Questions tagged [rotation]

Circular motion about a central point or axis

Filter by
Sorted by
Tagged with
2
votes
1answer
51 views

Are rotation matrices tensors?

Are rotation matrices tensors? If no, why? I'm not sure about it, for example considering the $z$-axis rotation matrix when I rotate the coordinate system the rotation matrix around the old $z$-axis ...
0
votes
1answer
47 views

Rate of angular momentum at the center of mass

I'm currently trying to calculate the Zero Moment Point for a game I develop, however im terrible at physics and therefore have trouble calculating the “rate of angular momentum at the center of mass”....
0
votes
1answer
29 views

The units when calculating Gyroscopic precession rate don't make sense [on hold]

I was doing a problem set for my physics course and I ran into some odd units for calcualting the gryeoscopic precession rate. As it is the angular velocity of the wheel around the axis, it should be ...
3
votes
1answer
38 views

Intermediate axis theorem in higher dimensions

The intermediate axis theorem states that the rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not. ...
0
votes
1answer
18 views

Does direction of angular velocity/acceleration have any physical implications?

when first learning about the angular velocity/acceleration, the right hand rule is mentioned. According to it, the direction of angular velocity/acceleration is along the axis perpendicular to the ...
0
votes
1answer
30 views

How would I go about solving for the magnitude of the force the pivot exerts on the bar?

Assuming the bar Is uniform in density. My idea was: since the system is in both translational and rotational equilibrium. $T\sin\theta = F$ (Pivot on Bar) Solving for $T$ let M = mass of bar let ...
1
vote
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 $\...
0
votes
1answer
25 views

How to calculate inertia tensor of composite shape with angle? [duplicate]

I have I have some objects assembled like this : The inertia tensor would be : $$I=I_1+I_2+I_3-m_1 \,\tilde{r}_{01}\,\tilde{r}_{01}-m_3\,\,\tilde{r}_{03}\,\tilde{r}_{03}$$ Where : $$\tilde{r}_{01}...
0
votes
1answer
18 views

Vector in an inverted frame of reference using Euler's Angles

Having some issues regarding the Euler's angles. Following is the short description of them problem. In the first step, I determined the Euler's angles to invert my frame of reference that is X, Y ...
1
vote
1answer
41 views

Heat produced if earth stops rotating

In my textbook there is a question that is as follows:- If earth stops rotating about it's own axis,the increase in its temprature will be(Here R=radius of earth,ω=angular velocity of earth,J=...
-1
votes
0answers
17 views

Collision of ball with a hinged rod

In a collision of ball with hinged rod i have read that we cant apply conservation of linear momentum when axia of rotation of rod is fixed.I didnt get it why.Can anyone explain deeply about it
1
vote
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 ...
0
votes
0answers
24 views

Ball rotating on flat surface with kinetic friction

Suppose you have a ball with moment of inertia $I$, rolling on a surface with kinetic friction coefficient $\mu$. Initially, it has a linear velocity of $v_0$ and an angular velocity of $w_0$. Also, ...
0
votes
1answer
58 views

Rotation of helium balloons [closed]

A number of balloons are attached to a circular disk with string. Some balloons are filled with air and some balloons are filled with helium. The disk is hung freely from ceiling of a room and is disk ...
1
vote
1answer
69 views

Why is the position operator a vector operator?

Suppose we don't know (yet) about the angular momentum operator, and just associate a (unitary) rotation operator $\hat{R}$ to every element $R$ of the 3D rotation group. My question is : why does ...
0
votes
2answers
98 views

How much water to put in cup for maximum stability? [closed]

I found this problem in ‘200 puzzling physics problems’ An empty cylindrical beaker of mass 100 g, radius 30 mm and negligible wall thickness, has its center of gravity 100 mm above its base. To ...
-5
votes
1answer
111 views

How can I calculate the internal angular acceleration? [closed]

This is a very well known topic and affects angular velocity. How does changing the moment of inertia affect angular velocity? An object that changes the moment of inertia simultaneously changes the ...
0
votes
0answers
29 views

How does vibration transform after rotation of the vibrating object?

I can't find the math of that. Imagine a vibrating object, like a circular membrane, with vibration modes $\phi_{ij}(x,y)$. Let's express the initial vibration state like $u(x,y,t)=\sum_{ij}a_{ij}e^...
0
votes
1answer
23 views

Transforming a tensor from Crystal to Laboratory frame of Reference

I want to transform the stiffness tensor of a rhombohedral crystal from crystallographic frame of reference to laboratory fame of reference, how to do it ? For crystal structures having orthogonal ...
0
votes
0answers
15 views

Recent/More accurate rotation velocity measurement?

I've been researching for papers for hours and can't seem to find this. Where can I find the most accurate equatorial rotational velocity measurement for Mars?
1
vote
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 ...
2
votes
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,...
1
vote
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 $45°$ ...
1
vote
1answer
43 views

Is there an easy way to tell whether this “Curlmeter” would rotate or not?

Let us say we have the following symmetrical apparatus: Four equal positive charges, all connected to a shaft that can rotate, the connecting rods are insulated, and so does the shaft. Now ...
0
votes
1answer
30 views

A thin rod is standing on a smooth surface [closed]

A uniform thin rod of mass m and length l is standing on a horizontal surface. A slight disturbance causes the lower end of the rod to start falling. find the velocity of the centre of mass of the rod ...
3
votes
1answer
135 views

Will an object dropped from a high building displace due to the Earth's rotation?

I read that in the 16th and 17th century, the question of whether the Earth rotates around its axis or all celestial bodies rotate around it was extensively debated. One of the anti-rotation arguments ...
0
votes
2answers
57 views

Why does twisting make it easier to remove a lid with a seal?

