Questions tagged [rotation]

Circular motion about a central point or axis

Filter by
Sorted by
Tagged with
0
votes
0answers
40 views

Stress-strain question [closed]

A thin uniform metallic rod of length $0.5$ m and radius $0.1$ m rotates with an angular velocity $400$ rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) ...
0
votes
2answers
34 views

Kinetic energy of a rolling disc when slipping

To derive kinetic energy expression for a rolling body, we consider the instantaneous center of rotation and write the angular energy about that point. After some algebraic simplification, we conclude ...
3
votes
0answers
41 views

Show that any proper homogeneous Lorentz transformation may be expressed as the product of a boost times a rotation

I am trying to read Weinberg's book Gravitation and Cosmology. In which he derives the Lorentz transformation matrix for boost along arbitrary direction, (equations 2.1.20 and 2.1.21): $$\Lambda^i_{\,\...
-5
votes
0answers
41 views

Please help me with this i cant even start this problem [closed]

An L = 70 m long thin tape wound on a spool of radius ro = 10 mm makes a tape roll of outer radius R = 25 mm. A motor used to wind the tape rotates the spool at a constant angular velocity and takes T ...
1
vote
0answers
29 views

Thermal transport in a rotating fluid

Suppose that we have a rotating fluid with nonzero heat conductivity and the rotation is uniform and stationary. The centrifugal force should then be compensated by the gradient of temperature (assume ...
0
votes
1answer
207 views

When applying the equation of torque and equating it to $I\alpha$ which moment of inertia do we take?

I believe $T=I_{cm}\alpha$, where $I_{cm}$ is the moment of inertia about centre of mass and $\alpha$ is the angular acceleration. But do we take $I_{cm}$ even if the torque has been taken about a ...
1
vote
4answers
142 views

Is $U^\dagger(R)\hat{H}U(R)=\hat{H}$ always true?

Consider a Rotation transformation on momentum state, $$U^\dagger(R)\hat{\mathbf{p}}U(R)=R\hat{\mathbf{p}}$$ Now the question is whether, $$U^\dagger(R)\hat{H}U(R)=\hat{H}\,?$$ Here, $\hat{H}$ is the ...
1
vote
4answers
109 views

How do you interpret the radian in physics? [duplicate]

When calculating $\sin x$, $x$ needs to be radian to calculate it. so for example when solving Uniform Circular motion, $x(t)$, $y(t)$ can be expressed $$x(t)=R\cos(ωt) [m] $$ $$y(t)=R\sin(ωt) [m]$$ ...
1
vote
3answers
745 views

What exactly does accelerometer measure on a vertical rotating disk?

I am trying to understand an aspect of rotational dynamics. I am having some trouble arriving at a solution. Consider a disk of uniform mass distribution, and radius R centered at the origin of an xy ...
4
votes
2answers
98 views

When a sphere is in pure rotation, will all particles in its surface have same linear speed?

Imagine this sphere to rotate about its diameter, from the centre to the point of surface if we take all of them have equal distance that is 'r(radius of the sphere)'.So same linear speed right? I ...
0
votes
2answers
35 views

Angular momentum of different bodies

How is the change of radius of a dancer spinning around their axis different from the change in the radius of orbit of a satellite revolving around a body? Why doesn't angular momentum remain the same ...
3
votes
2answers
52 views

How can there be radial acceleration without any radial force?

It is a problem from Kleppner mechanics: A bead of mass $m$ slides without friction on a rod that is made to rotate at a constant angular speed $\omega$. Neglect gravity. (a) Show that $r = r_0 e^{\...
0
votes
2answers
33 views

Where am I going wrong in finding direction of angular momentum?

