Questions tagged [rotation]

Circular motion about a central point or axis

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2answers
153 views

How will two equal discs, rotating with equal but opposite angular velocities and put on top of each other affect the spacetime “surrounding” them?

In this article the Ehrenhaft paradox is described. You can read in it that, according to Einstein's General Relativity (to which this paradox contributed), the spacetime around a rotating disc is non-...
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0answers
224 views

Does the spin1/2 rotation operator rotate spin in real space?

in quantum mechanics, the rotation operator for spin one half is $R_{\alpha}\left(\hat{\boldsymbol{n}}\right)=\mbox{exp}\left(-i\frac{\alpha}{2}\boldsymbol{\sigma}\cdot\hat{\boldsymbol{n}}\right)$. ...
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0answers
66 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 ...
3
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0answers
126 views

How would I explain why a top wobbles to someone who has never taken a physics course?

I found this this website that explains the precession of a top, but obviously, it is not comprehensible to a younger student. I am not referring to why tops stay up, just why they make circles that ...
3
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0answers
147 views

Acceleration vector of tipping object (robot)

I am about to develop a simulation application of a robot. For that reason, I would need to calculate the acceleration of the robot (centre of mass) when its centre of mass exceeds its feet (ie it ...
2
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1answer
91 views

Are there physical quantities constitute of magnitude, direction and rotation along that direction?

There are scalar quantities(magnitude) and vector quantities(magnitude and direction), but are there fundamental quantities that also depends on how it's oriented/rotated along the direction(magnitude,...
2
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1answer
329 views

Difference between torque, moment and couple

I know the basics of them like Torque is force multiplied by the distance (from the point where there is no rotation like centre of gravity). Couple acts because of two equal and opposite forces ...
2
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1answer
425 views

The dynamics of a cornering wheel

Can a rolling wheel create a side force without first rotating on a vertical axis? There is something wrong with the way we describe how a cornering vehicle wheel creates a cornering force. I think ...
2
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2answers
96 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. ...
2
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1answer
27 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 ...
2
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4answers
497 views

Deriving the unitary operator $U(R)$ associated with a rotation $R$ using Wigner's theorem

A rotation $R(\hat{\textbf{n}},\phi)$ about an arbitrary axis $\hat{\textbf{n}}$ through an angle $\phi$ in the three-dimensional physical space is given by $$R(\hat{\textbf{n}},\phi)=e^{-i(\textbf{j}\...
2
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1answer
100 views

Constraints on the factorization of a unit quaternion rotation operator

In Jack B. Kuipers' Quaternions and Rotation Sequences page 194-195, section 8.7.1 explains how to decompose a tracking sequence quaternion $q = q_0 + \vec{i}q_1+\vec{j}q_2+\vec{k}q_3$ into two other ...
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0answers
216 views

Electromagnetic field transformations under rotations

If you have magnetization vector in vertical magnetic field, it starts precessing. If you do a transformation to rotating coordinate system you obtain a stationary magnetization. Is there a direct ...
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0answers
117 views

Euler angles and curvilinear coordinate systems

If I have a curvilinear coordinate system and supposing I impose the condition that back transformations to Cartesian coordinate system are not permitted. I perform a rotation of the three axes( say ...
2
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0answers
166 views

Is there an absolute accelerated frame of reference?

I know from special relativity and from a little common sense that there is no absolute inertial frame of reference; that is, physics acts the same no matter what velocity you go at. However, that ...
2
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0answers
109 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation $\omega~\text{rad/s}$....
2
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0answers
95 views

Stable planetary rotation states

In reading an article about theories as to how the slow retrograde rotation of Venus may have come into being, the article Why Venus Spins the Wrong Way (Franzen, 2001) stated that it is bound to ...
2
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0answers
3k 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 http://en.wikipedia.org/...
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0answers
54 views

How is the idea of an orthogonal matrix equivalent to $\lambda_{ij}$?

In my classical dynamics class, my professor showed how a vector under rotational coordinate transformation behaves. During the lecture, he used $\sum R_{ij} \mathbf{V_j} = \mathbf V_i'$ where $\...
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0answers
26 views

Angle of friction force of a weighted ball on a surface

If a block had constant density and laid on a slope with angle $\theta$ then the angle of friction and the horizontal would be $\theta$. If there was a ball with constant density then the friction ...
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0answers
142 views

Ray Tracing and Rotations

I would like to be able to write the matrix operations to be able to define the first arm of the picture below. How can I do that? I have learned beam physics, have read Siegman's Lasers, if that ...
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0answers
38 views

Spacetime rotation matrix using mostly minus conventions

When trying to find the Lorentz transformation in matrix form in the $x^2+x^3$-direction, I tried simply mapping the Lorentz boost in the $x^2$-direction to the $x+x^3$-direction by rotating it $45°$ ...
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0answers
34 views

How many illusionary axes of rotation can coexist?

Consider the answer to this question: How many different axes of rotation can coexist? Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation. Now, that ...
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1answer
39 views

Electromagnetic field of a point charge seen from a rotating reference frame

Let us consider a point charge sitting in the origin of our coordinate system. If we change to a rotating system, will the field of the point charge still look the same? Intuitively I would say yes, ...
1
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2answers
51 views

Angular momentum as an operator on triple product space

General arguments about introduction of angular momentum to QM is that under a transformation of coordinates the x and y position operators mix (as it is usually written) $$\hat{x}' = \cos(\theta) \...
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0answers
25 views

How to properly align my relaxed molecule onto my gold electrode?

the question is described below since it can be considered a chemistry or physics question: How to translate from one plane to another? originally posted on mathematics SE I am trying to get ...
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0answers
17 views

How will a rotating, circular, and cylindrical body of a superfluid develop in outer space?

