Rotating frames Definition and 23 Threads

I have been reading Kleppner's An Intro to Mech recently and have found an interesting discussion on the nature of rotational motion in the book. The authors wrote: Newton described this puzzling question in terms of the following experiment: if a bucket contains water at rest, the surface of...

This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...

Hi On the Earth , apparent gravity comes from the vector addition of the gravitational force directed towards the centre and the outward centrifugal force. It means that for a pendulum at rest , the direction the bob hangs downwards is not directly towards the centre of the Earth but there is a...

Hi, I am trying to gain insight into using stationary vs. rotating coordinate frames for natural frequency calculations. I have seen many FE codes suggest that critical frequencies can be calculated differently in rotating and inertial frames, so i wanted to do a 1D calc to see for myself how...

Suppose we have a rotating frictionless disk and there is a rotating observer on the center of it. Furthermore, suppose a very small ball on the disk's edge. Now we clearly know that the ball is not moving but the rotating observer sees the ball following a circular path with an angular velocity...

Hello there, I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps. Case 1 Imagine two observers (people with telescopes maybe) in space that are standing thousands of...

Referring to slides 3-4 (page 2) of this link: https://www.princeton.edu/~stengel/MAE331Lecture9.pdf The author states the relationship between body rates [p q r] and Euler angle rates [φ_dot θ_dot ψ_dot]. I want to verify this but have been failing miserably... My reasoning: 1) p, q, and r...

Homework Statement A cylindrical container of water with a radius of 6.0 cm is placed on a phonograph turntable so that its outer edge just touches the outer edge of the turntable. The radius of the turntable is 14.5 cm, and the turntable rotates at 33 and a 1/3 revolutions per minute. How much...

After the recent discussion here about the Sagnac effect** I wanted to see if there is any frequency shift if light is sent from one point on a rotating worldline to another a small distance away. It looks like this cannot happen because ##\gamma=dt/d\tau## is the same at every point on the...

I was reading a little about the behavior of non-inertial frames in relativity, since I'm interested in knowing how can we measure time on Earth and the sequence of events here. So as we know Earth is rotating and therefore the clocks on surface that are mutually at rest get desynchronized. Can...

It's a pretty straight-forward question, and it got me confused since most articles on the internet mention planes of simultaneity in the context of inertial frames. So if rotating frames also have planes of simultaneity, what SR says about it and how does it differ from the planes of...

I got stuck going over the derivation of fictitious forces in rotating frames. see specifically http://en.wikipedia.org/wiki/Rotating_reference_frame#Time_derivatives_in_the_two_frames this page to see the proof I'm talking about (sorry i'd love to be able to explain it by myself but...

Hi, I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation: \mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} = \left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} + \boldsymbol\Omega \times...

Can one approximate an "ether" frame by analyzing "superimposed" rotating frames? If we assume the axiom that all motion is ultimately curved, however small the curvature, it would appear that for every momentum you are going to have a radial vector associated with the non-zero deflection of...

Homework Statement You are standing on a slowly rotating merry-go-round, turning counterclockwise as viewed from above. You are holding a string from which is suspended a rubber stopper of mass 45g. You are 2.9m from the center of the merry-go-round. You take 4.1s to complete one revolution...

Please see the attached figure.

I've got a problem understanding a line of proof in my lecture notes. Given that you have a charge of +Q and mass m orbiting a fixed particle of charge -Q' in the presence of a magnetic field B. The particle is moving slowly enough for relativistic effects to be ignored. Given that...

Homework Statement This is an example problem from the book. However, I have absolutely no clue how they solved it. I cannot follow their logic. If someone can just solve it and explain it for me lucidly step by step, I would really appreciate it. Here it is: "A bicycle travels with...

Afternoon, I'm studying Engineering Dynamics (4th Year Undergraduate) and I was wondering if anyone can point me to a resource with regards to rotating reference frames and vector notation? The notes I've been given aren't particularly helpful. Much appreciated.

Hi, I've run into a relativistic kinematics question that I'm not sure how to approach. The question states: "A source and a detector are spaced a certain angle \phi apart on the edge of a rotating disk. The source emits radiation at frequency \omega in it's instantaneous rest frame. What...

In flat spacetime, if you are at rest in a rotating frame, how would you be able to detect that rotation? For instance, on a small planet surrounded by nothing, how can a reference frame that rotates at the angular velocity of the planet be declared noninertial? Thanks for any replies.

Suppose there is an inertial frame S in which there exists some object A at rest, located at (x,y,z)=(10^8,0,0). Now consider the non-inertial frame S' whose axes are coincident with those of S at t=0, but which is rotating about the common z-axis with constant angular frequency w. If S' has a...

A question that led to an interesting answer was posed in a newsgroup recently that I thought I'd share here. Someone proposed a scenario where there were two rocket ships that would travel at constant speed along a circle in opposite directions. They would pass each other twice per revolution...