Rotation Definition and 1000 Threads

Hello! I am a bit confused by the reference frames used in derivations for rotational motion in classical mechanics (assume that there is no translation and the body rotates around a fixed point). As far as I understand there are two main frames used in the analysis: a lab frame, which is fixed...

Hello! I am a bit confused about the rotational motion in molecules. Assuming the bond length is constant, the motion can be described as a rigid rotor. In the center of mass frame the energies are given by ##BJ(J+1)## and the wavefunctions are spherical harmonics. However when we measure the...

Hello! I am a bit confused by the quantum numbers used to describe the rotation of a nucleus. In Wong's book these are J, M and K, which represent the rotational quantum number, its projection along the lab z-axis and its projection along the body intrinsic symmetry axis, respectively. However...

How do "sinϕ - cosϕ sinϕ" become 0 ?

Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects. The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment...

Please refer to the image

Hey! :o Let $F\subseteq \mathbb{R}^2$. A map $\pi:\mathbb{R}^2\rightarrow \mathbb{R}$ is called symmetry map of $F$, if $\pi(F)=F$. A symmetry map of $F$ is a map where the figures $F$ and $\pi (F)$ are congruent. Let $\pi_1:\mathbb{R}^2\rightarrow \mathbb{R}^2$, $x\mapsto \begin{pmatrix}0...

So Earth and everything is spinning around at 1000mph at the equator. From our perspective we are at a standstill. But let's say a fighter jets flies east to West against Earth at same speed, so now relative to someone in space, the Earth spins but the plane is at a standstill. Wouldn't that...

Hi, The context for my question is: A thin plate, which lies in the x-y plane, contains a small hole of radius a . Consider a polar co-ordinate system r,􏰆 with its origin at the centre of the hole and 􏰆defined as the angle that a radial line makes with the x-axis. A uniform uniaxial tensile...

v1=460m/s×2, v2=0 m1=m2=5kg R=6378km a1=460m×460m/s/s/6378/km/1000/m×km=0.13m/s/s a2=0 F1=m1×a1=0.66kg×m/s/s F2=m2×a2=0 G=9.81m/s/s F3=(m1+m2)×G=98.1kg×m/s/s (F3-F1)/10/kg = 9.744m/s/s Where the heck did I go wrong?

Therefore, if someone were to ask what the magnitude of centripetal acceleration is at the top of the wheel at a given instant (relative to the ground): ##v_{cm} = v_{translational, center-of-mass/wheel}## ##ω = ω_{point-of-contact}## ##v_{top} = 2(v_{cm}) = 2(rω)## ##a_{c(top)} =...

Summary:: Calculating the inclination angle A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...

I tried to use the right hand rule to find torque but I’m not sure to go from there.

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...

Recently, I've been studying about Lorentz boosts and found out that two perpendicular Lorentz boosts equal to a rotation after a boost. Below is an example matrix multiplication of this happening: $$ \left( \begin{array}{cccc} \frac{2}{\sqrt{3}} & 0 & -\frac{1}{\sqrt{3}} & 0 \\ 0 & 1 & 0 & 0...

A gear A has 50 teeth and another B has 10 teeth, how many times does the small gear rotate around the big one? I thought 5 but its 6! Note: The gear is curved like 360 degrees.

I farm and have built water control devices for my rice operation that use a cable and drum setup. The moving part is a 24"water tight rotary union that we rotate with a cable that originates in a dual spool winch above the center line of rotation for the drum. The winch cables secure to the...

Hi, I find this... Please tell me your opinion on this. Thanks.

For some reason I have become very unsure but my gut feeling says i can calculate y=(1-x^(a/b))^(d/c) I already know the formula for calculating the volume. but can transfer the whole thing as a function of y(x) and take the integral then as a single integral?

Summary: What if the Earth rotated about its axis in a N-S direction instead of doing so in an E-W direction. Hi, Just curious: What would be the effects/consequences if the Earth rotated about its axis in a North-South ( or South-North) direction instead of an East-West one as it currently...

I have questions concerning group theory, esprecially Rotation groups. The first is: Are rotations groups f.ex. SO(2) defined for rotations in the actual physical 2 dimensional plane or are general rotations in any 2 dimensional space included? Someone wrote that "the action of an element of...

torque=Force*radius*sin(theta) center of mass x direction = ( 0(6 x 10^9 kg)+ (118m)(6 x 10^9 kg)+ (236m)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 118m center of mass y direction = ( 0(6 x 10^9 kg)+ (140m)(6 x 10^9 kg)+ (0)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 46.7 m radius = (118^2 + 46.7^2)^(1/2) =...

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?

I was recently trying to explain to a grandchild the relative nature of velocity (the different paths of a coin dropped by a passenger on a train, as seen by the passenger on one hand and a trackside observer on the other), and the invalidity of the concept of absolute velocity. For some reason...

