Questions tagged [rotation]
Circular motion about a central point or axis
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Restricted Rotation using electromagents [on hold]
I was wondering if I could restrict the rotation of a part over another in one direction alone using an electromagnet but allowing me to have a continuous rotation if forced (maybe by using some ...
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2answers
83 views
Rotating Rod in Special Relativity
Statement of the Problem
In frame $F'$ with co-ordinates $(t',x',y',z')$, a straight rod rotates in the $x',y'$ plane with angular velocity $\omega ′$ about one of its ends. The fixed end is located ...
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1answer
66 views
The physics of a cornering wheel and its centripetal force
There is something wrong with the way we describe cornering vehicle wheels. My question is: can anyone else see this?
Centripetal force is a force always orthogonal to the motion of a body. When a ...
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0answers
17 views
Pendulum moving in linear motion [closed]
Given a diagram below,
the linear velocity of the point of rotation is v_linear and the angle that the tension line makes with vertical axis is theta, and its angular velocity theta dot.
Assuming ...
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0answers
29 views
Windowless space station: rotation vs. gravity ring vs. frame dragging?
Imagine a windowless hollow cylinder, with an observer sitting inside on the curved wall. Something is pulling the observer against that wall. The observer can also walk easily along the inner ...
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2answers
47 views
Is the acceleration of a rotating body always it's centripetal component? [closed]
For constant circular motion where a rotating mass accelerates angularly.
Would the linear acceleration of the rotating mass always be equal to its centripetal acceleration
e.g. The earth's ...
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1answer
31 views
How can I find the power given only the torque?
I have a system where I am trying to find the power generated by a DC electric generator. However, I am not very familiar with generators, so I am having difficulty determining the rotational velocity....
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1answer
29 views
Why should the friction between two disks be zero when there velocity is same? [duplicate]
In this video here, Walter Lewin mentions two discs of different radius $r_1$ and $r_2$, of the same density, where the first disk is initially rotating, while the second is at rest. In the videos ...
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1answer
33 views
Should there be a significant differential in wind velocity indoors vs outdoors in relation to Earth's rotating atmosphere?
What is the behavior of a rotating Earth's atmosphere indoors? Should there be any differences experienced between the atmosphere spinning in lockstep with the Earth outdoors vs. closed-off indoors?
...
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1answer
37 views
If a ball were to roll through a loop, would the normal force change when compared to a frictionless block?
I am currently working through the following problem:
Reaching part c), we are required to repeat the former parts using a spherical mass instead of a frictionless cube. I have no problems with the ...
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1answer
70 views
Vehicle Dynamics Problem: Cornering wheels must slide on the road [duplicate]
Can anyone see this geometric fact that cornering wheels must slide on the road?
What I mean is that the tread within the contact patch of the rolling wheel, which is travelling along a curved/...
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2answers
49 views
Rotation of a Bicycle Wheel
Circular motion at a constant velocity requires a net force toward the center of rotation.
If I stand a bicycle on its seat, wheels upwards and spin the wheels with my hands, they start rotating. ...
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1answer
68 views
How to obtain $Y$ rotation with only $X$ and $Z$ rotation gates on the Bloch sphere?
Let's say you have a system with which you can perform arbitrary rotations around the $X$ and $Z$ axis. How would you then be able to use these rotations to obtain an arbitrary rotation around the $Y$ ...
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2answers
62 views
Rolling objects released from rest: time down the ramp [closed]
Since we are given the values of I for each object, I was able to calculate the KE's of each:
the solid spheres had KE of $1/5mv^2$; the hollow sphere had a KE of $1/5 mv^2$, and the hoop had $1/2mv^2$...
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0answers
60 views
What does a basis rotation correspond to physically for linear position-momemtum?
For polarization and angular momentum, rotating the basis corresponds to a very straightforward physical transformation, namely, the physical rotation of an experimental apparatus about an axis in ...
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0answers
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Angular velocity & acceleration experiment design problem
You know, there is a classical demonstration on the conservation of angular momentum, where you sit on a turning chair with two dumbbells in your hands and push yourself while your arms are open. Then ...
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1answer
47 views
Relation between Spin 1 representation and angular momentum and SO(3)
This is a naive question. It occurred to me while studying in detail the the Spin 1 angular momentum matrices.