Let's consider a rotating (about its center, in the plane cutting the initial circular and cylindrical form into two halves), circular, and cylindrical body of a superfluid somewhere in outer space. ...
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0answers
44 views

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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0answers
43 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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29 views

Why is tangential acceleration always downward in this system?

Point A is rotating about an axis with angular velocity $$w_0=w_i \hat{i} + w_k \hat{k}$$ and has position in the x-z plane $$r=r_i \hat{i} + r_k \hat{k}$$ In addition, the angular velocity vector ...
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1answer
191 views

Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3 The rotation matrix associated with 1.2a and ...
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0answers
27 views

Attitude quaternion from 2 vector measurements

I am using a method proposed by R. G. Reynolds to estimate attitude based on two vector measurements, taken from: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990052720.pdf Suppose we ...
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1answer
53 views

Does an object that's freely swinging about its pivot point have translational motion?

For example, a pendulum rotates about its pivot point, but does the pendulum also have translational motion? I ask this because in the following link, the author assumed in his first equation that a ...
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0answers
51 views

Computing Resultant Point And Magnitude Of Rotation

Say that I have a free body quad rotor aircraft with torque induced rotation at points A, B, C and D with angular velocities $\omega_a$, $\omega_b$, $\omega_c$ and $\omega_d$ respectively. I have ...
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1answer
51 views

Spinning ball gently lowered onto rough floor

Trying to reconcile the real world observation with first principles, here is a problem I came across. Consider a ball initially rotating with axis parallel to the floor lowered gently onto a rough ...
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0answers
262 views

What are the 3 Euler angles?

I am currently reading up on inertial measurement in aircraft systems. Euler angles are one of the concepts I am a bit confused with. In an Euler angle-rate matrix there seem to be 3 parameters: p, q, ...
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1answer
321 views

Rotational motion activity for physics of sports class

I'm looking for a really solid rotational motion lab for a physics of sports class I'm teaching for younger students (HS Freshmen mainly). It should be something that the students can gather data ...
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0answers
187 views

About the aerodynamic force on a rotating maple leaf seed

Every matured (ready to fall), wing-shaped seed of the maple leaf tree ends up in a rotating motion, no matter what it's initial position is (the seed follows the path of least action, or in more ...
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2answers
496 views

Motion of an object spiraling outwards on a rotating disk with friction

I recently came across the following problem: A spinning disk has an object initially located at radius R. The object is moving with the same angular velocity as the disk (which I will call ω). ...
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0answers
24 views

Is the rotational velocity of a vortex consistent across its height?

I am trying to locate information about calculating the rotational velocity of a vortex. Is the velocity at the vertex maintained across the entire vertical height of the vortex? As the radius ...
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1answer
74 views

Which way to rotate a coin?

The picture shows rotation of a coin in two ways along a axis passing through the centre of gravity.Which method is easier to rotate the coin?
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0answers
248 views

rotational invariance

I have been treating this Hamiltonian: $$H=v\vec{p}\vec{\sigma}+\vec{A}\vec{\sigma}$$ where $\vec{\sigma}=(\sigma_x , \sigma_y)$. It is relevant for 2D graphene quantum dots with some vector ...
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0answers
346 views

Torque of a wire tensioner dancing arm

I'm creating a wire tensioning sub-system for a coil winder, and I've decided to use a dancing arm to measure the tension in the wire as it is pulled off a supply reel, like so: As the tension in the ...
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0answers
66 views

Is there some kind of aether for rotations only?

Currently I'm reading "A briefer history of time". I understand how the Michelson–Morley experiment refutes the theory of an aether (like in "absolute frame of reference") for translation in space and ...
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0answers
124 views

Effect of atmospheric drag on earth's rotation

Okay, so I had a question answered regarding the earth rotating and planes flying east and west but one part of the answer talked about how the atmosphere is moving along with the earth (same angular ...
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0answers
85 views

Dampening a swinging mass

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads attached to it (red, green): Because the bar sits on a ball, the bar can swing clockwise or anti-clockwise. Suppose the ...
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0answers
139 views

Are there characteristics that distinguish our universe?

Are there any defining characteristics of our universe that could be different for other universes (or "instances of our universe") that operate under the same laws of physics? And which, if any, are ...
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1answer
113 views

Calculate the distance from the axis beyond which the particles have slid off a rotating disk

A collection of small particles is distributed on the top surface of a disc that is rotating at 91 revolutions per second, about an axis, which is vertical. Some of the particles slide off, and some ...
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0answers
74 views

Clarification regarding Eq. (2.6.21) Weinberg Vol. 1

While reading the action of time reversal operator for massless particles, I was going through the derivation for Eq. (2.6.21) from Weinberg Vol. 1 which proceeds as follows $$ \begin{aligned} U^{-1}(...
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0answers
34 views

Feasiblity of a long spinning top using an electromagnet to pull on Earth's magnetic field

Would it be feasible to build a infinitely spinning top (ref. Inception) by including a battery powered electromagnet who's polarity flipped in sync with the top's rotation such that the pull against ...