Circular motion about a central point or axis

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554 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 ...
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1answer
193 views

Rotation motion like the number 8

I'm a college student majoring in culinology and I'm trying to find out the reason or method of the number 8 motion. Responses doesn't have to be in culinology examples, but that would be a great help ...
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1answer
72 views

Calculate the distance from the axis beyond which the particles have slid off a rotating disk

A collection of small particles is distributed on the top surface of a disc that is rotating at 91 revolutions per second, about an axis, which is vertical. Some of the particles slide off, and some ...
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1answer
213 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 ...
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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 ...
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94 views

Determination of Euler angles from known angles between the axes of two coordinate systems

Suppose there is a unprimed coordinate system XYZ, tilted w.r.t. a primed coordinate system but their origins coincide. Let the angle between $X,X^\prime$, $Y,Y^\prime$ and $Z,Z^\prime$ are ...
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40 views

Electromagnetic field transformations under rotations

If you have magnetization vector in vertical magnetic field, it starts precessing. If you do a transformation to rotating coordinate system you obtain a stationary magnetization. Is there a direct ...
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210 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
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49 views

Euler angles and curvilinear coordinate systems

If I have a curvilinear coordinate system and supposing I impose the condition that back transformations to Cartesian coordinate system are not permitted. I perform a rotation of the three axes( say ...
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87 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation $\omega~\text{rad/s}...
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206 views

Find the exact angle as a function of time for a rod that swings on a frictionless axle

This is a simple problem I thought of that I haven't been able to solve. Given a rod of uniform mass attached to a fixed axle, find the angle it makes with the horizontal if it is dropped from rest ...
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71 views

Stable planetary rotation states

In reading an article about theories as to how the slow retrograde rotation of Venus may have come into being, the article Why Venus Spins the Wrong Way (Franzen, 2001) stated that it is bound to ...
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2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia http://en.wikipedia.org/...
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29 views

Effect of atmospheric drag on earth's rotation

Okay, so I had a question answered regarding the earth rotating and planes flying east and west but one part of the answer talked about how the atmosphere is moving along with the earth (same angular ...
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0answers
37 views

Dampening a swinging mass

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads attached to it (red, green): Because the bar sits on a ball, the bar can swing clockwise or anti-clockwise. Suppose the ...
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0answers
57 views

Why does a fan blade appear to spin backwards when spun really fast?

This a phenomenon which I notice everyday but never really took an interest in. Why does a fan (or any other rotary object), when spinning really fast, 'appear' to slow down, upto a certain rpm, then ...
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0answers
40 views

Are there characteristics that distinguish our universe?

Are there any defining characteristics of our universe that could be different for other universes (or "instances of our universe") that operate under the same laws of physics? And which, if any, are ...
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56 views

Clarification regarding Eq. (2.6.21) Weinberg Vol. 1

While reading the action of time reversal operator for massless particles, I was going through the derivation for Eq. (2.6.21) from Weinberg Vol. 1 which proceeds as follows $$ \begin{aligned} U^{-1}(...
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22 views

Feasiblity of a long spinning top using an electromagnet to pull on Earth's magnetic field

Would it be feasible to build a infinitely spinning top (ref. Inception) by including a battery powered electromagnet who's polarity flipped in sync with the top's rotation such that the pull against ...
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27 views

Angular velocity in body frame to displacement in lab frame?

For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis: $$ \omega_1 = w_1 \cos (w_3 t) $$ $$ ...
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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 ...
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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 ...
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59 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 ...
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67 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 ...
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35 views

What if you spin a fluid in one direction at center and at the same time opposite direction at outside?

This question keeps me busy for couple of weeks. To be clear, If I put a fluid into a blender and start it, it will spin in one direction. This will create a small vortex. What if I am able to spin ...
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140 views

what does exactly 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 ...
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201 views

When rotating a liquid-filled jar what determines how much force goes to spinning the specimen floating inside?

Another way of stating it: When you have leaves in a (cylindrical) tea cup, if you rotate the cup (eg clockwise), the leaves largely stay in place relative to the table, but spin clockwise a little. ...
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88 views

Rotate the phase of a wavelet

Let's take a zero-phase Ricker wavelet which is given by: $$ \psi(t)=\frac{2}{\sqrt{3\sigma}\pi^{1/4}}\left(1-\frac{t^2}{\sigma^2}\right)e^{-t^2/2\sigma^2} $$ in the time domain which is often used ...
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105 views

Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...
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29 views

Is there a physical formula or equation to describe change in size of rotating tire?

