Rotation Definition and 1000 Threads

TL;DR Summary: I am writing a research paper on the rotational motion of the blades of a helicopter. Does anyone know of any good reliable sources for articles, videos, or research papers on this topic? Hi! I am writing a research paper on the rotational motion of the blades of a helicopter. I...

I have very little clue as to how to imagine (visualise) the rotation and how the axes will look. All I can do is to draw the image of what I mean by the task. Of course, this is before the rotation takes place. In the diagram, ##\mathbf{OP}## is the axis of rotation. For simplicity, we may...

When you hold a screwdriver with your hand, a pressure is exerted on it. Does the pressure you exert determine the magnitude of torque in rotating the screwdriver?

So, If we imagine a ball, give it some initial angular velocity ω, and launch it straight up, with a translational initial velocity u. What will be the path traced by a point on the periphery of the ball (the point on the either of the two extremes horizontally, left or right)? (air resistance...

Suppose there is a disc rotating around axis through its centre, with force F acting on the rim. The equation of torque is simple, however, what happens if it is written about an arbitrary point on the rim? How can the angular acceleration about that point be understood? Do I have to transition...

This fact blew my mind when I realized it: in 2-dimensional space one can make a bounded set into its strict subset by means of rotation. I still cannot comprehend how coud this be possible and how much of math gets blown by it. I think, it is used to prove the Tarski paradox. While most...

Friction before force is applied, f=μmg. After force is applied on element dx, at a distance x from hinge, the is a bending moment on that element dM which is given by normals on either side (say N1, N2) by dM=N1-N2 and N1+N2=mg+F.

Is this absolute motion ?

What is the best way that you all think that I can make these long two vertical pieces of metal spin on this stepper motor in the orientation as shown in the picture. I preferably dont want to cnc but I can and would if necessary. Thank you all!

So to begin with, I did this: $$ \begin{align*} dm &= \frac{M}{2\pi} d\theta \\ dN &= dm \cdot g = \frac{M}{2\pi} g \, d\theta \\ df &= \mu_k \, dN = \mu_k \frac{M}{2\pi} g \, d\theta \\ f &= \int df = \int_0^{2\pi} \mu_k \frac{M}{2\pi} g \, d\theta \\ f &= \mu_k \frac{M}{2\pi} g...

Here in 3D one may either have an object constrained to rotate only in a single plane or have a freely rotating object that can rotate in any combination of the three planes. It seems to me that you can't have an object constrained to rotate in only combinations of two planes. You can't have...

Hello. I understand that plotting the hauptpole (I believe it's called "instantaneous center of rotation" in English) in STATICS is useful for virtual displacements. I know the rules: Hauptpol (ICR, which is denoted (0, #member) ) are located where a support of a member is fixed. For a member...

I'm trying to rotate an RPP 45 degrees around the y axis (BUT NOT THE ORIGIN Y AXIS, rather the y axis at x=a, z=b). Is there a way to do this in MCNP? I've tried every single possible combination of angles and inputs to no avail. Again, I have an RPP that is not centered at the origin and I...

Excuse my lack of knowledge and please correct me on anything! I'm making a lamp right now and the vision is to have a dimmable lamp in which there are two strings controlling to the potentiometer. To increase the brightness, one string is pulled down and the other will go up. I have a lamp with...

I have been thinking about rotation number of regular smooth curves in different surfaces. Here is how I’ve been defining these things: a regular smooth curve is a map from ##S^1 \rightarrow \mathbb{R}^2## whose derivative is non-vanishing. If we have a regular smooth curve ##\gamma## as well...

I would like to create a thread to ask a question about plumbing. I have used my cell phone to take photographs of a book about plumbing, and I would like to post these photographs on my thread about plumbing. But when I was in the process of creating a thread, and I posted the photographs on...

I did a thought experiment and I can't figure out what the mistake is. There is a system of 2 electric motors weighing 1 kg each with batteries in the Earth's orbit. The motors are rigidly connected by a 1-meter-long bar. If one motor starts rotating in one direction on a signal, the entire...

I'm trying to learn about adding angular velocities, and I'm confused about something. In this diagram... https://i.sstatic.net/S6C03.png there is a large orange disc rotating with angular velocity A (relative to the ground), and attached to the large orange disc is a small green disc, which is...

Posting this as I have so far not been able to find a straightforward answer to the following question. The formula for the outer event horizon of a kerr black hole is given by the following equation: $$r_+ = \frac{GM}{c^2}\left(1+\sqrt{1-\frac{J^2c^2}{M^4G^2}}\right)$$ Where ##J## is the...

Let the mass of the ball m₁ and the disk m₂ m₁vrsinθ = I₁ω + Ι₂ω I₁ = m₁r² and I₂ = ½m₂r², r=3m, rsinθ = 2m. Is this a correct approach? if not, what is? Can this be solved using energy conservation?

Hello, I am currently doing research on the Foucault pendulum, specifically on its rotation period. I was wondering where I could find data concerning the observed rotation periods of various Foucault pendulums at different latitudes around the world (not calculated using the Formula T=24/sinλ)...

Hi All, Do the left side and right side engines of a plane rotate in the same or opposite directions? Is the angular momentum (gyroscopic effect) of the engine shaft, blades, etc., sufficient to affect the flight path of a plane with large engines? In military fighters, such an effect could be...