I have a pot with a lid that has a rubber seal (not a screw cap). When taking the lid off, it is incredibly difficult to lift the lid by pulling straight up on it, but twisting the lid whilst pulling ...
1
vote
2answers
52 views

Emergence of rotational symmetry on 2D square lattice

On page 74 of David Tong's Statistical Field Theory lecture notes, it is said that $(\partial_1\phi)^2 + (\partial_2\phi)^2 $ respects both $D_8$ (that includes discrete four-dimensional rotation ...
1
vote
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 ...
0
votes
1answer
59 views

The Lorentz Transformation of the electric field of a moving charge

If I have a moving charge observed in frame $S$, may a Lorentz boost from $S$ in a direction not parallel to the charge's velocity in $S$ result in an electric field that has a different magnitude of ...
0
votes
0answers
16 views

Libration vs. rotation for mass on rotating disc

Hello I have a question about the difference between rotation and libration. In some textbook it is stated that for libration \begin{equation} q (t+\tau) = q(t) \\ p (t + \tau) = p(t) \end{equation} ...
0
votes
0answers
24 views

Velocity composition effect of moving line charges acting on a moving charge - By what velocity (boost) is the E-field unchanged along the boost?

Claim 1) An infinitely long line current can be modeled as the linear superposition of two infinitely long line charges. Claim 2) An infinitely long line current can exert forces on charges with ...
0
votes
0answers
26 views

Finding the total rotation about an arbitrary axis

I have a rigid body which is fixed in a x,y,z system and is free to rotate. The z vector is parallel to gravity. x and y are arbitrary and perpendicular to z. The moving coordinate system is x',y',z' ...
0
votes
2answers
35 views

Are the tides scale independent?

What I mean is the following. Imagine two smooth massive spherical bodies ($M_1\neq{M_2}$), with equal and homogeneous mass densities. Both masses have a layer of water on them for which holds ($R_1$ ...
1
vote
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, ...
0
votes
0answers
26 views

Transformation of dielctric constant tensor

I have a dielectric tensor $$K = \begin{pmatrix} 2000 & 0 & 0 \\ 0 & 2000 & 0 \\ 0 & 0 & 50 \end{pmatrix};$$ which I want to transform to a new coordinate system given by ...
1
vote
1answer
33 views

Rotating coordinate frame connection of coordinates and mass

Hello I am still confused about rotating coordinate frames and want to ask a question about it. Is it correct that strictly speaking the mass must be connected with the axis of rotation in the ...
2
votes
6answers
578 views

Acceleration in circular motion

Can motion of a particle be circular if the radial acceleration is zero, but the tangential acceleration is not $0$?
1
vote
1answer
90 views

Change of reference frame for a wavefunction: same modulus but different currents?

Suppose that, at a certain $t=0$, one has a wavefunction $$ \psi=\psi(x,y) $$ defined on a plane and well normalized to $1$. Coordinates (x,y) refer to the frame $xOy$. How does the wavefunction ...
0
votes
0answers
27 views

Vorticity - Rankine vortex: how can we say that $\frac{\partial u_\phi}{\partial z} = 0$

\subsection{a} A Vortex formed in a bathtub, tornado or in other real world scenarios, exhibit nearly a solid body rotation in the core while far away from the center the flow is irrotational. This ...
1
vote
2answers
144 views

Griffith's Electrodynamics problem 1.9 (rotation through (1,1,1))

I was compiling some solutions to Griffith's E&M, and I can't get my solution to square with the others I have found online. The question asks: 1.9 Find the transformation matrix R that ...
0
votes
1answer
26 views

Conservation of Angular momentum or Work = 0 , which is valid?

In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in ...
1
vote
2answers
68 views

Rotating coordinate frame

Hello I have a question about rotating coordinate frames. Following the book of Brizard the Lagrangian is given by \begin{equation} L(\mathbf{r}, \mathbf{\dot{r}}) = \frac{m}{2} \vert \mathbf{\dot{r}} ...
0
votes
2answers
87 views

What is a rotation group and how do we get its unitary representation?

The rotation group is ${\rm SO(3)}$. It is the group of $3\times 3$ orthogonal matrices $\{g(\theta)\}$ with unit determinant. So these are already defined in terms of $3\times 3$ matrices. But we use ...
1
vote
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) \...
1
vote
1answer
87 views

Parametrizing $SU(2)$ with Hermitian matrices

There is something that is not clear to me Here is what I know: Pauli matrices are $\sigma_1 = \begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$, $\sigma_2 = \begin{pmatrix}0 & -i \\ i & 0\...
0
votes
4answers
125 views

A rod rotating about a pivot

A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is nudged from rest in a vertical position as shown in figure. At the instant the ...
0
votes
0answers
29 views

Does acceleration of the rim mean just tangential or both tangential and centripetal acceleration?

On my physics homework, the problem specifies that the acceleration of the rim of a flywheel can't exceed 100g. Does this mean that the tangential acceleration only, or the sum of the tangential and ...
0
votes
2answers
34 views

Point of application of tangential velocity in rotational motion

The tangential velocity of a particle in a rigid body is given by: $\vec{v}=\vec{\omega}\times \vec{r}$. Since the cross product is perpendicular to both $\vec{\omega}$ and $\vec{r}$, the velocity $\...
0
votes
0answers
31 views

Single number to quantify difference between two local reference frames?

I'm working with some satellite data that defines the spacecraft reference frame from two star cameras and two different measurements of orientation configuration of the cameras, and I'm trying to ...