The rotation tag has no wiki summary.
2
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1answer
106 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
330 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
1answer
147 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 ...
2
votes
1answer
426 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
82 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?
...
2
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0answers
551 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
vote
3answers
65 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
697 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
3answers
365 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
220 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
77 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.
$$ \begin{array}{lcl}
x' &=& x \cos\theta - y \sin\theta \\
y' ...
1
vote
2answers
295 views
3D: Get linear velocity from position and angular velocity
I want to find out the linear velocity of a point in 3D space, (Euclidean), given:
Its position
Its angular velocity
The point it's rotating around (fulcrum)
(This is a problem I need to solve ...
1
vote
2answers
70 views
Slowdown rate of rotating body due to friction force [closed]
This isn't a homework question, but it might as well be. The problem I have been pondering is:
If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
1
vote
2answers
52 views
Relativistic Lagrangian transformations
I need to study the relativistic lagrangian of a free particle.
It's
$\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
1
vote
2answers
423 views
Applying angular velocity to a rotation matrix
I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
1
vote
1answer
198 views
Non-commutative property of rotation
Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
1
vote
1answer
101 views
Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$
If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this:
$$[J^2,R]~=~0?$$
This is stated in ...
1
vote
1answer
118 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
109 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
167 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
2answers
109 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
0answers
143 views
Error caused by pulley eccentricity [closed]
Not sure if this is perfectly a physics question:
A rope is wrapped around a cylinder of diameter D. The cylinder is slightly eccentric so that the distance between the axis of the cylinder and the ...
0
votes
2answers
967 views
Argument for proving Earth-Centered Earth-Fixed (ECEF) reference frame is non-inertial
Today I heard an argument to prove that the Earth-Centered Earth-Fixed (ECEF) reference frame is non-inertial. It seriously doesn't make any sense to me but I also heard that same argument was made by ...
0
votes
3answers
104 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 ...
0
votes
1answer
61 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 ...
0
votes
2answers
56 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
2answers
299 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 ...
0
votes
1answer
171 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 ...
0
votes
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 ...
0
votes
3answers
293 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
votes
1answer
88 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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1answer
154 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
320 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
1answer
473 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 ...
0
votes
2answers
27 views
3D Vector Rotation of Point Mass
Triangle defined by points OA, OB and OC : (-i,3 j,-4 k), (i,2 j,2 k) and (3 i,7 j,- k) where i, j, k are unit vectors along x,y,z axis. Point mass is placed at OA. Triangle rotates with angular ...
0
votes
2answers
67 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 ...
0
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0answers
32 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 ...
0
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0answers
69 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 ...
0
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0answers
466 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 ...
-2
votes
0answers
29 views
Angles of Two Rotating Beams Connected by a Rod [closed]
Two beams with radii $R_s$ and $R_m$ are hinged a fixed distance $d$ apart. They are connected at their tips by a rod of fixed length $x$. If the beams start out parallel to each other and ...
-3
votes
1answer
137 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?
-5
votes
1answer
72 views