The generators of SO(3) are
$J_x=
\begin{pmatrix}
0&0&0 \\
0&0&-1 \\
0&...
2
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2answers
78 views
Rolling Without Slipping and Rotational Energy
I'm a little confused.
Translational energy and rotational energy add separately, according to my textbook, to give the total kinetic energy of a moving object.
That means that for a disk ...
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1answer
92 views
Integrating over Euler Angles
I have a $6\times6$ matrix having its elements being functions of Euler's angles (ZXZ rotation scheme) representing a tensor physical property. To find the average of the tensor property, I need to ...
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0answers
16 views
What is the unit of polarization mode dispersion?
I calculated the differential group delay (DGD) from measured data following a chapter in the book "Polarization Optics in Telecommunication" by Jay Damask.
Basically, I measured a unitary matrix $U(...
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2answers
51 views
Rigid bar on a pivot
Say we have a solid bar in space. It is on a pivot, the pivot being right at the bar's center of mass
There is a massless rocket pushing on one end of it, making it spin, faster and faster.
Suddenly,...
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1answer
71 views
A rotating solid bar in space [closed]
Say there is a solid bar in space. Imagine it vertically, with the top point labeled $A$, and the bottom point labeled $B$ (these aren't points on the bar, but points in space between which the bar ...
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2answers
59 views
What is the tangent vector representing rotation?
I am reading Mathematics for physics: A guided tour for graduate students by Michael Stone. On the page 379, the book says
The surface of the unit sphere is a manifold...We may label its points ...
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1answer
44 views
Relation between rotation vector derivative and angular velocity when the rotation angle is constant
$\def\va{\vec{\alpha}}
\def\vw{\vec{\omega}}
\def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
2
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3answers
85 views
Multiple Centers of Mass [closed]
This may sound like a trivial question, but I am wondering: is it possible for there to be multiple centers of mass? And if it isn't, why?
For example, take some arbitrary 3-Dimensional object, ...
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2answers
53 views
Dynamics of a sphere in a horizontal plane driven by a force
I'm studying the dynamics of a sphere in a horizontal plane driven by a force. The situation is the following: I have a stationary sphere of mass $m$ and radius $r$ in a pool table whose lining has ...
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2answers
68 views
If a particle is undergoing a uniform circular motion, then how is its angular momentum conserved about its centre in its plane? [closed]
I didn't understand why is there no torque of the gravitational force of the particle?
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3answers
39 views
Rotor why not opaque?
Helicopter rotors spin at around 300RPM. Now for the naked eye they look like transparent, like if the rotors were not even there.
https://www.quora.com/Why-do-we-see-individual-helicopter-rotor-...
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1answer
52 views
Velocity in rotating frame projected onto axis in inertial frame
I want to look at the projection of the velocity of a particle in the rotating frame onto an axis in the inertial frame as a function of time. For example, I am calculating
\begin{equation}
\frac{d\...
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1answer
81 views
Irrep corresponding to a rotation, what's the definition?
My character tables for point group $T$(Schönflies-notation but easily convertible into other point group notations) tell me that the rotation around the $z$-axis, $R_z$ (the $z$-direction ...
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votes
3answers
87 views
Rotation around which axis [closed]
Imagine you have a rigid rod which is free to move and a force is applied at a point away from the center of mass of the rod. This would create torques at multiple points on the rod as the force ...
4
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1answer
78 views
Does rotation always slow down in general relativity?
Suppose I have a rotating object in empty space. Will it lose angular momentum due to interactions with spacetime?
The most obvious case if if the object has a quadrupole moment. Then the quadrupole ...
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1answer
71 views
Rotation matrix with deficit angle
I need to find the rotation matrix for a space with a deficit angle. The question is as pictured
The following is my answer to the question:
If $\theta$ could vary between $0$ and $2 \pi$,
...
2
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2answers
131 views
Why doesn't Foucault's pendulum show Earth's spin at the equator but works at the North/South poles
If you where directly above the North/South pole and set up Foucault's pendulum, why does it show the Earth's spin even though the Earth isn't spinning there? This is also where it takes the shortest ...
