The rotation tag has no wiki summary.
2
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1answer
60 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 ...
3
votes
0answers
25 views
What's wrong with this application of Thomas Precession to circular motion velocity measurements?
If you happen to have the Third Edition of Classical Electrodynamics by John David Jackson, turn to section 11.8, as that's where I'm getting all this from. If not, you should still be able to follow ...
8
votes
5answers
875 views
How is it that angular velocities are vectors, while rotations aren't?
Does anyone have an intuitive explanation of why this is the case?
0
votes
1answer
39 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 ...
2
votes
1answer
68 views
Convert a 200mm linear stroke into 90 degrees motion
Can anyone help me Convert a 200 mm linear stroke into 90 degrees motion with as much mechanical advantage as possible or into two 90 degrees motions with as much mechanical advantage as possible?
...
13
votes
1answer
150 views
Is period of rotation relative?
My question is inspired by the following answer by voix to another problem:
"There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
2
votes
2answers
61 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
58 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 ...
28
votes
4answers
1k views
Does the sun rotate?
As implied from the question, does the sun rotate? If so, do other stars not including the sun also rotate? Would there be any consequences if the sun and other stars didn't rotate? Me and my friends ...
28
votes
8answers
5k views
Would it matter if the Earth rotated clockwise?
In the Futurama episode "That Darn Katz!" they save the world by rotating the Earth backwards saying it shouldn't matter (which direction Earth rotates). If Earth rotated clockwise and remained in ...
1
vote
3answers
339 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 ...
1
vote
2answers
688 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 ...
3
votes
2answers
57 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 ...
3
votes
2answers
233 views
What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?
Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating ...
1
vote
1answer
68 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
247 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 ...
3
votes
2answers
297 views
Pauli matrix rotations
When doing physics with two-level systems and introducing rotations, a term that appears quite often is the rotation of a pauli matrix by another one:
$e^{- i \sigma_i \theta/2} \sigma_k e^{i ...
2
votes
1answer
99 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
94 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?
1
vote
2answers
101 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 ...
2
votes
0answers
495 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 ...
0
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1answer
87 views
What happens at the end of Coriolis Deflection
Consider we launch a cannonball due south from a point at 45 degrees latitude in the Northern Hemisphere (e.g the point defined with the co-ordinate system on this diagram). The cannonball travels for ...
1
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1answer
182 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 ...
-3
votes
1answer
130 views
How can the Earth's day increase and its rotation slow down at the same time? [closed]
I heard that the Earth rotation is slowing down, but I also heard the Earth's length of day is increasing.
Does the two theories go together or conflict with each other?
13
votes
1answer
644 views
Which way do spiral galaxies rotate?
Is it known whether spiral galaxies typically (or exclusively?) rotate with the arms trailing or facing?
Intuitively it feels weird to think of the arms as facing the direction of rotation, but ...
5
votes
4answers
657 views
Video of Earth spinning?
If the Earth is spinning or rotating at a really fast speed, why haven't we seen any videos from space of it spinning when we get a lot of photos of it?
0
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3answers
267 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.
...
0
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0answers
31 views
Research on galaxy “stiffness”? [duplicate]
Possible Duplicate:
Are galactic stars spiraling inwards?
Has there been any research on the effects of interstellar gravitational attraction that would make collective star motion in a ...
9
votes
1answer
277 views
If the Earth didn't rotate, how would a Foucault pendulum work?
How does the Foucault pendulum work exactly, and would it work at all, if the Earth didn't rotate?
2
votes
2answers
517 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 ...
0
votes
1answer
162 views
What are the known relationships between rotation of planets/moons and their distance to Sun?
What are the known relationships between rotation of planets/moons and their distance to Sun? Or any other known attributes? For example, the sidereal year for planets is directly related to their ...
4
votes
2answers
194 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 ...
1
vote
1answer
98 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 ...
4
votes
2answers
212 views
Equivalent Rotation using Baker-Campbell-Hausdorff relation
Is there a way in which one can use the BCH relation to find the equivalent angle and the axis for two rotations? I am aware that one can do it in a precise way using Euler Angles but I was wondering ...
0
votes
3answers
101 views
Why is $F = mg - T$ in this case?
The situation is as follows:
I am told that $F_{net} = mg - T$ in this case, but doesn't that not take into account that $T$ isn't applied to the center of mass? Newton's second law is defined for ...
4
votes
4answers
924 views
Two axes for rotational motion
I understand that angular momentum is a vector, etc..
But, what really happens when some object, say a ball for example, is set to rotate along two axes? What would the resulting motion look like?
0
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2answers
53 views
How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A, they move with same angular velocity?
How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A( circular motion), they move with same angular velocity? In this special case if ...
0
votes
1answer
140 views
Two Different Sorts of Inertia: Inertial Mass and Moment of Inertia
There are two different sorts of inertia: inertial mass and moment of inertia.
I am currently reading about moment of inertia. Now, I know inertia is an important concept; with it, we can determine ...
3
votes
2answers
942 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 ...
0
votes
1answer
293 views
Finding Constant Angular Acceleration
The question is, "A centrifuge in a medical laboratory rotates at an angular speed of 3500 rev/min. When switched off, it rotates 46.0 times before coming to rest. Find the constant angular ...
0
votes
2answers
260 views
Vector Nature Of Angular Velocity
I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
1
vote
1answer
109 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 ...
2
votes
2answers
225 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 ...
1
vote
2answers
376 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 ...
4
votes
2answers
209 views
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 ...
1
vote
1answer
106 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 ...
2
votes
1answer
318 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:
...
4
votes
2answers
219 views
Why does the wheel of a car appear to be moving in opposite direction?
When a car is about to stop, the speed of its wheel reduces. Why do we see or feel that the wheel of the car is moving in the opposite direction? This can also be observed of a fan at home. So why ...
0
votes
0answers
67 views
How to control heavy ball in x and y direction? [closed]
I'm trying to build a device that holds a rather heavy ball and I want to be able to control it's "movement" in the X and Y directions (they are horizontal as well as orthogonal).
My current ...
7
votes
3answers
283 views
Can one make a ball rotate around a vertical axis using only a combination of horizontal axis rotations?
This is a nice problem that I would like to share.
Problem: In a public garden, there a statue consisting of a spherical stone and a stone cup. The ball is 1 meter in diameter and weighs at least a ...
