Rotation Definition and 1000 Threads

I have a velocity vector as a function of a latitude and longitude on the surface of a sphere. Let us assume I have a point V(lambda, phi) where V is the velocity. The north pole of this sphere is rotated and I have a new north pole and I have a point V'(lambda, phi) in the new system. I have...

Happy new year. Why everybody uses this definition of rotation matrixR(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta \\[0.3em] \sin\theta & \cos\theta \\[0.3em] \end{bmatrix} ? This is clockwise rotation. And we always use counter clockwise in...

In Newmann-Penrose formalism, a Null rotation with ##l## fixed is $$l^a−>l^a\\ n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\ m^a−>m^a+cl^a\\ \bar{m}^a−>\bar{m}^a+\bar{c}l^a$$ Using this transformation, how to prove? $$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$ Ref: 2-Spinors by P.O'Donell, p.no, 65

What is the density of galactic centre? Thus what form of Kepler's law account for the galaxy rotation curve increasing near the galactic centre?

in this notes , the author gave that the IG is the moment of inertia calculated about an axis which is perpendicular to the page ... moment of inertia calculated about an axis which is perpendicular to the page here means id due to Ft(tangential force) only ? not include Fn ( normal force ) ...

I am new to this forum. I was reading this document : http://math.kennesaw.edu/~plaval/math4490/rotgen.pdf Here the author says that from this figure http://i.stack.imgur.com/KBw9l.png that we can express $v_{\perp}$ like this : $$T (v_{\perp}) = \cos(\theta) v_{\perp} + \sin(\theta) w$$...

A rod and Cylinder with a same axis of rotation relative to its body have different rotational inertia equation. WHY? Thanks in advanced.

We have a rod and keep floating in ISS. If we tap giving force at one end, will it, 1. Rotate about an axis or 2. Has translational and rotational motion. If it rotates, where is the axis? I have interest in yoyo motion too. From YouTube, they spin them while holding. Can we rotate yoyo from...

Homework Statement I'm designing a device for changing a load position from vertical to horizontal. It has a wheeled frame (2) which allows an operator to transport the load after reorientation. The combined centre of gravity of a rotating platform (1) and the load moves forward due to...

Homework Statement A block of mass 2kg (mb) can slide down a frictionless 53 degree inclune, but it is connected to a pulley of mass 4kg (mp with a radius of 0.5m. The pulley may be treated as a disk. What is the angular acceleration of the pulley? Homework Equations a = rα The Attempt at a...

Homework Statement A certain machine can be modeled as a wheel between two translating bodies. Point P is on the upper translating body and is moving to the left at 6m/s and Point Q is on the lower translating body and is moving to the right at 3 m/s. The radius of the wheel is .3m. Find...

Homework Statement This is just a general case I'm having trouble trying to imagine: https://lh3.googleusercontent.com/-mTyOwzfLy0E/VluaNlxEddI/AAAAAAAAAEk/2Creguw3xzY/w530-h174-p-rw/Screenshot%2Bfrom%2B2015-11-29%2B21%253A34%253A50.png Suppose there is a cylinder, kind of like a yo-yo, that...

I've been struggling with part (a) of this question. I'm not quite sure what the relation is. Any help is greatly appreciated! Thanks! Consider a spiral galaxy with a “flat” rotation curve beyond the central 2 kpc. a. Derive the general relation giving the orbital period, P, of a star (or...

The question mentions an orthogonal matrix describing a rotation in 3D ... where $\phi$ is the net angle of rotation about a fixed single axis. I know of the 3 Euler rotations, is this one of them, arbitrary, or is there a general 3-D rotation matrix in one angle? If I build one, I would start...

Just curious, explanation if youre going to answer please! 2 horizontal disks stacked on one another spinning at constant v, (about a frictionless axis perpendicular to their center), both have mass. Okay, so let's say its possible to instantaneously remove the top disk. So would that make...

In my textbook they used the right hand rule to show that rotation has vectors instead of just being positive or negative relative to its direction of rotation of a vinyl record. In the image the record was going clock wise so by the right hand rule it was going downward which makes sense, but...

Hi, I am having some problems conceptualizing the Euler's Theorem. Any help will be greatly appreciated. In Goldstein's book the Euler's theorem is stated as 'Any displacement of a rigid body, whose one point remains fixed throughout, is a rotation about some axis', then he has proven that the...

Hello this is my first question here :) So here is my problem: We have a circle radius 50 (m), made out of iron wire mass 5.506206591207348477884587 Kg per meter of rope. Rope diameter 11/8 inces or 3.4925cm The wire rotates with 3 rpm in zero gravity 1)How can i calculate the tension? Thx...

For conditions where an object is rolling without slipping on a rough, flat surface, the object posses a net torque about the center of mass provided by friction at the contact point. Hence, why doesn't the object accelerate radially indefinitely? For ex, if we had a slippery bowling ball...

Hello! :) When solving a problem, I had to calculate the angular velocity of a homogenius rod when it comes to vertical position, after being released from a horisontal position (the rod is fixed at one end). This is as usually done with energy conservation, using the rotational energy of the...

axis A is always normal to plane of the circle and passes thru centre of circle axis B is always parallel to plane of circle and is always parallel to y- axis of lab frame. axis B passes thru centre of the circle the infinitely long line MN always lies on the plane of the circle and passes thru...

in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body - Rotation of a rigid body about a fixed axis is defined as...

I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization, http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html and it reminded me that...

Here is the problem I am working on. I have found answers for all of them except part (f), which is the one I need help with. I will report the answers I have so far: A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00...

