Circular motion about a central point or axis

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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 ...
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26 views

Where does the lorentz boost for a dirac spinor come from?

I have read, that if you have a dirac spinor \begin{equation} \psi = \begin{pmatrix} \phi_R\\ \phi_L \end{pmatrix} \end{equation} that you can apply a lorentz boost along the z-direction with ...
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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 ...
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33 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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115 views

Earth magnetic field [closed]

I gather that, in these days, the most common explanation for the Earth magnetic field existence and strength is the theory of convetive currents of molten iron and nickel atoms in the outer core of ...
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1answer
41 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} + ...
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1answer
46 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 ...
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92 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 ...
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2answers
33 views

Spring on a rotating disc [closed]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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2answers
24 views

Stroboscope's unit

Can someone please tell me why does stroboscope's unit is rps or rpm. Revolution per minute/second. Although the stroboscope used was an electronic stroboscope. Is it has something to do with the ...
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0answers
25 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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3answers
525 views

Object moving in a circular path without accelerating

A train is moving with a constant speed on a straight portion of track. Then, it encounters a curve in the tracks, and goes along the curve. However, it does not change the magnitude of acceleration ...
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49 views

Angular momentum-torque relationship in a rotating frame?

I have read that $$\vec\tau=\frac{\mathrm{d}\vec L}{\mathrm{d}t}$$ holds true whenever the origin is not accelerating. But I cannot see why this holds true for a rotating frame of reference (such as ...
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How can the contact point of rolling body have zero velocity?

They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion?
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1answer
57 views

Effect of Eath's rotation on a ball thrown upwards

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
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2answers
155 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
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23 views

A free axis of rotation

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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1answer
57 views

Angular velocity and instantaneous rotation axis

Let's suppose that we have a cylinder of moment of inertia $I$ rolling on the floor without sliding, moving with linear velocity $v$ and rotating around an axis passing through the center of mass with ...
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1answer
34 views

Starting point for a derivation of fictitious forces

I came across this expression at the start of a derivation of fictitious forces: $$(dA/dt)_L = (dA/dt)_R + \omega \times A$$ Where the $L$ subscript refers to the laboratory (inertial) reference ...
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1answer
32 views

force acting on a small point mass dropped over a rotating rigid body

I came across a situation where I must find the force exerted by a rotating rigid body on a point mass $m$, dropped over it. The rotating rigid body will smash the point mass away in a direction ...
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1answer
43 views

In a rolling ball (no slipping) do all points move at the same velocity?

For example does the centre of the ball rotate at the same speed as a point on the surface of the ball?
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1answer
236 views

Would time dilation cause a planet to rotate?

For the sake of the argument lets use a black hole so the time dilation effects are greater and the planet in question is orbiting close enough to have significant TD effects but far enough to not ...
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2answers
317 views

Why isn't in counting the no. of degrees of freedom, rotation about the axis running down the length of the molecule counted?

I was reading about the Equipartition Theorem. Then I got the following quotations from my books: A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis ...
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4answers
873 views

Puzzling : Relative motion of two points on a rotating disc

Consider two points on a radial line for a rotating disc. One point, $A$, is at the circumference and the other, $B$, is at distance $R/2$ from disc's centre. Relative velocity of $B$ w.r.t. $A$ ...
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2answers
208 views

How do you rotate spin of an electron?

I can't seem to connect these two stories. Can you please help? I have heard that you have to turn electron by 720 degrees in order to get the same spin state. Has this been seen experimentally? How ...
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3answers
126 views

QM rotation operator

I have seen the proof that for fermions a rotation of $2 \pi$ does not return a spin angular momentum eigenstate to its original form, but instead multiplies the wavefunction by $-1$. Here is an ...
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2answers
104 views

Half-integer spin and infinitesimal rotations

On p. 692 of 'Quantum Mechanics' by Cohen-Tannoudji, he states that: Every finite rotation can be decomposed into an infinite number of infinitesimal rotations, since the angle of rotation can ...
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1answer
56 views