The bigger circle is a hollow cylinder (steel) with a length of 0.6m and a diameter of 0.133m and a mass of 8kg. The 2 smaller circles are rubber wheels with a diameter of 0.080 and mass of 0.2kg. Both the roll and the wheels have ball bearings and are mounted on a shaft. On both the shafts of...

Answer choices: N2L for Translation, N2L for Rotation, Both, Either1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. My solution = N2L for rotation 2. You are asked to find the angular acceleration of a low-friction pulley due to a...

The graph in Wikipedia, article Milky Way, section Galactic Rotation, shows the actual rotation speeds in blue and the calculated speeds due to observed mass in red. (The graph is to the right of the article.) At about 3 kpc the actual speed is about 205 km/s. To account for the decrease in...

A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...

(The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite). I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...

Hi. I searched and found no answer to this simple question: Is the spinning wheel in this videoclip keeping the same rotation (kinetic energy) when flipped upside down and back again? (if we forget about friction)

If a plane departs from the North Pole (where the Earth's rotation speed around its axis is 0 Km / h) on the median line to Romania, around the 45th parallel (where the Earth's rotation speed around its axis is 1178, 80 km / h) would the plane reach its destination only by flying to *South* (...

How have we been able to measure galactic rotation? I have seen graphs showing the relation between the velocity of stars in a galaxy and their distance from the center. These graphs show that the observed velocities of stars are much faster than they are expected to be, particularly ones that...

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...

First off, I was wondering if the acceleration of the conveyor belt can be considered a force. And I'm not exactly sure how to use Newton's second law if the object of the forces is itself on an accelerating surface. Also, I don't know whether it rolls with or without slipping. I thought I could...

Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I...

I think the answer is ##\frac{mV}{M}## but I am not sure. Won't the cylinder tries to rotate due to the collision at one end? Is this anything related to Angular Momentum? The Answers given were,

I am experimenting with using a radiometer as an approximate indicator of pressure in my homemade high vacuum system, running a small turbo pump. I am interested in the relationship between pressure and vane rotation speed, with light intensity being constant. I have only been able to find...

Hello, A force couple is compose of two forces of equal magnitude, opposite direction and parallel lines of actions separated by a distance ##d##. The moment due to a force couple is called a pure moment because its value does not depend on the point about which the moment is computed. The...

Hi Everyone! I am trying to a DIY project to make a food maker. I am 50% succeeded with that and need help for the remaining 50%. The idea is to produce the output shown in the first image. That food is made with a flour. So I have the setup a pressing machine shown in image2. In this I was...

There is a disaster movie about a global cataclysm that results in Kilimantzaro becoming the north pole or something. Maybe this is plausible in terms of plate tectonics. Or maybe not. But I've got another question, a purely mathematical one: if the Earth were a solid sphere, no plates and such...

Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure. Find the maximum velocity the ring must roll so that it doesn't...

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.

Problem Statement: i have a steering wheel mounted on an electric motor, and i want to stop the driver from going beyond a certain angle. i can read the torque applied by the driver, and the steering wheel angular velocity as well. how can i stop the steering wheel, without sending it harshely...

How do the Pauli spin matrices transform under an inversion ? I think I mean to say the 3 dimensional improper rotation which is just in 3 dimensional matrix notation minus the identity - so exactly how are the 2 dimensional Pauli spin matrices changed. And under a 180 rotation do the 'y' and...

Starting from this post, we are able to define the concept of (proper) acceleration or rotation without any reference to something else About this definition which is the physical meaning of gyroscopes axes pointing in three mutually orthogonal spacelike directions ? In other words, from a...

Say we have the moment of inertia of any object. If we removed the radius squared part of the moment of inertia and just leave mass, would heavier, further-from-the-axis mass on one end of the object be as easy to rotate as the lighter mass, maybe closer-to-the-axis of rotation on the other end...

Imagine a 400-meter-long pipe with a 1600-meter diameter, floating in inter-planetary space. It is spinning at 0.5 gravity along its major axis and there are no secondary-axes spins. We need to increase rotation to 0.85 g. Its density is a uniform 2.3 kg/m³ and it weighs 49,120,056 kg. Thanks to...

For parts A and B I used energy to find the vcom and omega, but that won’t work for C. I have an answer by combining the three formulas that use acceleration above. My answer for alpha=-5g/3r. The next two are easily solvable if you find C, but I still feel like I’m missing something. Any help...

Hello everybody, I am currently working on an experiment investigating the formation of planets. I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together). From the imagery I can see those agglomerates which are build up by smaller...

So for part (a), I used the fact that 1/N = the period = T. I solved for the velocity, where i got v=2πRN. I plugged that v into F=(m v^2)/R, which is the centripetal force, but also the force of friction. My answer to part (a) is 4(π^2)mR(N^2). I'm a bit confused on part (b). I know that...