Homework Statement Let A∈M2x2(ℝ) such that ATA = I and det(A) = -1. Prove that for ANY such matrix there exists an angle θ such that A = ## \left( \begin{array}{cc} cos(\theta) & sin(\theta)\\ sin(\theta) & -cos(\theta)\\ \end{array} \right) ## It is not sufficient to show that this matrix...

Hi folks!First of all, English is not my native language so I hope there is not much misleading spelling mistakes, discrepancies and inaccuracy. I’m currently working with a hobby-project of a flying drone/UAV with two adjustable angled rotors. I’m able to make it fly more or less in a way it...

[this thread was split off from https://www.physicsforums.com/threads/confusion-in-general-relativity.840710/] I read that Einstein gave the following argument: If we look at a rotating (and hence accelerated) frame from an Inertial frame, which is supposed to be away from all gravitational...

I'll start with this question, how much "mass" does something have to have before centrifugal force exceeds gravity on earth? I used basic physics of centrifugal force and gravity, used force vectors, and the math doesn't jive. This is what I mean. There are 2 forces on Earth that everything...

what would be the rotational equivalent of: work = force * displacement ? I assume that the force should be replaced with torque, but have no idea what the displacement should be replaced with, angles in radian? I'd appreciate it to see some units too.

Homework Statement in this diagram , we know that the whole thing wouldn't rotate about y and z axis , right ? why the sign of prevention of rotation are not shown there ? i added green sign = prevent rotation in the z axis , red = prevent rotation in the y axis Homework EquationsThe Attempt...

Hello people, I know it seems like a silly question. In case 1, its clear that no rotation will occur around z axis. Anyhow, case number 2 is confusing me; I can't decide clearly if a rotation will occur since a moment should be generated around z axis, but in the same time, the line of the...

If there is a disk of mass M and radius R that is already rotating, then someone puts a block with mass m on it a meters away from the center of mass. What is the rotational inertia then? Is it I=(M+m)R^2?

Homework Statement Hi! I just found this forum after trying to calculate something regarding a satellite's orbit. Hope that you can help me here. So, I need to calculate the matrix of a satellite's site vectors. I have found it in the ECEF form, but since the satellite is doing observations in...

The diagram below is from https://en.wikipedia.org/wiki/Galaxy_rotation_curve . I would much appreciate a derivation explaining the shape of the "Expected from visible disk" curve in the diagram. Naively, based on Newtonian mechanics for the orbital velocity of a circular orbit, V = √GM/R ∝...

Can you help me find the kind of force that can result in a rotation?(the force that can be considered as centripetal force) I know that static friction, contact force, tension, gravity can cause rotation, what else? can you help me find as many as possible? and kinetic friction can't cause...

Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't...

1. The problem statement, all variables and given/know Say I have a can of water, and I am rotating it about its central axis at a constant angular rate. The water in the tank should make a 3D almost parabolic curve as it touches the the walls of the tank. Can I use Bernoulli's equation along...

Homework Statement A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed v0 in forward direction and angular speed ω0##=\frac{v_0}{2R}## in counter clockwise direction. Find time after which pure rolling starts. Homework Equations For pure rolling...

Homework Statement A dipole consists of charges +e and −e separated by 0.57 nm . It is in an electric field 2.6×104 N/C . What is the work required to rotate the dipole from being oriented parallel to the field to being antiparallel to the field? Homework Equations PE = (dipole...

I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...

Homework Statement Determine the rotation period of a disc with 2m radio , that makes 20 rotations per minute. Homework EquationsThe Attempt at a Solution I did T= 60/20 to find the period , but is that it ? what about the 2m?

Homework Statement IMO , the M2 and M1 should rotate clockwise, and the moment should point downwards based on right hand grip rule . Why the book gave in in other way ? Homework EquationsThe Attempt at a Solution

Homework Statement for the 400cos45 force , i think it should rotate anticlockwise, am i right? but the book gave it is rotated counterclockwise... Homework EquationsThe Attempt at a Solution

I'm currently working through chapter 7 on Riemannian geometry in Nakahara's book "Geometry, topology & physics" and I'm having a bit of trouble reproducing his calculation for the metric compatibility in a non-coordinate basis, using the Ricci rotation coefficients...

Suppose an aircraft attitude is given by Heading=040 degrees Pitch=15 degrees Up Bank=20 degrees left bank And then the aircraft “yaws”, or rotates 30 degrees left about its yaw axis. What are the new Heading, Pitch and Bank angles? What do the rotation matrices look like that describe...

We were asked a question about why there are spokes in a a bicycle wheel. Our teacher hinted that It was related to moment of inertia. Ok so this kind of a wheel will have a higher moment of inertia than say, a solid disk-like wheel. But how is that useful?

Homework Statement Assuming positive x direction is counterclockwise, then why would the force 50n and 40n are turned clockwise ? (they have negative value) Homework EquationsThe Attempt at a Solution

Homework Statement Figure shows a massless wheel of radius R on which at a point a mass m is fixed and a uniform chain of mass 2m is tied to it which passes over the rim of the wheel and half of its length is hanging on other side as shown in the figure. When a small clockwise jerk is given to...

Homework Statement A space station of mass 6.0 × 104-kg is to be constructed in the shape of a thin annular cylinder (or ring). The inner radius of the annular cylinder is 100-m, and the outer radius (and location of the floor) is 105-m. Artificial gravity equivalent to free-fall acceleration...

http://im54.gulfup.com/ZtJZd5.png http://im54.gulfup.com/SJgJXh.png Till now compared with other subjects that I studied by my self, linear algebra is really the toughest one :bow: Anyway, here I found a plane using characteristic eq. which really surprised me since det(M)=1, M is the matrix...