Rotation Definition and 1000 Threads

Hello I am hoping someone can explain a sentence to me. Unfortunately, I do not even recall where I read it. I wrote it down years ago and long since lost the source. (Now I think some of it is making sense, but I don't remember the source.) Consider R(t) as an orthogonal rotation matrix...

Hi, I'm working on the interaction between a two level atom (|g>, |e>) In my exercise we have to use the rotation operator : R(t)=exp[i(σz+1)ωt/2] with σz the pauli matrix which is in the {|g>,|e>} basis : (1 0) (0 -1) If i want to represent my rotation operator in the {|g>,|e>} basis. Then...

Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...

If I were to put attach a long rod to the side of a door (the exact opposite of the side where it is hinged, the slim part) And then I apply a force to the the right side of the rod I attached, would the door rotate to the right, or would the hinge completely oppose the force and the door...

When we push off with with our foot on the ground and accelerate, why do we fall forward and catch ourselves with our swinging leg, while when push forward the inertia of our body must actually tilt it backwards, how do we fall to the front?

Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...

Lets say I have a massive rod laying on a table with little froction, screwed into the table on one side to become our pivot point, and I lay next to it with my feet pointing towards the rod. First scenario: I position myself very close to the pivot point and push, the rod rotates and I move...

Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...

Homework Statement https://i.imgur.com/WPAKuf4.png seeking G(s) = \frac{\theta_2(s)}{\tau(s)} Homework EquationsThe Attempt at a Solution What does it mean when the viscous drag is parallel to the axis of rotation?[/B] It also turns out that this system needs two equations. I can sort...

How do we experimentally apply the operator ## \exp{\left(-i\phi\frac{ S_z}{\hbar}\right)}## on a quantum mechanical system? (Here ##S_z## is the spin angular momentum operator along the z-axis) For example, on a beam of electrons?

I am Professor of Inorganic Chemistry of the State University of Southwest of Bahia - UESB. I have a PhD from UFMG in Natural Product Chemistry. I use the polarimeter in my experiments and would like to understand what happens on a micro scale (chiral molecules) to provide the phenomenon of...

Homework Statement Hi everyone. We were discussing conservation of angular momentum as a consequence of rotational invariance in class. There was one point where we needed to compute the change in a vector A when the coordinate frame is rotated by angle Δ(Φ). Homework Equations The teacher...

Can anyone give me geometric and intuitive insight on Rotation matrices which has two sets of coordinates after Transformation?

Hi everyone, i have a question Moment of inertia changes during rotation. Calculate the work that changes kinetic energy? Angular moment (along the axis of rotation) L = I * w A point mass M rotates along an axis attached to a mass-negligible rod, of length r. If someone moves the mass M at...

Homework Statement A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 20 of...

I apologize for the simple question, but I have not been able to find the answer. For the inner portion of a galaxy rotation curve (where the outer portion is the part invariant to distance and the inner part is where rotational velocity increases with radius), how much is simply due to...

Hello, I have a setup whereby: 1) A circular plate with fillet under-edge, is sitting like a bowl on some ball bearings. Imagine if you will a bowl sitting in a way that it can rotate and move a bit up and down etc. without much friction. 2) The plate needs to rotate at about 4 or 5 rpm. 3) The...

Hey guys, I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page: So a couple of questions here: (By the way, I know the answer is C) 1. My teacher explained that the net torque here on the assembly would be zero(will ask him again later). Is this...

Homework Statement Here is a problem we worked in class. I already know the answer, just had a question on the method. Two cylinders are connected with by a small rod (with presumably negligent mass) through their centers. The cylinders can roll freely. A spring is attached to the small rod...

Homework Statement A pulley hangs of mass, m, and radius, R, hangs from the ceiling. Two blocks of masses, m1 and m2 are connected by a massless, non-stretchable rope on the pulley (assume no slipping). What is the angular acceleration of the pulley and what is the ratio of the tension forces...

Homework Statement A 700g ball rotates around a vertical shaft supported by two strings. If the tension in the upper string is 20.0 N, determine (I have attached the file) a. The tension in the lower string. b. The rotation rate in rpm of the system. Homework Equations [/B] F=ma F= m...

Homework Statement Two weights are connected by a very light flexible cord that passes over a 40.0-N frictionless pulley of radius 0.300 m. Weight #1 is 125 N and Weight #2 is 75 N. The pulley is a solid uniform disk and is supported by a hook connected to the ceiling. What force does the...

Pardon me if this seems like an incredibly naive question. Perhaps the question could also be rephrased as such: "Why do the laws of classical mechanics hold true with Earth as a frame of reference?" A quick google search turned up the usual answer: the Earth rotates at a constant speed...

HI! I'm a student, this question appeared in one of the old tests. I though I had it solved but apparently I must have missed somewhere. Could someone please at least hint me where I went wrong? Homework Statement Thin wire is wound into circular frame with radius ## r = 0.05m ## which...

Homework Statement A coin of radius R rolls around a coin of radius 3R which is fixed.If the coin rolls without slipping, How many times does the coin rotates around its axis ? Homework Equations Xpm=RΘ for non slipping The Attempt at a Solution The center of mass moves a distance of...

Homework Statement A Rod of Mass "M" is attached to a two-way hinge on the floor. It is being pulled by a spring (extension spring, so force is pulling the rod to the right, causing it to move clockwise). The hinge is frictionless. the rod has a mass of 5kg evenly distributed the pulling...

