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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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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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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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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
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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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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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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&...
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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
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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 ...
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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
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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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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 ...
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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 $2 \pi$, ...
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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
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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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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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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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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, ...
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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
38 views

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 ...
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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(\...