Questions tagged [rotation]

Circular motion about a central point or axis

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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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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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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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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 ...
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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 ...
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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,...
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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 ...
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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 ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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}(...