Circular motion about a central point or axis

learn more… | top users | synonyms

0
votes
1answer
27 views

How to spatially rotate the frame of reference Faraday Tensor? Special Relativity and Galilei Transforms

Hey I'm currently just starting out doing special relativity and I stumbled upon following problem: If I have the faraday antisymmetric tensor $F^{\alpha \beta}$ and I perform a spatial rotation of ...
0
votes
0answers
48 views

Confusion in Special Relativity: Rotating frame of reference

Suppose we are observing a rotating frame from an inertial frame, free from gravity, and try to measure the circumference of a circle drawn in the rotating frame. Since our measuring rod would be ...
0
votes
1answer
98 views

How does the tension force of a massless string affect the speed of a mass on its end?

i,j, and k are the unit vectors in the following question, and $\omega$ is the angular velocity. Lets say you have a mass m attached to a mass-less string of length $L$ tied to a peg with no friction....
1
vote
1answer
91 views

How to conserve angular momentum?

If i want to conserve angular momentum from the point of contact of the solid sphere and the ground how should I do it? I know we can use $mvh = I\omega + MvR$ ,if the collision is elastic. But in ...
0
votes
3answers
446 views

Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by: $$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$ $g$=acceleration due to gravity $\theta$=angle of inclined plane $k$=radius of gyration ...
0
votes
0answers
100 views

Moment of Inertia of a Motion Simulator Frame

I have a rather specific question. I'm trying to build a motion simulator for flight and racing sims, similar to this: https://www.youtube.com/watch?v=JQAZB3EnI_w . The basic concept is a platform ...
1
vote
0answers
20 views

integrating small angular velocities

I know that for a constant angular velocity the following is true: $R=e^{W t} R_0$ where $W$ is an angular velocity tensor, $t$ is a time, and $R$ is a rotation matrix I believe the following is ...
0
votes
2answers
119 views

When does angular position, or angular displacement, not obey the rules of vector addition?

The only examples I've found talk about rotating an object about one axis and then about another axis. When you reverse the order, the object ends up in a different position. However, as those ...
1
vote
2answers
164 views

Can a quantity have two units?

We know that Force has unit of newton and torque has unit of newton meter. Then if you define the energy, which has same magnitude of work then, $W=Fx$ has unit of Joule ( $J$ ) (or $Nm$ ) while $W=\...
1
vote
2answers
1k views

Instantaneous Centre of Rotation

Let's say a body is undergoing both rotational and translational motion. I know that ICR of the body as a whole will be the point about which the body is doing pure rotation, so basically will be the ...
0
votes
0answers
62 views

Smallest possible spinning clock?

The earth's rotation acts as a clock and defines a rather precise unit of time called the day. We could go out in outer space and spin a marble and get a reasonable clock. On the other hand, it is my ...
2
votes
1answer
3k views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
1
vote
0answers
72 views

Is there an absolute accelerated frame of reference?

I know from special relativity and from a little common sense that there is no absolute inertial frame of reference; that is, physics acts the same no matter what velocity you go at. However, that ...
-1
votes
1answer
121 views

What is the force that stops a rotating wheel eventually? [duplicate]

Assuming a car is traveling on a road. At some point, the driver stops accelerating the car, so it travels some distance and then stops. Since the car's wheels are round and are rotating without ...
2
votes
3answers
329 views

Sign of torque when rolling an object down an incline

Suppose you have an object rolling down the incline at 30 degrees. Given the point of contact is instantaneously at rest, I decided to analyse torques at that point. Therefore, the only force ...
1
vote
1answer
238 views

A smaller sphere purely rolling down without slipping over another larger sphere [closed]

In this question we have to find out the angular velocity of the smaller sphere about its own axis at the instant it leaves the surface of the larger sphere and it is given that the smaller sphere is ...
1
vote
0answers
57 views

Solving for position of a SO(3) rotating object, given the integrable functions for components of angular velocity along the principle axes

Assuming that you have approximated or solved the Euler's Equations for components of angular velocity along its principal axes of inertia $x$, $y$ and $z$ - i.e. in the coordinate system that is ...
2
votes
2answers
98 views

A Confusion in Rotational Dynamics

I am trying to analyse the following situation using classical mechanical concepts. Consider a a straight rod $AB$ of mass $M$ and length $L$ placed on a frictionless horizontal surface. A force $F$ ...
0
votes
1answer
206 views

rotation behavior of spinning discs

If two discs of equal mass and volume are parallel to each other but not touching, share an axle but using magnetics do not touch it, are not under gravity, and begin to rotate in opposite directions ...
5
votes
2answers
471 views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
2
votes
3answers
139 views

Is centripetal acceleration mandatory for circular motion?

If we consider a case where a closed circular wall is present, and inside the boundary, just adjacent to the inner wall, two particles are placed touching the surface of inner boundary such that the ...
0
votes
1answer
153 views

Confusing concepts in proof of spherical addition theorem

In http://scipp.ucsc.edu/~haber/ph116C/SphericalHarmonics_12.pdf, section 4, pages 6..9 is a proof of the spherical harmonics addition theorem. Page 8 has eq.(25), an application of Laplace series: ...
1
vote
1answer
67 views

Work done by tension when a particle is tied to a vertical cylinder using a thread and given a velocity perpendicular to the thread

For a particle attached to a rope moving along a circle that has the length of rope as radius, the tension provides centripetal force and work done by tension is zero since velocity of particle is ...
2
votes
1answer
405 views

Why do Uranus and Venus rotate from East to west?

