What is Rotation: Definition and 1000 Discussions

A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.

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  1. D

    Axis angle rotations and changing rotation values

    I have two 3d applications and when an object(a cube for example) is transferred between them, the rotation values of the cube change(the object stay at the same location. translation and scale values stay the same) and I can't find why that occurs and it's driving me crazy. app 1 rotation...
  2. A

    Understanding the Rotation of a Freefalling Rod

    This has been brought up numerous times but I don't really understand it. Consider a rod in freefall. If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on...
  3. Gh778

    Pressure forces from a liquid in rotation

    Hi, A liquid in rotation give two kind of forces: 1/ centripetal 2/ pressure forces (Fa, Fb in the drawing) I'm ok that centripetal forces can't give energy (we lost kinetics energy) but Fa/Fb seems in direction to external circle, why it's not possible to recover energy from these...
  4. T

    Rotation of a Rigid Body: Finding Center of Mass and Moment of Inertia

    Homework Statement A 0.9 kg mass at (x, y) = (20 cm,20 cm) and a 2.0 kg mass at (20 cm,100 cm) are connected by a massless, rigid rod. They rotate about the center of mass. Homework Equations x=(m1*x1+m2*x2)/(m1+m2) y=(m1*y1+m2*y2)/(m1+m2) I=1/12*ML^(2) The Attempt at a...
  5. Saitama

    Rotation and varying friction coefficient

    Homework Statement (see attachment) Homework Equations The Attempt at a Solution I am not able to understand the question and build a scenario in my mind. The question asks the distance traveled when the cylinder starts slipping. I can't think of the situation when the cylinder...
  6. N

    Object rotation about a fixed axis? question about derivatives in this problem?

    Object rotation about a fixed axis?? question about derivatives in this problem?? An object rotates about a fixed axis, and the angular position of a reference line on the object is given by θ=0.40e^(2t), where θ is in radians and t is in seconds. Consider a point on the object that is 4.0 cm...
  7. O

    Simple energy question with rotation

    Homework Statement a small solid sphere of mass m and radius r starts from rest and rolls down a hill without slipping. the sphere encounters a loop of radius R where R >> r. Given R determine the min height h such that the ball remains on the track throughout the loop Homework...
  8. I

    Using the rotation operator to solve for eigenstates upon a general basis

    Homework Statement I need to express the rotation operator as follows R(uj) = cos(u/2) + 2i(\hbar) S_y sin(u/2) given the fact that R(uj)= e^(iuS_y/(\hbar)) using |+-z> as a basis, expanding R in a taylor series express S_y^2 as a matrix Homework Equations I know...
  9. M

    Find rotation matrix that diagonalizes given inertia tensor

    Homework Statement In a particular coordinate frame, the moment of inertia tensor of a rigid body is given by I = {{3,40},{4,9,0},{0,0,12}} in some units. The instantaneous angular velocity is given by ω = (2,3,4) in some units. Find a rotation matrix a that transforms to a new coordinate...
  10. C

    Rigid body rotation near galactic center

    Homework Statement Equate the expression for centripetal acceleration with the gravitational acceleration to show that the central parts of the galactic rotation curve are consistent with rigid body rotation. The attempt at a solution Say a star near the galactic center has mass m and the...
  11. M

    Wick rotation, scalar field and invariants

    One point about Wick rotation is puzzling me and I can not find explanations in books. It concerns the invariants formed from scalar product and solutions to equation. So I will expose my way of reasoning to let you see if it is correct and at the end ask more specific questions. Let's start...
  12. M

    Simulating earth rotation and (excess) Lenght of Day calculation

    Hello everybody :smile:, I'm new here and hope you can help me with this problem. I have to simulate the Earth rotation with eulers equations of motion (without external torques at first). I have given: Solution of eulers equation without external torques: \omega = (x, y, z)'...
  13. D

    Weird? About the direction of rotation of wheels

    Weird!? About the direction of rotation of wheels Suppose we consider a car moving on rough road in forward direction, wheels rotating clockwise. Since wheels rotate clockwisely they will push road backwards so friction acts forwards i.e. in direction of motion of car.The car will move...
  14. S

    Formula to calculate rotation

    I'm working with 3D applications, and I'm trying to figure out how to calculate the rotation of x number of points between two points. I've made a video to illustrate what I mean: https://www.youtube.com/watch?v=CmIk8I8itrQ So the thing is, I need to find some kind of formula that...
  15. J

    Addition of angular momenta, rotation operators

    Hey, I have a question regarding the invariance of a 'mixed' Casimir operator under rotation, By 'mixed' Casimir operator I refer to: \vec{J}_1\cdot \vec{J}_2 Where J1 and J2 are two independent angular momenta. I want to show that this 'mixed' Casimir operator is invariant under...
  16. T

    Change of weight with faster Earth rotation.