If I consider the situation of the problem below, and try to calculate the angular momentum of the rotating (without slipping) solid sphere about point $P$, then obviously I'll use the formula: $$\...
3
votes
1answer
69 views

Representing a rotation around an arbitrary axis using Wigner $D$-matrix

It is known that an arbitrary rotation can be expressed in terms of three consecutive rotations called the Euler rotations. So instead of expressing the rotation operator as $\hat{R}(\hat{n},\phi) = \...
0
votes
3answers
850 views

Derivation of yaw, pitch, roll equations for an accelerometer

I'm struggling to find a good resource that explains how roll, pitch, yaw angles are calculated from the X, Y, Z measurements of an accelerometer. I came across this document but the explanation on ...
2
votes
3answers
411 views

Rotation of a Spinor

I have a question about an intuitive approach on spinors as certain mathematical objects which have certain properties that make them similar to vectors but on the other hand there is a property which ...
1
vote
1answer
549 views

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

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 ...
6
votes
7answers
897 views

What happens to the rotational kinetic energy? [duplicate]

There is a classic example that a spinning skater pulls his arms back. The angular momentum is conserved, the moment of inertia decreases. And therefore, it's angular velocity increases, so the ...
0
votes
0answers
35 views

The role of diffeomorphism in physics

Suppose space time is the manifold $M $ isomorphic $ \mathbb{R^4}$ with the metric $-\eta_{00}=\eta_{11}=\eta_{22}=\eta_{33}=1$ in the Cartesian coordinates $\Psi(p)=(x^0,x^1,x^2,x^3)$ for $p \in M $ ....
1
vote
1answer
78 views

Are strings (in string theory) able to rotate?

I read in this Wikipedia article: In the late 1960s, experimentalists had found that hadrons fall into families called Regge trajectories with squared energy proportional to angular momentum, and ...
2
votes
2answers
53 views

Relation between time-derivatives observed from fixed and rotating frames

I will begin by stating the question and then I will explain my doubt. The relation between time-derivatives of a vector $\vec{u}$ observed from fixed and rotating frames (with a common origin) is $$ \...
1
vote
3answers
728 views

Do particles rotate around themselves or they just move while the object rotates?

In this question, I'm not talking about particle spin. I guess, when an object rotates, its atoms also rotate. When an atom rotates, its particles must move in space. I wonder that if the particles ...
1
vote
2answers
804 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). ...
2
votes
1answer
86 views

Why a group that describe rotations always have $su(2)$ Lie algebra?

I'm reading the book Physics from Symmetry by Jakob Schwichtenberg. In part II the author explain the Lie group theory and in particular he treat the $SU(2)$ group. At a certain point the author tells ...
1
vote
1answer
28 views

Is there a rotation of the polarization plane in rotating refractive media?

Since there is a transverse Fresnel–Fizeau effect according to Jones, R. V. (1972). "'Fresnel Aether Drag' in a Transversely Moving Medium". Proceedings of the Royal Society A. 328 (1574): ...
2
votes
2answers
33 views

Do angular quantities (such as torque) depend upon the distance from the axis or distance from the origin?

One of my books and some of my friends say that torque and other angular quantities depend upon the perpendicular distance from the axis of rotation. This, in effect, would mean that translating your ...
2
votes
1answer
60 views

How much will rolling bodies like cylinders set on a surface of a fast moving body attenuate its friction with atmosphere?

A car, train or a spacecraft feels a certain drag when moving through the atmosphere. I think that rolling bodies produce less drag, and hence, my question is why rolling bodies as little spheres or ...
0
votes
1answer
18 views

Different rules predict contradictory directions of torque

Consider a coordinate system set up as follows: One way to find the direction of the torque is to find the algebraic sign of the component of torque along the axis of rotation. We can assign an ...
0
votes
1answer
542 views

Relative angular velocity of a referential system translating and rotating

I pretend to determine the angular velocity of a referential system, $S$, translating and rotating in relation to an inertial referential, $S_o$. I need to know this concept to determine, for ...
2
votes
2answers
67 views

A body rotating around a fixed axis relative to another rotating body

A question in my book goes as follows: A planet P revolves around the Sun in a circular orbit, with the Sun at the center, which is co-planar with and concentric to the circular orbit of Earth E ...
3
votes
1answer
132 views

Solving the Schrödinger equation for a rotating triatomic linear molecule

This source is showing that solving the Schrödinger equation for a triatmoic linear molecule yields the same formula for the rotationaI quantum states $BJ(J+1)$ as for dipoles. For dipoles, the total ...
0
votes
1answer
64 views

Does the gravitational distortion of a black hole depend of its rotation?

