answers
120 views

Rotation in the x-t plane

I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation ...
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2answers
119 views

Physics of tidal locking: can the process be underdamped?

Is it possible for a satellite undergoing the process to overshoot the required rotation rate for tidal locking? For example, if its rotation rate is being slowed, can it become slower than it needs ...
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Instantaneous axis of rotation and rolling cone motion

Suppose a cone is purely rolling (no slipping) around a fixed axis. I mean, it is revolving around a fixed axis perpendicular to the ground and passing through its vertex and also rotating, so the ...
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1answer
173 views

What exactly is the definition of motion and its relation to Mach's conjecture?

The notion of "movement" seems to be well understood in physics. In fact, I don't recall any physics text-book defining motion. Special relativity theory says that there is no absolute frame of ...
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130 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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89 views

What is the difference between translation and rotation, in the Lagrangian/Hamiltonian frameworks?

This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian ...
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1answer
246 views

What's a pseudo-rotation?

I'm sorry for this lexical, probably extremely elementary, question. But what is a pseudo-rotation? I just read this term for the first time, in the beginning of the 4th chapter book of CFT by Di ...
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1answer
288 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 ...
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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 ...
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1answer
217 views

Angular momentum-torque relationship in a rotating frame?

I have read that $$\vec\tau=\frac{\mathrm{d}\vec L}{\mathrm{d}t}$$ holds true whenever the origin is not accelerating. But I cannot see why this holds true for a rotating frame of reference (such as ...
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135 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?
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1answer
467 views

Why can we use just one angular velocity vector to describe the rotation of a whole non-inertial reference frame?

The other day in class the professor was explaining non-inertial reference frames. We were working out how to find the acceleration of a point as measured from the non-inertial reference frame, and ...
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1answer
58 views

Finding rotation axis of an operator on Bloch sphere

I would like to find the action of an operator $V$ on the Bloch sphere. The matrix representation of $V$ is $V=\sqrt{\frac{i}{2}}\begin{pmatrix} i &-1 \\ -1 &i\end{pmatrix}$. $\rightarrow |\...
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1answer
130 views

Rotating hoop with fixed body inside of same mass [closed]

Please help me to solve this problem. I am unable to understand which force will cause the hoop to bounce. A small body $A$ is fixed to the inside of a thin rigid hoop of radius $R$ and mass ...
3
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1answer
36 views

Reference for the polar parameterization of quaternions

I would like to find the original reference in which the polar parameterization of quaternions was given (i.e. the relationship between the components of a unit quaternion and the polar angles of an ...
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4answers
561 views

Would this box on the floor rotate based on friction?

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 ...
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2answers
520 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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2answers
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Euler angle: space-fixed vs body-fixed axes

I am sooo confused!! Between active and passive, intrinsic and extrinsic, vectors and basis .... Stipulate that we stick to active rotations only. Then Standard derivation of $R(\alpha, \beta,\...
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1answer
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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 ...
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1answer
327 views

Finding frame of reference where angular momentum appears zero

Consider a isolated system of $n$ non-interacting classical particles. We can easily select a barycentric frame of reference, where total momentum will be zero, so we have our $\vec x(i)$ — ...
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3answers
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Object moving in a circular path without accelerating

A train is moving with a constant speed on a straight portion of track. Then, it encounters a curve in the tracks, and goes along the curve. However, it does not change the magnitude of acceleration ...
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3answers
181 views

What does “transform among themselves” mean?

I'm reading a script on atomic physics, and there's a chapter on irreducible tensors. I can't understand the meaning of "transform among themselves" in this context: An arbitrary rotation of the ...
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3answers
140 views

Is centripetal acceleration mandatory for circular motion?

If we consider a case where a closed circular wall is present, and inside the boundary, just adjacent to the inner wall, two particles are placed touching the surface of inner boundary such that the ...
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2answers
275 views

Rotation of Taylor expansion of a scalar

I have a scalar magnetic field in a volume expressed by the formula $$B(x,y)=B_0 + \frac{\partial B}{\partial x}(x-x_0) + \frac{\partial B}{\partial y}(y-y_0)$$ which approximates the non-...
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3answers
384 views

Two-rotation coordinate transformation

I've designed an electronic device that uses a 3-axis accelerometer to measure the acceleration of an automobile. I'm only interested in accelerations in the plane of the road surface, so I want to ...
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4answers
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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 ...
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4answers
188 views

Rotation of a vector

Is a vector necessarily changed when it is rotated through an angle? I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. ...