I've heard that tires will actually grow larger when you are moving, and shrink back down when you stop. I was wondering if there is a way to calculate the size of a given tire, and what the variables ...
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0answers
22 views

What is the exact physics behind the heading indicator?

If I know right, the really basics of its functioning is that a quickly rotating gyroscope's axis of rotation moves into the north-south direction, due to the torque resulting from the tangential ...
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7 views

Pointer to reference for rotational dynamics for large torques?

It's my understanding that when dealing with rotational dynamics (e.g., a gyroscope like at time=2155 seconds of https://youtu.be/N92FYHHT1qM?t=2155) that the equation for relating the speed of ...
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30 views

Rotation operation on spin-1/2 particles

How does rotation operators work on a particle? What does it do on the particle conceptually? Also does particles spin on its axis?
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15 views

Finding the inner rotational velocity of a vortex incrementally

This is for improving accuracy in a prototype hydro design spreadsheet. Hypothetically: In a 6.6m tank, water enters tangentially at 0.575m^3/s with a velocity of 0.7m/s. The height of the resulting ...
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9 views

What is the analytical approach for a fiber cutting machine?

Folks, so today in the Lab I came up with this problem (see picture). It shows a cross section of a cutting machine. There's a blade moving with a constant speed dx/dt towards the center of the roll ...
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100 views

Will future spaceships for very long distance rotate?

I have seen in the movie Interstellar and The Martian they use the model of spaceship which rotate around it's axis. This is the spaceship model from Interstellar. This is spaceship model from The ...
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72 views

Rolling Resistance Coefficient

I found that rolling resistance can be expressed with this equation: $$F_\mathrm{rr} = \frac{C_\mathrm{rr} W}{r}$$ Where $C_\mathrm{rr} =$ coefficient of rolling resistance $W =$ normalforce $r =$...
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58 views

Correct formulas for two wheeled robot motion

I'm trying to write a simulation of a two wheeled robot, which can be controlled by varying the speeds of his wheels, independently. However, the physics engine that I'm using can only rotate a body ...
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30 views

Considering rolling without slipping using axis at contact point with surface

For a ball rolling down a ramp without slipping, we can use $\Sigma \tau = I \alpha$ about two axes: an axis through the center of the ball, and an axis through the contact point with the surface. The ...
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65 views

Accelerometer reading in a uniform circular motion

Question - there is an accelerometer kept in a car moving in a uniform circular motion. The accelerometer is kept in such a way that the z axis points downwards, x axis is pointing towards centre of ...
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33 views

Rotation of Spin-operator

I have to calculate the rotated Spin operator and been given the equation for the Rotation Matrix $R(\Theta,\mathbf{n})$ as well as its action on an arbitrary vector $\mathrm{a}$: $R(\Theta,\mathbf{...
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38 views

Why do linear momentum and angular momentum have to be conserved in ground frame only?

According the Newton's second law of translational and rotational motion respectively if the net external force /torque acting on a body is zero then the linear/angluar momentum is a constant . So ...
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145 views

Tension in a rod rotating about a fixed point

A rod of mass $m$ and length $l$ is rising about a fixed point in the ceiling with an angular velocity $\omega$ as shown in the figure. Now, on taking a small element on the rod, the net tension ...
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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 ...
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102 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 ...
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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 ...
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102 views

Why and how is acceleration absolute?

Is there a testable model which explains why rotation of an object in space and straight-line acceleration appear to be absolute while uniform translation is relative? I know of Mach's explanation, ...
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364 views

Does non-rotating object have rotational inertia if it is attach to rotating object by a spring

My question relating to the Rotational Inertia as a whole system. As I learn that the Rotational Inertia is defined for a rotating object to an fixed axis but I got problem in the case a rotating ...
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120 views

Determining rotational period of sun using sunspots

I know that at the equator at 0 degrees latitude , you could track a sunspot and then use T=2pi/w and w=∆theta/∆t to work out the period the equator rotates, but how would you do it for, say, sunspots/...
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41 views

Deriving 'frame dragging' in elliptical coordinates?

I'm currently trying to derive the equation that demonstrates 'frame dragging'. I am familiar (of sorts) with the Kerr metric, but I am most comfortable working in cartesian/elliptical coordinates? ...