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1answer
126 views
Minimal angle that will cause a cube to tip on an inclined plane
Let's say that I have a cube with side $a$ and a ramp such, that the coefficient of friction between the cube and the ramp is $\mu$.
I want to determine the minimal angle of inclination of the ramp ...
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3answers
1k views
Why do things spin?
Let's say I have 2 boxes, one of mass M and one of mass 2M. They are separated by a distance of 1 meter. I drop them from the same height and see that due to the earth's gravity, they accelerate at ...
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0answers
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A hemisphere rotating on a flat surface ends up on the flat side. Why?
So I was playing with my kid and this wooden half Kiwi (radius about 20 to 25 mm) got my attention:
What I noticed was, when I give it a spin on its pointy end and if a certain initial speed of ...
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2answers
69 views
Day/Year Length Of Larger, but same mass, Earth? [closed]
I’m wondering how the length of a day and year would change on Earth if it was twice as big, but the same mass (less density)?
Also, would such a difference cause it to orbit closer or further from ...
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0answers
64 views
Comparison between Euler angles and Rodrigues rotation formula under small rotation hypothesis
Sorry for boring you during summer vacation, my friends. I am haunted by the comparison between Euler angles and Rodrigues rotation formula under the small rotation hypothesis. Maybe, they cannot be ...
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0answers
76 views
Rotating and Moving Water Container
I'm trying to solve the following problem, but I'm getting a different answer than the one in the book. I can't understand what I'm doing wrong. (The question is from Hibbeler's fluid dynamics)
So ...
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1answer
74 views
Approximation of Euler angles with small rotation hypothesis
Sorry for boring you during summer vacation, my friends. I am haunted by the approximated expression of Euler angle rotation matrix found in this textbook. In the appendix, the author declares that ...
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1answer
68 views
SO(3), orbital angular momentum, vector product
I have a big confusion with group theory terminology. I know that orbital angular momentum (OAM) is $\mathrm{SO}(3)$-symmetric in 3D-space. Let's define QM orbital angular momentum (OAM) ...
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1answer
48 views
Torque around the origin of a particle using moment of inertia (in 2D)
(You can skip this derivation and go down to my final question if you already are familiar with the results $(1)$ and $(2)'$ from this derivation)
Suppose we are in the xy-plane:
In two dimensions, ...
2
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1answer
248 views
Can I avoid spaghettification with a spin?
I am aware of spaghettification effect caused by entering a black hole, as well as fundamental physics of an object in space, so here is my theoretical construct:
if I place an object in space where ...
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0answers
99 views
Two step calculation of roll, pitch and yaw using accelerometer and known acceleration
I have a 3-axis accelerometer fixed in a driving apparatus. I do not know how the accelerometer is mounted, the orientation of $x$, $y$ and $z$ axes are unknown (the rotation about the x axis is roll $...
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1answer
22 views
For what angles (and why) does the equation for finite rotation fail to work?
I am learning rotations and group theory/representations and my lecturer's note mentioned that:
"The group is considered connected, but not simply connected [...] As a result, the formula for a ...
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2answers
95 views
Are rotation matrices faithful representations of the rotation group?
I would like to use rotation matrices as representations of the rotation group. I would like to know if these representations are faithful, i.e. isomorphic to the rotational group elements.
I read ...
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0answers
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Rotations about a unit vector which doesn't pass through the origin in 3 dimensions
I am trying to understand how rotating a vector about an aribitrary axis which does not pass through the origin of the coordinate system $(x,y,z)$. Let the $\vec{r_{1}} $ and $\vec{r_{2}} $ be two ...
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0answers
62 views
Center of mass and velocity of rotating object [closed]
I tried to solve this problem with V = R$\omega$, using $\omega$ = 2$\pi$/T and R = R - 2r (where the point opposite of contact is). However, I am not getting the correct answers at all. I looked at ...
2
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1answer
143 views
Spherical tensor operators: The existence of rotations
A spherical tensor operator of rank $k$ is defined such that under a rotation $\mathcal R(\alpha,\beta,\gamma) \in \mathrm{SO}(3)$, it transforms as:
$$\hat U(\mathcal R) \hat T_q^k \hat U^\dagger(\...