I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation...

If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?

If someone from the outer space suddenly teleport to the Earth , will it feel the rotation of the earth? will it be disturbed by the fast rotating earth.

Hey! :o I want to rotate the point $(10, 11)$ with rotation angle $\frac{\pi}{3}$ around the point $P=(-1,-1)$. I have done the following: We translate about $-\vec{OP}$: \begin{equation*}P'=(-1\mid -1)-(-1\mid -1)=(0\mid 0)\end{equation*} We rotate around the origin...

For a microscale electric generator (where the driving force is a fraction of a Newton), can losses from eddy currents be significant enough to noticeably alter the rotational velocity of the rotor? Because my understanding is that the rotation is basically taken as a constant when examining the...

Homework Statement I am working in Matlab, and have a 3D plot that I made: x is parallel to axis labeled "lateral direction (m)" y is parallel to axis labeled "long. dir. (m)" z is normal to these (right hand coordinate sytem) The original view was looking parallel with +y. To get the...

Does anyone know if the following is available as an off-the-shelf component and what would it be called? One-way rotation mechanism Has detents or stops at specified intervals (such as every 90 degrees) Fairly small - for attaching an approximately 2" diameter wheel or circular disc to Doesn't...

Hi all! I have a cyclette with 8 resistance levels set magnetically using a knob (a magnet is moved near the rotating disk thereby increasing its rotating resistance). The distance from the pedal to the center is 0.165 m. At resistance level 4, if I put a weight greater than or equal to 0.750...

Hello. Let's image a bar. In one side is attached to a body so the bar can rotate over this axis. There is no friction between the two bodies. The system is at rest in t=0. A force acts forming a 90° angle with the bar. The bar moves and begin to rotates. The force dissapear. There is no force...

Homework Statement Linear Algebra Problem: Solving for Euler between two ordered bases I've got a problem I need to solve, but I can't find a clean solution. Let me see if I can outline the problem somewhat clearly. Okay, all of this will be in 3D space. In this space, we can define some...

What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...

Homework Statement Rotation of a small drum of mass moment of inertia 0.44kg.m^2 and with frictional resistance torque 0.3 N.m is initiated by a string wound around its 20 mm diameter shaft and attached to a stretched spring, as shown in the figure. If the spring, which has a stiffness 2N/mm is...

Homework Statement The rotor of an electric motor weighs 10 pounds and is 4 inches in diameter. What is the length of time required for the motor speed to increase from 0 to 1800rpm, assuming a constant electrical torque of 20 in-lb and zero external load during this period? Assume the rotor is...

This is my first time posting here so I hope I am in the right place. So I have read about some scientists who have built a ring laser that is sensitive enought to detec the Earth's rotation. I can get how a ring laser can detect the rotation of a missile say if the laser path is perpendicular...

Homework Statement Analogy to rotation: $$(x')^2+(y')^2+(z')^2-c^2(t')^2=x^2+y^2+z^2-c^2t^2$$ It isn't Homework Equations Lorentz transformations: $$x'=\frac{x-ut}{\sqrt{1-u^2/c^2}}$$ $$t'=\frac{t-ux/c^2}{\sqrt{1-u^2/c^2}}$$ The Attempt at a Solution ##~(x')^2-c^2(t')^2~## must equal...

Please help me solve a problem that has puzzled me for years. I am not a mathematician or a physicist, so please bear with me. Imagine the apparatus pictured to be a depiction of the x, y and z axes. The x is represented by the green stick. The y is represented by the yellow stick, and the z...

I was reading about the Ehrenfest Paradox and it got me thinking about something (that I think is) similar: Suppose we take a large, flat, and rigid disk, and we attach to various parts of it a number of clocks (some very close to the center of the disk, some along the edge, others in between)...

When oil is taken from the ground, it leaves a cavity that doesn't get backfilled. If material were taken from anywhere on a billiard cue ball, it would throw it out of balance. Trillions of gallons of oil have been displaced over roughly 100 years, shouldn't that affect Earth's rotation on...

Suppose i have an equilateral triangle and i want to find the principal axes of rotation passing through one of the vertex. How can i do that? I am thinking along the following lines but I'm not too sure: 1)Since the equilateral triangle has symmetry about a median, that definitely is one...

<Mentor's note: ^Moved from a technical forum and therefore no template.> at the instant shown during deceleration, the velocity of the tire is 40 ft/s to the right and the velocity of point A is 5ft/s to the right. locate the instantenous center of rotation. Can the instantaneous center of...

Homework Statement The question is uploaded. Value of g = ## \small \rm 10~ms^{-2}## Inertia of the individual square lamina = ## \rm \small \frac{1}{12}mr^2 ~kgm^{2}## The Attempt at a Solution $$\ C=Ia$$ $$\ Moment~of~Weight~of~Particle=1.594a$$ $$\ 0.3*2g=1.594a$$ $$\ 6=1.594a$$ $$\...

Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...

I am curious how the deflection of a shaft changes due to rotation. In the force diagram image the green arrows show the rotational fixture locations and the purple arrow show the location of the applied force. The second image shows the deflection during a static test. If the force is applied...

For example let's a satellite was orbiting the moon which has no atmosphere. If the moon suddenly started spinning twice as fast would it effect the satellite's orbit even though the satellite is separated by the vacuum of space from the moon? Easier way to put it, if the Earth suddenly spun...