Questions tagged [rotation]

Circular motion about a central point or axis

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1answer
26 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
103 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
42 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
77 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
191 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(\...
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1answer
182 views

Rotation rate of Mercury vs. a day on Mercury

In the latest episode of Last Week Tonight (June 3rd), John Oliver says a day on Mercury is 1,407 earth hours (58 days and 15 hours), which is correct. Neil D. Tyson says The time you gave is ...
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1answer
2k views

Moment of inertia of a non uniform rod [closed]

How to calculate moment of inertia of a non uniform rod about its geometrical center (linear mass density=kx, where k is some constant)?
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0answers
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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2answers
39 views

Increasing speed of a car using more motors? [closed]

I am making a robot car with four wheels. Every wheel will be attached to a motor. If I use four motors and four wheels , will I get more speed then using two motors?(If all the motors rotate at same ...
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1answer
36 views

Stopping a spinning object with a flexible gripper

I would like to know how deformation of the contact surface affects friction of a spinning object. In the image below I have a 2D problem of a spinning circle with two elastic "fingers" pinching it ...
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1answer
59 views

Bearing spinning longer Horizontally

While performing a physics experiment, a fidget bearing was held horizontally, while spinning, and held vertically. The same torque was applied vertically, as well as horizontally on the bearings' ...
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1answer
65 views

How would you calculate the speed of a rotating disk with an object that enters and leaves the disk? [closed]

How would I find the speed of a moving object that enters a rotating circle and then leaves it again? The object moves at s and the distance between entering and leaving is calculable. The object ...
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2answers
34 views

How to measure change in degrees per second, given force applied at a certain angle? [closed]

Example: a rectangular spaceship weights 10.000kg, and has a lenght of 20 meters. A force of 1.000 newtons is applied at a 90° angle and 9 meters away from center of mass. What will be the change in ...
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1answer
39 views

Magnitude of translational acceleration

The angular speed of a point following a circular path with radius r=0.171 m can be described by the equation: ω=8.79t+8.59 rad/s. At t=1.50 s, what is the magnitude of the translation ...
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1answer
181 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
24 views

How does pulse duration and shape affect the rotation of a quantum state?

If I have some quantum state $|\psi>$ and I apply a pulse to this to rotate it by 90 degrees, the model would normally assume a rectangular pulse. However, realistically, the pulse will probably ...
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1answer
30 views

Thought experiment regarding a posible preferential configuration of tectonic plates

Oceanic and continental tectonic plates have different densities, and their relative position have a very important effect on the evolution of Earth's climate on geologic time scales. There are many ...
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4answers
453 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}\...
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3answers
132 views

What do the antisymmetric matrices $J_i$ represent in classical mechanics?

In physical three-dimensional space, a rotation about an arbitrary axies $\hat{\textbf{n}}$ through an angle $\phi$ can be represented by $$R(\hat{\textbf{n}},\phi)=e^{-i(\textbf{J}\cdot\hat{\textbf{n}...
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1answer
63 views

Rotating a cube to the verge of tipping over [closed]

The problem: A $100\,\mathrm{kg}$ cubical box lies on the floor. A child pushes horizontally at the top edge. What is the magnitude of force to put the box on the verge of tipping over, given that ...
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0answers
26 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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2answers
52 views

In which case will the kinetic energy be more after reaching the bottom? [closed]

In which case will the kinetic energy be more after reaching the bottom? The shaded surface have friction and other are smooth. I thought about these questions: Does the answer depend on whether ...
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1answer
51 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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2answers
66 views

Is there proof for condition of rolling?

I want to know whether the condition of rolling has been proven or if it is just the result of observations only? rolling without slipping { $v = \omega r$ where $v$ is transactional velocity ...
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1answer
92 views

Finding the frame of reference in which Newton's law of gravitation applies

I've always wondered, in which frame of reference does Newton's law $$ \boldsymbol{g} = -\frac{GM}{r^2} \widehat{\boldsymbol{r}} $$ actually apply? In general it can't be the one in which the the ...
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1answer
661 views

How to derive the moment of inertia of a thin hoop about its central diameter?

For lack of a better image, I am searching for the moment of inertia of this where$\ r_1 = r_2$ (negligible thickness), and where the object would be rotating around its central diameter, which is ...
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3answers
1k views

Why is angular velocity a vector quantity? [duplicate]

Angular velocity is $$\omega= \frac{dƟ}{dt},$$ here $\theta$ and $t$ are scalar quantities. But $\omega$ is a vector quantity. Why is it such? So far I know the direction of $\omega$ is along the ...
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2answers
122 views

Classical physics is all reflection in Euclidean a rotation in higher dimension space?