I would like to know if there is a difference produced by the added spin of a black hole to its gravitational space-time distortion. I am considering the distortion of space-time from a point far ...
0
votes
1answer
35 views

Any 3D model that shows how Earth rotates around the Sun and How Space-time curvature looks like?

I understand that Gravity will effect on space-time and create a curvature, which tells the mass how to move, therefore, the SUN can rotate smaller objects because it has stronger gravitational pull. ...
0
votes
1answer
109 views

How do Cogs and belts work? / Cogs and belts in an ICAS exam

Does the left red wheel turn in the same direction as the leftmost orange wheel?If so P and S go up? If not, Q and S go up? My reasoning: If so Leftmost orange cc Left red cc (by assumption) ...
0
votes
2answers
309 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 ...
0
votes
1answer
30 views

How is the angular momentum conserved in this case? [duplicate]

So imagine we have a mass attached to a string and spin it. If angular momentum is conserved then why does the object not have a tendency to move in a curved path if the mass is suddenly let go off. ...
0
votes
0answers
15 views

Rotational energy in index notation

I have a question about the meaning of an expression given in a textbook. The expression is \begin{equation} \frac{1}{2} \omega^{ik} M_{ik} \end{equation} where $M_{ik}$ denotes the angular momentum ...
5
votes
2answers
100 views

When the Center of Mass and Center of gravity does Not Coincide

"The centre of mass of a system of particles is the point that moves as though (1) all of the system's mass were concentrated there and (2) all external forces were applied there." (Resnick ...
0
votes
3answers
53 views

Angular acceleration

The angular acceleration is an axial vector when the axis of rotation is fixed. Angular acceleration and angular velocity vectors along that axis. Is there anybody who can explain this statement, ...
1
vote
1answer
43 views

Does the rotation of a massive body affect its $g$-field according to GR?

I want to know, according to GR, if a fast-rotating massive planet/star would affect its gravitational field. Especially, I want to know if, besides an ordinary $g$-field, there appears some kind of ...
7
votes
2answers
201 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-...
1
vote
0answers
19 views

Which set of rotation matrices describes an object's orientation in ECEF coordinate frame? [closed]

I'm trying to calculate what's known as the Angle of Attack (AOA) for a missile given some missile data. it would be more of a theoretical value for the AOA since I don't have any wind data. I posted ...
1
vote
1answer
57 views

How does circular motion begin in this case?

In the figure, Suppose the rod system(shown black) starts moving with some angular velocity say $\omega$ with the bob hanging to the string. So, after sometime the ball too rotates with the same ...
2
votes
1answer
33 views

How big (in meters) could the difference be between ECI and ECEF coordinates at midnight UTC?

Is the only difference due to leap seconds, etc. or other differences between UTC and updated forms of universal time, such as UT1? In other words, are all earth-centered inertial (ECI) coordinate ...
0
votes
1answer
133 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 ...
1
vote
2answers
49 views

The direction of the centripetal force in a vertical circular motion under uniform gravity

Consider the vertical circular motion of a point mass connected to the centre by rigid string. Here the uniform gravity $m\vec{g}$ acts. I illustrated the situation in the diagram below. Here if we ...
2
votes
0answers
233 views

About the force on a rotating wing seed

Every matured (ready to fall), wing seed 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 colloquial language, the path of ...
3
votes
5answers
673 views

How can the Normal Force on an upside down roller-coaster car point upward?

Q: An amusement park proprietor wishes to design a rollercoaster with a vertical circular loop in the track, of radius $R = 20\, \rm m$. Before the cars reach the loop, they descend from a maximum ...
9
votes
5answers
1k views

How can different points on a rigid body move with different speeds but also be relatively at rest?

For a rigid body rotating with a constant angular speed, the points near the axis must have lower linear velocity than the points farther away. If they have different linear velocities, they must have ...
0
votes
0answers
27 views

Is a bar magnet precessing in an applied external magnetic field and if not, then why?

We assume that a magnetic field produced by a static bar magnet is due to superposition of magnetic fields of all electrons rotating around protons inside the magnet that has a distinct direction or ...

1
2 3 4 5
16