Why do only Uranus and Venus rotate from East to west, while others rotate in opposite direction? Is it because of the angle of their tiltness? Or due to the process of their formation?
0
votes
2answers
160 views

Does a body always rotate purely about its center of mass? [duplicate]

For example : A rod is held stationary in vertical position on a smooth horizontal ground and then released. Now the center of mass has velocity and acceleration and every point of the rod has some ...
1
vote
1answer
201 views

How can angular velocity be constant even when there is a torque by friction?

A cylinder at rest lying on a rough ground is given an impulse which imparts a translational velocity (no angular velocity) to it. The question goes ahead with finding time after which rolling starts ...
0
votes
1answer
48 views

What are the limitations of using instantaneous axis of rotation? [closed]

I know when the body rotatates as well as translates IAR or ICR shouldn't be used but I am not able to understand why?
0
votes
1answer
100 views

Resultant center of rotation due to multiple moments

Say, there are multiple moments (M1, M2, M3) acting on a body (of irregular shape) at points P1, P2, P3 respectively. The body is free to rotate about any point. Now, which resultant center (the ...
1
vote
1answer
51 views

Will a gas rotate as fast as the spherical container it is contained within?

Let's say I have a sealed spherical glass container 30 cm in diameter which contains plain air. The glass container is rotated about its axis at 1 revolution per minute. My question is, would the gas ...
4
votes
1answer
516 views

Angular velocity relative to different frames

In Goldstein it is said "It is intuitively obvious that the rotation angle of a rigid body displacement, as also the instantaneous angular velocity vector, is independent of the choice of origin of ...
1
vote
3answers
211 views

Why does earth spin counter-clockwise?

If we observe the earth from the north pole, we can see that the earth is rotating counter clock wise direction. The earth spins due to angular momentum, but why only in counter clock wise. Why ...
1
vote
1answer
106 views

How does Foucault's pendulum work in a place other than the poles?

I find it easy to understand how Foucault's pendulum works at the poles, the pendulum oscillates in a fixed plane and we, along with the earth, rotate around it. So it appears that the pendulum's ...
0
votes
1answer
39 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
7
votes
4answers
1k views

Will the sea form a concave surface?

Without neglecting the fact that the earth is rotating, let us be in a ship (such that there is no relative motion between sea and ship) in a sea that surrounds the northern most or southern most ...
0
votes
1answer
103 views

Negative sign in rotation operator again

In Wikipedia's page on the rotation operator, section "In relation to the orbital angular momentum", they write $$ R(z,t) = exp((-i/h) \varphi L_z) $$ where $\varphi$ is the angle being rotated ...
3
votes
2answers
276 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
0
votes
0answers
18 views

Why do rotating devices make air colder? [duplicate]

I end up thinking this question frequently recent days. It seems an easy question but i cannot find the answer. You could say "faster the air, cooler it becomes" in that case i am expecting an ...
0
votes
1answer
563 views

Moment of Inertia of Water. [closed]

Determine the moment of inertia $\Theta$ of a water molecule ($m_H=m,m_O=M$) for a rotation around the axis which is perpendicular to the molecule plane and goes through the center of mass S of the ...
1
vote
1answer
63 views

Warship cannons influence on speed/direction [closed]

I've been looking at great warships like the Iowa or equivalent ww2 warships, and I raised question. This kind of war is pretty much only about strategic placements, accuracy and fire power. Hence ...
1
vote
1answer
44 views

Euler Angles with respect to base body when Euler Angles with respect to another body is known

Let's say I have a fixed base body $B_0$ with a reference frame $X_0Y_0Z_0$, and two other bodies, $B_1$ and $B_2$, rotated arbitrarily with respect to this base body. Coordinate systems fixed to $B_1$...
0
votes
1answer
153 views

Only get part of commutator form expanding to third order in generator expression

(Shankar 12.2.4) Let $U[R(\epsilon_z\hat k)] = I - {i\over\hbar}\epsilon_z L_z$ be the infinitesimal generator for rotation operators, and $T(\vec\epsilon) = I - {i\over\hbar}\vec\epsilon\cdot\vec P$...
1
vote
4answers
204 views

Infinitesimal Rotations

Have a little question regarding infinitesimal rotations. In the Cohen Book, volumen 1, Complement B-VI, it says that the transform of a vector $\textbf{OM}$ under an infinitesimal rotation can be ...
0
votes
1answer
351 views

On application of angular momentum conservation laws

Consider a situation like this: a massless ring is kept fixed at rest on a horizontal plane. A massless thin string attached at its one end to a point on the circumference of the ring while its other ...
1
vote
1answer
62 views

Patterns in a spinning wheel [duplicate]

Why do we see patterns on a rotating wheel with spokes which seem to rotate counterclockwise or clockwise as and when the wheel accelerates or deaccelarates. What I mean is the patterns like this
7
votes
4answers
407 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
1
vote
1answer
268 views

Determining the three Euler angles from the acceleration

I want to know, given the measurement of an accelerometer at rest (so not really an acceleration but a force per unit of mass) the inclination of this accelerometer, along the three axis. For this, I ...
1
vote
0answers
66 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
1
vote
1answer
117 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + \...
2
votes
1answer
638 views

How can I set up an equation for distance traveled for a rubber band powered car?

I am to make a rubber band powered car, and I have to maximize it's distance traveled. The time taken to reach said distance, top speed of the car, acceleration of the car, is not relevant. I just ...
3
votes
3answers
119 views

Rotation in the x-t plane

I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation ...