# Tagged Questions

Circular motion about a central point or axis

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### Distance in relativistic circular motion in invariant spacetime

I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor. My question is, if something travels in a ...
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### Can a ultracentrifuge be used to test general relativity?

With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to ...
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### In counting degrees of freedom of a linear molecule, why is rotation about the axis not counted?

I was reading about the equipartition theorem and 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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### Does the rotation of the earth dramatically affect airplane flight time?

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S). During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles ...
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### What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?

Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating ...
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### Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
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### Two axes for rotational motion

I understand that angular momentum is a vector, etc.. But, what really happens when some object, say a ball for example, is set to rotate along two axes? What would the resulting motion look like?
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### Understanding the “$\pi$” of a rotating disk

Let us say you are in an inertial reference frame with a circular planar disk. If you take your meter measuring rods (or perhaps tape measure) you can find the diameter and circumference of the disk. ...
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### Would it matter if the Earth rotated clockwise?

In the Futurama episode "That Darn Katz!" they save the world by rotating the Earth backwards saying it shouldn't matter (which direction Earth rotates). If Earth rotated clockwise and remained in it'...
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### Simple Harmonic Motion - What are the units for $\omega_0$?

I'm trying to understand the units in: $$mx''+kx=0$$ And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring ...
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### 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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### How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?
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### Which way do spiral galaxies rotate?

Is it known whether spiral galaxies typically (or exclusively?) rotate with the arms trailing or facing? Intuitively it feels weird to think of the arms as facing the direction of rotation, but that'...
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### Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...
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### What does “clockwise” mean, exactly? [closed]

I am in the middle of a discussion with a friend about the meaning of the term "clockwise". Wikipedia indicates that a clockwise rotation goes as top-right-down-left. However, my friend argues that "...
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### Argument for proving Earth-Centered Earth-Fixed (ECEF) reference frame is non-inertial

Today I heard an argument to prove that the Earth-Centered Earth-Fixed (ECEF) reference frame is non-inertial. It seriously doesn't make any sense to me but I also heard that same argument was made by ...
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### Proof that the Earth rotates?

What is the proof, without leaving the Earth, and involving only basic physics, that the earth rotates around its axis? By basic physics I mean the physics that the early physicists must've used to ...
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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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### Shape of rotating rope (lasso problem?)

Let's take a wire or a rope. I usually do this with a chain or my scarf. I fixate one end in my hand and apply rotation (by subtle movements of this endpoint like spinning a lasso). The rope gets ...
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### 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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### Does a tire need to slip to generate force?

Recently, I have been doing some research on racing and tire modelling. While I was doing this, I encountered many curves like those shown below. While I understand the need of slip angles to ...
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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 ...
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### Equivalent Rotation using Baker-Campbell-Hausdorff relation

Is there a way in which one can use the BCH relation to find the equivalent angle and the axis for two rotations? I am aware that one can do it in a precise way using Euler Angles but I was wondering ...
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### How to derive relation for time derivative in a rotating reference frame

I am looking for an appropriate derivation of the $(\frac{d}{dt})_{\text{laboratory}} = (\frac{d}{dt})_{\text{rotating}} + \omega \times$ relationship that enables one to calculate all desired ...
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### 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 ...
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### What point of application of force ensures more acceleration in a rod?

Suppose there is one rod and a force F is applied in two cases: Case 1: exactly at the middle on center of mass Case 2: at one end of rod In which case would the center of mass of rod be accelerated ...
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### Why does the wheel of a car appear to be moving in opposite direction?

When a car is about to stop, the speed of its wheel reduces. Why do we see or feel that the wheel of the car is moving in the opposite direction? This can also be observed of a fan at home. So why ...
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### Rotation of a vector

Is a vector necessarily changed when it is rotated through an angle? I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. ...
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### 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?
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### Understanding rotational motion on a rough surface

I am having trouble gaining an intuitive understanding of rotational motion for an object rolling on rough surface, and I have a few questions regarding it. Let's say that there's a cylinder that ...
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### Does the Earth rotate vertically too?

We know that the earth has seen several Ice Ages. And we know the Earth's magnetic poles seem to flip once in a while. Could all of this be explained by a once every 250 Million Years or so the ...
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### 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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### Rotation, cats landing on their feet, and conservation of angular momentum [duplicate]

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity. It is well-known that θ can change even when the body is not rotating, using the conservation of angular ...
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### A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix  \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\...