I'm reading book in classical physics where it mentioned that, quote: " the transformation matrix (of two different cartesian coordinate systems) was orthogonal, so the transformation was ...
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1answer
311 views

Where does the '2' Factor come from in the Coriolis Force? [duplicate]

Say we have a disk rotating at $\omega$, and an observer standing at radius $R$. The observer throws something of mass $m$ with radial velocity $v_r$, and the goal is to make this object go in a ...
2
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1answer
298 views

Problem regarding concept of conservation of angular momentum [duplicate]

Two cylinders of radii r1, and r2 having moments of inertia I1, and I2, about their respective axes. Initially, the cylinders rotate about their axes with angular speeds w1, and w2 as shown in the ...
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0answers
44 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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2answers
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Flying with or against rotation of a planet

So, I've read a bunch of articles about how, somewhat contrary to intuition, it's usually faster to fly with the rotation of the earth versus against it. All the answers have to do with wind and ...
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1answer
78 views

Splitting velocity into linear and tangential velocity

Imagine a mass $A = 1kg$ and a mass $B = 12kg$ are connected by a rigid, inextensible, massless rod of length $2m$. The masses and rod are in a horizontal line. Three other $1kg$ masses are similarly ...
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0answers
86 views

Why does a Yo-Yo spin at all?

A yo-yo has ball bearings in between the two halves of it. When we drop the yo-yo, the two halves turn too. But if the string is wrapped around the bearing’s ring the shouldn’t it just rotate? Why do ...
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1answer
50 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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1answer
312 views

Which force act at pivot and How the maximum value of the normal component of the force at the pivot is 850 N?

A horizontal bar has mass 5 kg, length 0.30 m and has a mass M at one end as shown in the accompanying schematic sketch. A cable is attached at point A, 0.05 m from the pivot point (fulcrum) P and its ...
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1answer
261 views

The cycloid path

Today I had been reading a physics book. The book stated in the important points section that The point of a point on circumference of rolling disc is a cycloid and the distance moved by this point ...
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1answer
310 views

Gyradius (Radius of gyration) and CoM

Full disclosure, I'm trying to do an exercises but failing to understand it. The course takes for granted some notions I touched many years ago. There's a solid object rotating around a joint. ...
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1answer
326 views

Time evolution with rotation Hamiltonian

At $t=0$, the wave function of a particle with Hamiltonian $$\mathcal{H}=\mu B L_y \equiv \omega L_y$$ is given by $$\left \langle \mathbf{r}|\alpha \right \rangle \equiv \psi\left ( \mathbf{r} \...
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1answer
41 views

Author doesn't explain this equals sign in $R(\theta)\stackrel{?}{=} R(\frac{\theta}{N})^N$

I am struggling to convince myself that the following relation holds: $$R(\theta)\stackrel{?}{=} R\left(\frac{\theta}{N}\right)^N,$$ where: $R$ is an $SO(2)$ matrix $\theta$ is some finite angle. ...
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2answers
945 views

Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane?

In three-dimensions, the rotation generators are represented by $J_1$, $J_2$ and $J_3$ where $1,2,3$ respectively stands for the generator of rotation about $x,y,z$ axes respectively. In general, in ...
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3answers
507 views

How can a black hole rotate if time dilation stops time at the event horizon?

How does a black hole rotate if time is dilated to infinity (e.g. stopped) at the event horizon? Note: this is relevant to this question, but different: How can a singularity in a black hole rotate ...
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1answer
123 views

Power and work of tension force of a rotating body [closed]

Suppose that we have a body rotating on a massless string with a uniform velocity. What can we say about the work done by this tension. Moreover, what is the power related to this work. I do not have ...
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2answers
24k views

Work done in rotating electric dipole in uniform field

For an electric dipole $p$ in a uniform field $E$ we write the work done by an external agent in rotating dipole as $\text{d}W = pE\sin\theta \, \text{d}\theta$. I'm having trouble understanding ...
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1answer
941 views

Why is it possible to derive the infinitesimal rotation matrix by small angle approximations?

I am currently studying dynamics and trying to understand the relation between angular velocity $\omega$ of a rotating frame and the eulerian rotation matrix $\mathbf{R=\mathbf{R}\mathrm{(\psi)\mathbf{...
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4answers
239 views

Can there be a fictitious centripetal force?

Can their be a radially inward inertial force? https://en.wikipedia.org/wiki/Centrifugal_force is says nothing on Wikipedia about this.
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2answers
143 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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1answer
258 views

A question about the tennis racket theorem with degenerate eigenvalues $I_1, I_2 , I_3$

If a rigid body has a symmetry such that two of the principal moments of inertia are equals, i.e. $$I_1=I_2> I_3 \qquad{\rm or}\qquad I_1>I_2=I_3.$$ Are the rotations around the principal axes ...
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2answers
483 views

Rotation in Higher Dimensions

In a world of three spatial dimensions plus time, every atom rotates around a line, the axis of rotation. In a world of $N$ spatial dimensions where $N$ is greater than 3, must every atom rotate, ...
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1answer
108 views

Apparent paradox about active and passive vector rotations

Consider a single particle moving around the origin in a circle. If the particle's coordinates are $(x,y)$ at some time, it will reach $(x,-y)$ after some time as they lie on the circle. The position ...