    Homework Statement m=55kg r=6400km The Earth's rotation increases so on a bathroom scale, it now reads that you weight 0. how long is 1 "day" on Earth? Homework Equations I keep trying to figure this one out, but with different ways I've tried, I put Fg as 0 and it basically...
  17. P

    How does tyre rotation increase air pressure?

    the pressure of air inside a car tyre increases when the car is traveled at HIGH SPEEDS?why is this so?my guess is that at high speeds,the friction between the tyre and road surface increases..so kinetic energy is dissipated as heat energy due to friction.this heat is transfers to the inside of...
  18. N

    Rotation Matrix in 3D: Correcting Errors in 3D Coordinate System Rotation

    Homework Statement Hi I have a coordinate system as attached, and I want to rotate it along the y-axis in the clockwise direction as shown. For this purpose I use R = \left( {\begin{array}{*{20}c} {\cos \theta } & 0 & {\sin \theta } \\ 0 & 1 & 0 \\ { - \sin \theta } & 0 & {\cos...
  19. M

    Frame Dragging & Galactic Rotation: Implications for AGN & Black Holes

    Hi, I am interested in the issue of frame dragging used in a number of galactic rotation models. However, I wanted to first make sure that I have a better understanding the relativistic implications of frame dragging. While the issue of galactic rotation is not the subject of this thread, it is...
  20. U

    Earth ellipsoid due to rotation

    I recently saw a documentary, which claimed that if the Earth rotation slows down the water of the oceans will flood to the north and south because the centripetal force at the equator diminishes. In fact, earth’s radius is about 20 km longer at the equator than at the poles. However, I doubt...
  21. D

    Exploring Forced Non-Centroidal Rotation

    Hello all. I'm a newer engineer in rotor dynamics trying to better understand some things, so perhaps someone can provide some insight... First, I'm trying to better understand the physics of forced, non-centroidal rotation (for a spinning cylinder in particular). Non-centroidal rotation...
  22. D

    Understanding Rotation Curves: A Study of Galactic Density and Derivatives

    Hello, I make the calculation of the curve rotation. Casertano(1982г.) V^{2}=-8GR \int_{0}^{\infty}{r} \int_{0}^{\infty}{ [\frac {\partial p(r,z)} {\partial r}] \frac {K(p)-E(p)} {\sqrt{R r p}}}dzdr p = x - \sqrt{x^{2}-1} x=(R^{2}+u^{2}+z^{2})/(2Rr) Density p(r,z) = p_{0} \exp(-r/h)...
  23. H

    Dot and Cross Product from Rotation Matrix

    I'm just learning this Latex(sic) formatting, so it's not ideal. I was trying to explore the geometrical significance of the cross product when I happened upon an interesting observation. I've seen things like this before, but never had time to really examine them. I define two vectors...
  24. K

    Instantaneous axis of rotation

    Homework Statement if a disc of mas m is pure rolling , with velocity v . the instantaneous axis of rotation would be the point of contact with the ground . As shown in the diagram this could be considered as a disc rotating about one of the point on circumference for an instant of time ...
  25. A

    Rigid body rotation. Need explanation

    Homework Statement https://dl.dropbox.com/u/66988308/Capture.JPG Homework Equations V=rWThe Attempt at a Solution I tried to plug in the forumla , and algebras but I keep getting rc/rf as answer instead of rf/rc as the book says. Work: Vf=(rf)W W=Vf/rf W=Vc/rc Vc/rc = Vf/rf (Vc)(rf) = (Vf)...
  26. M

    Translating Graphic back to Origin after Rotation

    I'm developing a game for the iPhone, and I have a situation where I have a graphic that the user can drag around the screen and there are some buttons the user can push to both rotate it and enlarge it. The graphic is located within a UIView, which is just a rectangular shape that fits tightly...
  27. S

    Universal Rotation: Kurt Godel's Time-Loop Theory

    was watching a documentary about Kurt godel and his idea about going back in time if you looped time, and the only real world way they said that this could be done was to loop time everywhere. The they said that the universe however does not rotate. Which interested me because i couldn't think...
  28. H

    Static Rotation as an Axial Vector

    If I rotate an object about an arbitrary axis, I can draw an arrow along that axis, and assign it a length proportional to the amount of rotation. I can project that arrow onto the basis of a rectangular coordinate system. The question arises, is it a vector? I can certainly transform it...
  29. A

    Why doesn't this matrix represent a rotation?

    The matrix is | 1/2 -1/2 | | 1/2 1/2 | Why is this matrix not representing a rotation? The form of rotation is | cos x -sin x | |sin x cos x | So in this case tan x = 1 and so x = 45...isn't this rotation of 45 degrees?On similar note, for the matrix | 5 6 | | -6 5 | it...
  30. D

    Injective Property of Rotation Function (x,y) to (y,x)

    Hi all, Q. A function takes (x,y) and gives (y,x). Is this function injective? For any function to be injective, f(x,y)=f(x',y')=>(x,y)=(x',y'). But here, I get, (y,x)=(y',x') How can I show the function is injective? It appears to be one. Thank You.
  31. N

    Rotation at close to the speed of light

    Let's say I had an object in space, a ring in this particular case, who was using light energy to spin itself up. The ring was built with a reactor inside of it along with a passenger/observer (we'll call the inside observer Bob for now). Bob, the ring, and the reactor are pretty much...
  32. C

    Rotation Operator Matrix Representation using |+z> and |-z> Basis

    Homework Statement Determine the matrix representation of the rotation operator R(\phi k) using the states |+z> and |-z> as a basis. Using your matrix representation verify that R^{\dagger}R=1 The Attempt at a Solution Do I need to write R| \psi> in terms of a matrix. If I...
  33. Matt Benesi

    Rotation from axis to axis in 4 dimensions

    I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0). To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0) I rotated around the z...
  34. S

    Why isn't rotation included when calculating the average energy of a monatomic gas?