In Dirac's "General Theory of Relativity", Chap. 34 on the polarization of gravitational waves, he introduces a rotation operator ##R##, which appears to be a simple ##\pi/2## rotation, since $$R \begin{pmatrix} A_0 \\ A_1 \\ A_2 \\ A_3 \end{pmatrix} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 &...

What it said in TL;DR: I want to describe a situation where a laboratory technician synthesizes the wrong isomer(?) of a naturally occurring venom, ending up with the left hand molecule when aiming for the right hand one. However improbable that may sound to a bunch of pros like you. It's for...

This question has been bugging me for quite a while, That what do we mean by direction of angular velocity or torque. As we know that the direction of angular velocity or torque even is determined by right hand thumb rule, and it come out to be perpendicular to the rotational plane. So my...

Why a free rigid body with mass m, when applied with an external force F, translates with center of mass and all particles of body having same linear acceleration = F/m, but it always rotates only about its center of mass, but not about some any other point on the body? And, thus if the line of...

[Image below] I'm trying to figure out how much information I can get from and accelerometer and gyroscope attached to a spinning plate that is thrown through the air. It has both linear and angular acceleration/velocity. The plate is hand thrown fairly parallel to the ground. Z axis points in...

I have asked this question last year (on discord; IPhO server) and I believe I wasn't satisfied by the answer at that time, but I let it go. Today, as I was going through some physics videos on YouTube a video about it popped up. So, I would like to address this issue now. Let's imagine an...

Is it a big assumption that Galaxies should follow Kepler's third law with rotation speeds decreasing with distance from the centre. Is the small tet of the behaviour of the Solar System not too small an example to make such a substantial assumption? Thanks Martyn

This is the answer to this question why? My attempt :

i got confused because if the connections btw the parts

In figure AO = OB = 4m. C is the midpoint of AO. The rod rotates with a velocity of 5 rad/s about the axis PQ. What will be the rotational velocity of the remaining rod if AC part is suddenly dropped from the rod? Assume that the mass of this uniform rod is M.

Since ##U## is a space and spin rotation, it would be $$U(R) = e^{-i\textbf{L}\cdot \hat{\textbf{n}}\phi/\hbar}\cdot e^{-i\textbf{S}\cdot \hat{\textbf{n}}\phi/\hbar}$$ And, then $$\psi'(\textbf{r}, m) = \langle\textbf{r}, m|e^{-i\phi(\textbf{L} + \textbf{S}) \cdot...

Hello, The idea I had was to time evolve the state ##U(\hat{\textbf{b}}, \omega t)| \phi(t) \rangle##, but I'm confused on how to operate with ##H## on such state. I Iwould be glad if anyone could point some way. Thanks!

I'm not sure where the equation E_k=(gmR^2)/4h comes from & I also don't really know where to start either :(

Hi , In one of my friends place , she cut the lemon in half and left it . She saw the lemon rotated to other direction by itself . She saw it twice on different days ,why does this movement occur ?

The Importance of Being Symmetric: Flat Rotation Curves from Exact Axisymmetric Static Vacuum Spacetimes ... Analyzing the low-velocity limitcorresponding to the Newtonian approximation of the Schwarzschild metric, we find an effective logarithmic potential. Thisyields flat rotation curves for...

Hi, i need to find a formula or calculation that would allow me to connect three lines when rotating. The three lines must fall so that they mirror themselves on the opposite side. I need to be able to calculate this for now just the example above but be able to apply to a range of lengths and...

You have a rope hanging over a fixed support with a heavy weight at one end and a lighter weight at the other end. You set the end of the rope with the lighter weight spinning in a circle and let the heavy weight end fall under gravity. As the heavy end falls the length of the rope that is...

Doesn't friction always oppose the motion? From the clockwise rotation here, shouldn't the cylinder be moving to the right? so why are the acceleration and friction in the same direction to the right, and in the same direction as the motion? (attached image for reference)

Source : [FONT=tahoma]JEE Advanced , Physics Sir JEE YT I tried to attempt it using Lagrangian , so according to the coordinate axes given in the diagram , the position of the particle is let's say ##(0,d,-z)## Let ##r## be the distance between the particle and the axis of rotation such that...

The equation that connects final velocity with distance traveled is ##v_f^2 = v_i^2 + 2a \Delta y## Since the system starts from rest ##v_i = 0## and the above equation becomes. ##v_f^2 = 2a \Delta y## Since there is rotation in this system we need to connect ##a## to the rotation of the...

Why this wind tunnel rotate?

If a circular rod is allowed to rotate freely and a moment (M) is applied to one end of the rod. A moment acting in the opposite direction, with magnitude (M/3), is applied to the other end of the rod. What is the maximum moment in the rod that would be used to calculate the maximum torsional...

Hello! I am curious about how different rotations on the Bloch sphere are done in practice. For example, assuming we start in the lower energy state of the z-axis (call it |0>), a resonant rotation on the Bloch sphere by ##\pi/2## around the x-axis will take you to ##\frac{|0>-i|1>}{\sqrt{2}}##...

This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod. Is there a classical thought...

EDIT: I forgot about Second Newton's law for rotations and this led to a mistake. Anyway, thanks for the people who answered it and remembered me about law of inertia. I was thinking about how to "make" things to move without rotate the object, then i tried to calculate the minimum force to...

Anomalous contribution to galactic rotation curves due to stochastic spacetime Jonathan Oppenheim, Andrea Russo Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Theory (hep-th) another way to explain MOND in...