Questions tagged [rotation]

Circular motion about a central point or axis

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Proving rotation about non-intersecting axes leads to translation

In Group Theory by Morton Hamermesh, he states on page 32: For a body of the finite extension, a molecule or the macroscopic form of a mineral, only the first two symmetry types [rotation, reflection]...
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Rotating a lever — small end has more force but less speed?

Suppose I have a massless lever with two masses at the ends and a fixed pivot as depicted below. Assume no gravity in this scenario. Further, let's say object $B$ is closer to the pivot, so $r<R$. ...
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Does the angular velocity of a rigid body equal to the angular velocity about an axis plus the angular velocity of the axis?

If so, how to prove that relation?
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How to comprehend the fact that parity is an improper rotation in the odd dimension, but not in the even dimension, physically?

Some "clarification" To begin with, I'm not even talking about relativity so, in the following, rotations always act on the Euclidean space or only the space subpart of the Minkowski space. ...
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How the object rotates?

Why the object actually rotates ? When I researched about this topic , I have gotten satisfying answer from here: Why do object rotate at all? All the atoms and molecules of the object are connected ...
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For rotational equilibrium of a rigid object, about which point does the torque of the body have to be zero?

In the definition of rotational equilibrium for a rigid body, the net torque about a point has to be zero. Now, about which point will the torque be calculated? Will it be the centre of mass or centre ...
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Why do we use moment of inertia about centre of mass to calculate rotational KE in rolling without slipping?

Say we have a cylinder rolling without slipping on a horizontal plane: Now, the instantaneous centre of rotation is P, so we can use $ v_A=\omega \ r_{AP}$ to find the linear velocity of the centre ...
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Symmetry relations of a Hamiltonian (Mirror, Chiral, Inversion, Rotation)

I'm reading a paper https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.235136. Regarding Eq. (4)~(6), I have the following questions: (A) Eq. (5) shows a mirror symmetry relation $M_z H \left( ...
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From the point of view of physics, why is it useful to know the irreps of rotation group?

In 3D, the rank two tensorial physical quantities, for example, the electric susceptibility, the conductivity, the stress tensor etc, are in general, not irreducible representations i.e. neither ...
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How to write a matrix $\mathcal{M}$ such that $\mathcal{M} \boldsymbol{x}=\boldsymbol{\omega}\times\boldsymbol{x}$? [duplicate]

As is well known, it is possible to use the $\nabla$ operator as if it were a vector.  Someone consider it an abuse of notation but surely something that works well and is very useful. Well, how is it ...
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Help me understand length contraction in an intuitive way—length contraction as four-dimensional rotations? [duplicate]

I am trying to understand length contraction in special relativity, in an intuitive way. So I am trying to visualize this phenomenon in the following way, and I would like to know if my example has ...
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Deriving torque and rotation without an ideal rigid body

Let's say that we have two masses that are connected by a massless rigid rod. I'm assuming there are no external forces acting on the system. If we were to apply a force where the force over time is ...
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Treating a rotating rod like a point mass at the cm

If I were to have a uniform rod that is rotating about one of its ends, am I able to treat the center of mass of the rod as a point mass and have the point mass rotate around the end? Image: My ...
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Torque due to external forces only

Suppose two parallel lines L1 and L2 at a separation of 100 metre . Suppose two charged particles are moving with constant and equal speeds , the first one on L1 and other on L2 ; and their direction ...
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Geometrical Rotation and Rotation operator relation and ambiguity

In Cohen-Tannoudji's it is said (vol.1 page 694): $|\psi \rangle$ is the state of the system before the rotation. $|\psi ' \rangle$ is the state of the system after the rotation. $|\psi ' \rangle= R |\...
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Does the angular velocity of a rotating rod change when its axis of rotation changes?

If a rigid rod of length $l$ rotates on one end around the origin with an angular velocity of $\omega$ and suddenly the end fixed to the origin is released allowing the rod to move freely without any ...
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Gravitational wave propagating in $x$-$y$ plane with angle $\theta$ with $x$-axis

I am going to ask a question related to a paper called "Spin angular momentum of gravitational wave interference" which its link is: https://doi.org/10.1088/1367-2630/abf23f. My question is ...
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Special relativity, what is an transformation with just spatial rotation?