    Greetings, this is my first post, though I have been reading these forums for a while. I understand that the average energy of each degree of freedom in a thermodynamic system in equilibrium is kT/2. My textbook says that for a monatomic gas particle, the only degrees of freedom that count...
  35. I

    Find Volume of Solid: Integral Rotation | y=1+sec x & y=3

    Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=1+sec x y=3 about y=1 Homework Equations The Attempt at a Solution I don't understand how to do...
  36. X

    Rotation of cartesian coordinate system

    Homework Statement Please see the rotation formula in the attachment. Homework Equations The Attempt at a Solution I understand this formula rotates x,y into x',y' by some angle theta. Problem is, how is this formula derived? I cannot for the life of me visualize the cosine and...
  37. S

    Euler angles equivalence with a single rotation

    imagine we rotate a vector centered at the origin with euler angles alpha,beta,gamma. now the question is, can we do this rotation by the means of defining a vector N(which its length is 1).and rotating the vector zeta radians counter clockwise around N? I think it must be possible and I want...
  38. E

    Determining angular velocity radius and velocity of the center of rotation

    Hey, I am trying to solve the following problem: va=vr+ ω × rra vb=vr+ ω ×(rra+rab) vc=vr+ ω × (rra+rac) I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid...
  39. B

    Opposing rotation of the Earth's core

    I heard an interesting proposal - it sounds plausible but I'm here to see what you guys think. It is a way of explaining a diverse set of natural phenomena on Earth with one mechanism - rotation. The proposal is this: The core of the Earth rotates in the opposite direction to the Earth's...
  40. A

    Frictionless world - Earth rotation

    If the world was frictionless, would the Earth orbit underneath your feet? Would buildings and things attached to the ground be slamming into you at the same speed as the Earth's rotation?
  41. T

    Why is the special orthogonal group considered the rotation group?

    I understand that the special orthogonal group consists of matrices x such that x\cdot x=I and detx=1 where I is the identity matrix and det x means the determinant of x. I get why the matrices following the rule x\cdot x=I are matrices involved with rotations because they preserve the dot...
  42. A

    Rotation around center of mass question

    I had quite a few posts about this some weeks ago, but I am still not sure about it. My question is about why you can always view the motion of an object as a traslation of the cm and a rotation around it. It makes sense in the light of the cm being the point which moves as a point particle only...
  43. C

    The Cause of Earth's Rotation: Faradey's Motor or Something Else?

    What is today the most accepted postulate about the cause of Earth's rotation? Faradey's motor or the elements that initially made Earth were rotating around a center of mass, and the velocity remained, or something else? English is not my mother language, sorry if I wrote something wrong.
  44. B

    Moment of inertia and force needed to tilt/change axis of rotation

    Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates. I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...
  45. B

    Accelerationg of rotating mass *along* the axis of rotation

    Says Wikipedia: "The moment of inertia is a measure of an object's resistance to any change in its state of rotation". Now consider a rotating mass m that I would like to accelerate along its axis of rotation by a. Does this count as a "change in its state of motion"? Will it resist the...
  46. D

    How Does Angular Momentum Affect Torque in a Suspended Hoop?

    Homework Statement This is problem 7.7 from [kleppners mechanics...
  47. S

    Invariance of U_harm of crystal to rotation

    Homework Statement Show that because a pure rotational displacement field u(r) has no effect, that the energy of a crystal only depends on the symmetric strain tensor epsilon_ij. Homework Equations As in Ashcroft & Mermin (22.72), the energy of a crystal as a function of displacement field...
  48. A

    Rotational vs. Translational Energy in Rotation

    Suppose you push a stick by a distance of s like on the picture. It will start to rotate as you along. My question is: Will the rotational energy that it gains be the distance that the point of applicance covers on the circumference of the circle of rotation, while the translational energy will...
  49. T

    Idea about change in Earth's rotation speed by Climate Change

    I know the two seem very unrelated at first, but actually I think the partial melting of the polar ice caps would actually give us longer days and nights. Most of the ice that would be melting is relatively close to the poles, the axis of Earth's rotation. But, when it melted, the mass of the...
  50. M

    3D Rotation of a rigid body in Fixed Axes (Not Axes Rotation)

    Dear All, I have come across with a seemingly very simple problem but could not solve it by searching on internet and books. May be I am confused. I want to rotate a 3D body around an arbitrary axis with fixed principal axes. The solutions I found is with Euler angles (Euler rotational...
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