Circular motion about a central point or axis

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365 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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1k 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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592 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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1k views

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
1k 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: ...
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117 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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226 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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75 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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4answers
917 views

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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143 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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108 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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561 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
96 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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1answer
165 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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2answers
78 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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7k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
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225 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
272 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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1answer
66 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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1answer
405 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
85 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 ...
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1answer
35 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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2answers
884 views

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, ...
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1answer
969 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 ...
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3answers
436 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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263 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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649 views

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
169 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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2answers
221 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 ...
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2answers
540 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 ...
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3answers
212 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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2answers
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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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1answer
100 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 ...
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4answers
14k 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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3answers
190 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 ...
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4answers
871 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 ...
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1answer
1k views

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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4answers
105 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 ...
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1answer
216 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?
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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 ...
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1answer
58 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 ...
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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 ...
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1answer
114 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 ...
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2answers
71 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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106 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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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 ...
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1answer
139 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 ...
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495 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 ...
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2answers
273 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 ...