Can someone help me understand how to mathematically represent a transformation of a matrix with a rotation of the spatial axes and why this transformation does not change the unit 3x3 matrix? This ...
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Spin, Orbital and Total Angular Momentum For Classical Vector Fields

I ask this question motivated by trying to understand vector spherical harmonics and find or come up with an elegant abstract derivation of their form. Suppose we have a 3D field of 3D vectors: $\...
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Vector subtraction coordinates in rotated axes

I'm going through Anthony Zee's Einstein Gravity in a Nutshell and got confused on one of his points that seems to be a more general confusion about rotating axes. Zee first defines the rotation of ...
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Centre of mass of a hollow cone with open base [closed]

Consider a hollow cone ( whose base is open) of Mass $M$ , radius $R$ slant height $l$ and height $h$ . I need to find the centre of mass of this cone in terms of $h$ only. My work : I thought that ...
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How do I visualize a stepwise rotation on the Bloch Sphere using $SO(3)$ and $SU(2)$?

Searching for an implementation (that helps me to understand how $SO(3)$ and $SU(2)$ relate to each other) I came across this interesting question Visual interpretation, on the Bloch sphere, when ...
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Confusion about the definition of negative angles between two D-branes

I have a conceptual question regarding a paper I am reading. More precisely, the first appendix starting on page 29. In this paper, schematically, the classical oriented open strings get quantised ...
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Wobble of an unbalanced fan suspended from the ceiling

A fan hangs several feet from the ceiling by a ball-in-socket joint, and it has one fan blade that is heavier than the others. When you turn on the fan, the additional centrifugal force of the heavy ...
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How do I determine at what angle to move to intercept another object moving along a circular path?

I came across this issue on my own. This is not a homework problem. Two people (you and someone else) are running along a circular track, with known positions in relation to each other, and known ...
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How can I get the mathematical model of the surface of a liquid rotating on a inclined surface?

So I was playing around with my lab equipment, and I saw that if I let water rotate like this: It seems that the motion of the surface is periodic.How can I calculate an equation for the motion of ...
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Can objects in space maintain a stable rotation spinning on two (or three) orthogonal axes simultaneously?

Could a space station spin on two (or three) orthogonal axes at once and maintain a stable rotation? If the station was a hollow sphere, would the centripetal force be equal everywhere on the interior ...
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Rotation of free to rotate rigid bodies

I recently came across this statement in a book that the line joining the point of suspension and center of mass of a body should be parallel to the acceleration due to gravity(g or more precisely, g ...
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The Forces of Rolling and Rolling Without Sliding

In Halliday's Fundamentals of Physics textbook the author says: "If a wheel rolls at constant speed, it has no tendency to slide at the point of contact P, and thus no frictional force acts ...
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Is it possible that the Dark Matter is not exist, but the spacetime itself rotating with a galaxy inside it?

Is it possible that a region of spacetime rotating with any objects inside it? In this case we don't need a dark matter to explain why distant stars have so big orbital speed. They moving with normal ...
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Why is radius of gyration for an ellipsoid derived from a tensor different than the formula?

The first method one can use to solve for radius of gyration, $R_g$, of an ellipsoid with semi-axes a, b, and c involves using the formula: $$ R_g = \sqrt{\frac{a^2+b^2+c^2}{5}}$$ However, it appears ...
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Do individual atoms have any semblance of rotation (aka yaw, pitch, rol)?

When describing a static 3d object in 3d space, we often use 6 numbers: x, y, z coordinates of one of objects points and yaw, pitch, rol for objects rotation. Do individual atoms have any semblence of ...
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If the liquid internal parts of the Earth solidify, what will be the consequences?

Will the Earth's radius just decrease, the daytime decrease, and the magnetic field seize to exist?
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Is it possible to rotate object as fast as the linear velocity of point on surface become greater than speed of light?