Wheel slowing down with constant acceleration

A wheel of radius $R$ spins about its center with a centripetal acceleration of $v^2/R$. I get that the acceleration at all points on the rim of the wheel point towards the center of the wheel. But, ...
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30 views

Applying a Force on a non fix body [duplicate]

If we apply a force on a fixed body and if that body rotates, we calculate torque about that pivot point. But if that body is not fixed and then we apply force that provides translational motion and ...
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1answer
32 views

A fluid in a wide tube being centrifuged

Imagine a large, awkward and imbalanced centrifuge with the glass test tube in the shape of a large rectangular prism, rotating about one of its ends parallel to the sides. Inside this glass test ...
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1answer
86 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
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0answers
31 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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1answer
80 views

Euler angle rotation - active/passive

I have a very simple problem, that I cannot wrap my head around and is hurting my brain. I have a very simple example of the problem, please consider the the figure below: In the first picture, you ...
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61 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 ...
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2answers
46 views

Can center of mass move without any force?

For instance, consider a weight on one end of the ring. Assume that the ring has negligible mass compared to the weight. When the weight splits into two, moves around the ring and recombines at the ...
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3answers
81 views

Newton's Second law of Rotation

In my book (Halliday Resnick Walker) there is a solved example which is as follows There is a uniform disk with mass $M$ = 2.5kg and radius $R$ = 20cm, mounted on a fixed horizontal axle. A block ...
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1answer
76 views

Physical interpretation of diffeomorphism from $SO(3)$ to $\mathbb R \mathbb P^3$

I am not good at picturing either $SO(3)$ or $\mathbb R \mathbb P^3$, the latter denoting the real projective space. Can someone give me a rough physical understanding of the geometry and implication ...
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2answers
66 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
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5answers
350 views

As a car turns around a circle, why does the force of static friction point towards the center of the circle [duplicate]

A car moves along a flat, circular road. It has a tangential velocity to the road, but the car tires change direction and the car experiences a force of static friction causing a centripetal ...
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2answers
87 views

Torque at a disc sandwiched between two rotating discs

I have a question in my mind regarding torque transfer taking place in the current situation. There are three rotation elements A, B & C as shown in the figure. The rotating element A is ...
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2answers
71 views

Physics of tidal locking: can the process be underdamped?

Is it possible for a satellite undergoing the process to overshoot the required rotation rate for tidal locking? For example, if its rotation rate is being slowed, can it become slower than it needs ...
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79 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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3answers
347 views

How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...
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5answers
1k views

Rotation vs translation

What is so fundamentally different between a rotation and a translation that one can be represented with a single n-vector and the other one needs an n-n matrix?
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1answer
75 views

Rigid Body Dynamics - Calculating Rotation of an Object

I've looked everywhere and I can't quite find a concise answer, especially due to my limited knowledge and understanding of terminology. I found something called Rodrigues' Rotation Formula that ...
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1answer
57 views

How many times does the ISS celebrate New Year each year? [closed]

My question is, how many times each year do the crew of the ISS have an opportunity to celebrate New Year? Does it vary each year or will it be a fixed number? I tried to work this out for myself ...
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3answers
824 views

Does the Earth actually rotate around the sun? [duplicate]

Why does one say that the Earth rotates around the sun? There should be no preferred reference frame and from an observer on the sun, the sun will rotate around the Earth.
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2answers
119 views

Is this a correct understanding of circular motion?

We say an object experienced uniform circular motion iff it moves in a circle of constant radius, with constant angular velocity. To experience uniform circular motion, must the net force on the ...
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1answer
39 views

inertial pressure on in a rotating syringe

First question on stackexchange. Hopefully somebody can help me out. I'm struggling to express the following eloquently. I have a rotating syringe tipped with a needle. rotation speed w, with radius ...
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1answer
36 views

Specific scenario involving rotation and inertial frames of reference?

We recently went over some rotational motion in my freshman physics class, I had a question for the professor on your frame of reference, and how that would effect the rotation of the object. Say you ...