The rotation tag has no wiki summary.
0
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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 ...
13
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1answer
147 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
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2answers
60 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
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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?
...
27
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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 ...
2
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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 ...
1
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1answer
67 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
242 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
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2answers
296 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 ...
3
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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 ...
2
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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
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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
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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
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0answers
489 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 ...
1
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1answer
180 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 ...
0
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3answers
264 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.
...
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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 ...
4
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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
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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 ...
0
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1answer
86 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 ...
0
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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 ...
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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
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1answer
138 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 ...
0
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1answer
291 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 ...
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2answers
941 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
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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
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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 ...
1
vote
2answers
374 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
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2answers
206 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
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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
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2answers
217 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 ...
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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 ...
2
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2answers
224 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
282 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 ...
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2answers
289 views
How long was a day at the creation of earth?
Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)?
I ...
0
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1answer
440 views
Rotation of parabola
I'm designing a parabolic solar concentrator and am doing ray-tracing on Matlab from scratch. I'm beginning to look into compound concentrators and would need to have an equation for a parabola ...
2
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2answers
155 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 ...
3
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0answers
65 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 ...
3
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3answers
243 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 ...
28
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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 ...
4
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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 ...
4
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2answers
126 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 ...
0
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1answer
60 views
Would we feel the rotation of a rotating habitat?
Assume that a space habitat is shaped like a can with the "top" open.
lets say we attach the can's top to a string with an astronaut standing on the base. We then rotate the can in deep space using ...
2
votes
1answer
142 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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2answers
1k views
Rotational kinetic energy during vertical circular motion of a particle
Why is it not necessary to take into account rotational kinetic energy when using the Law of Conservation of Mechanical Energy to solve vertical circular motion problems? After all, the particle is ...
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0answers
459 views
Rotating Disc and Magnetic Field [closed]
I'm studying for exams, and I am curious as to how the rotation of a disc would affect the magnetic field. The following problem stumps me:
A plastic disc of radius $R$ has a charge $q$ uniformly ...
4
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1answer
328 views
Is all angular momentum quantized?
Angular momentum is definitely quantized in elementary particles and electrons in atoms.
Molecules also have characteristic rotation spectra.
Is it true that all angular momentum is quantized, ...
2
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1answer
42 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 ...
7
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3answers
467 views
Shape of rotating rope (lasso problem?)
Let's take a wire or a rope. I usually do this with a chain or my scarf.
I fixate one end in my hand and apply rotation (by subtle movements of this endpoint like spinning a lasso). The rope gets ...