Is it possible? Or the rotation also cause the increasing of the object mass and energy needed for acceleration?
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Rotational mechanics ( Rolling cone ) [closed]

This is a question from Mechanics . It’s sort of similar to Irodov 1.57/1.56 question. In this question we are asked to find the angle covered . So I first found the half angle of a cone . That’s ...
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Is the position of the central peak of a crater on Moon showing that an asteroid hit it while it was not still sinchronised with Earth?

Is the position of the central peak of a crater on Moon showing that an asteroid hit it while it was not sinchronised with Earth? If the peak is in very center of the crater and the crater shown on ...
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Intrinsic $Z$-$Y$-$Z$ Euler angle sequence

Consider Euler angles $\alpha$, $\beta$, $\gamma$ with the intrinsic $Z$-$Y$-$Z$ convention. The effective rotation $S(\alpha, \beta, \gamma)$ can be written as: \begin{equation} S(\alpha, \beta, \...
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How does the physics of the rotation behaviour of the Roti can be explained?

Many times we see in kitchen when someone makes Roti, they first take the atta (flour) and make a circle shape (not perfect but ideal case let it be) we often see when the roller is moved above it to ...
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If two neutron stars of opposite spin collide will the resulting body have less mass due to lack of rotational energy?

If two neutron stars of opposite spin collide will the resulting body have less mass due to lack of rotational energy? Will the Penrose proccess lead to less gravitational mass?
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What are the observables of a particle's spin, esp. if it doesn't have an EM charge? Or any charge?

What experiment(s), specifically tell you that a spin-1/2 particle has rotated one full rotation (360°), but is (in some other respect) only 'rotated' by 180°? Or, conversely, if a spin-2 particle has ...
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How can there be a horizontal impulse applied to a sphere?

"Suppose a problem says that there is a solid sphere is rolling without slipping , suddenly a horizontal impulse(not along the midway diameter line) is applied on it and problem says to find some ...
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Is it possible to measure the electric current speed through the wire by this method?

This method is very simple but I am not sure if it would provide accurate measurements.The current electrons deriving from the battery should have some speed and in that way should interact with the ...
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Rolling motion, sliding, contact point, friction

I have a question about rolling motion. So suppose we throw a bowling ball with no initial angular velocity, only linear velocity $v_0$. At first it will be sliding on the ground. Let the kinetic ...
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Why are most QM Operator defined as Identity minus Generator? [duplicate]

I am currently rehearsing my lectures in quantum mechanics for the exam. I recognized that there is a pattern for different types of operators such as: Rotation operator, Time evolution operator and ...
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Maximum rotation speed of a planet of given mass and size

What will be the limit of the rotation speed of a planet with given radius and size? will it depend on factors other than mass and size? Neutron stars are known to rotate at very high speeds but they ...
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Rotation of basis vectors, contra/covariant explanation misunderstanding step

In the explanation for why the line element under transformations of type: $$\vec{x} \rightarrow M\vec{x}+\vec{b} $$ for rotation matrix M and arbitrary offset b, remains invariant: $$ds^2=\delta_{ij}...
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How does torque not increase velocity in a constant power engine/mechanism? [closed]

I know the formula of Power(P)=T(torque)*velocity(v) thus for constant power output, there is an inverse relationship between torque and angular velocity. But on an intuitive level, and without ...
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How does torque even work on intuitive level? [closed]

I just watched some videos on torque, and that created confusion in me. What exactly is torque?! Some people say it is the rotational equivalent of a force, but the units do not match out. Some say ...
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Does a cornering wheel turn (change the direction it travels) at its contact point or some other location?

According to vehicle dynamics, there appears to be two different ways a wheel travels a curved path. I don't think this requires an expert in vehicle dynamics because it is a simple physics problem of ...
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Are Newton's Laws applicable to torque too?

Since Torque is $Fd$ where $F$ is force, $d$ is perpendicular distance between line of action of force and axis of rotation, will Newtons Laws be applicable to torque too? For e.g., if a force od $5N$ ...
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