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.

View More On Wikipedia.org
Recent contents Top users
  1. K

    Available materials for Faraday rotation experiment

    I am a high school student experimenting with the Verdet constant of materials and how it affects the polarization of light in magneto-rotation. I have trouble acquiring the proper materials for this experiment. Here is what I have so far: -AC/DC Power Supply -Gaussmeter -Optical laser under...
  2. KhalBrogo

    Question re. flying against Earth's rotation

    What would happen if an aircraft was fast enough to match the speed of the rotation of the Earth and it decided to fly against it matching that exact speed (earth's rotation)? I would imagine it would look like Earth was speeding up but would there be any other physical effects on the aircraft...
  3. Clara Chung

    Rotation dynamics pulley concept confusion

    Homework Statement A light string is passed over a pulley and two masses m1 and m2 are suspended from the two free ends. The pulley is a uniform circular disc of mass M. Find the linear acceleration of the two masses. Friction may be neglected. Homework Equations I through center of the disc =...
  4. F

    I Why do nebulae tend to collapse into discs?

    As far as I understand it, a nebula initially tends to have a small amount of rotation (on average) and then as it collapses under its own gravity this rotation increases significantly due to conservation of angular momentum (assuming that there is no external torque,right?!). What I'm unsure...
  5. Alltimegreat1

    I How to define the rotation of a planet in retograde orbit?

    If a planet is in retrograde orbit, what direction would it rotate to also have retrograde rotation?
  6. Hamal_Arietis

    Instantaneous rotation centers

    Homework Statement Is the conservation of angular momentum theorem right for instantaneous center rotation? That: If all total momen of force is zero. The angular momentum will not change If right, prove that. Homework Equations All equations of rotational motion The Attempt at a Solution I...
  7. D

    I Why is this Isometry a rotation?

    Hello, i need a little help. Did someone have an idea how to prove this? Thanks in advance. Be ##\Phi## an direct isometry of the euclidean Space ##\mathbb{R}^3## with ##\Phi (\begin{pmatrix} 2\\0 \\1 \end{pmatrix})##=##\begin{pmatrix} 2\\1 \\0 \end{pmatrix}## and ##\Phi (\begin{pmatrix}...
  8. S

    A Octahedral rotation angle in Perovskite

    Hi, Can anybody tell me that is the formula to calculate the octahedral rotation angle in Perovskite. for example in SrTiO3, the TiO6 Octahedral angle. When SrTiO3 goes from Cubic to Tetragonal, this TiO6 Octahedral tilt. I have to find this angle. Thanks
  9. C

    What is the moment of inertia I for rotation around r_cm?

    Homework Statement A massless rod of length L connects three iron masses. If the first mass (at x=0) has a mass of 1.90 kg and the second mass (at x=L) has a mass of 8.77 kg and the third mass (located at the center of mass of the system) has a mass of 148 kg, what is the moment of inertia I...
  10. J

    What do you think of this paper?

    I have recently read a paper called "Engineering of Gravity and Time" for an undergraduate student. It contains a theory of gravity and time depending on rotation. Well.., I think it looks quiet percussive. However, fairly, it contains some worthwhile ideas, especially it answers some elementary...
  11. Hoophy

    B What Are Love Numbers and How Do They Impact Tidal Deformations?

    So I THINK I understand that the tidal bulge is resting slightly in front of the moon because of the Earths rotation and the moons gravity, it pulls the moon 'forward' a little adding energy to the moons orbit and expanding it, what I do not understand is why the Earths rotation is slowing. I...
  12. U

    I Spherical coordinates via a rotation matrix

    First, I'd like to say I apologize if my formatting is off! I am trying to figure out how to do all of this on here, so please bear with me! So I was watching this video on spherical coordinates via a rotation matrix: and in the end, he gets: x = \rho * sin(\theta) * sin(\phi) y = \rho*...
  13. Bill McKeeman

    A Exploring Galactic Rotation Data in 3D: A Search for Peculiar Motion

    Does anyone know of galactic rotation data (any galaxy) of the following form: For simplicity assume an [x y z] coordinate system with the origin in the center of the galaxy and [x y] representing the plane of rotation. At any point [x y z] there is a corresponding velocity vector [vx vy vz]...
  14. D

    A Interpretation of the EM tensor as a rotation matrix

    In special relativity, the electromagnetic field is represented by the tensor $$F^{\mu\nu} = \begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & 0 & -B_{x}\\ E_{z} & -B_{y} & B_{x} & 0 \end{pmatrix}$$ which is an anti-symmetric matrix. Recalling the...
  15. ShayanJ

    Derivation of rotation formula in a general coordinate system

    Homework Statement [/B] In a set of axes where the z axis is the axis of rotation of a finite rotation, the rotation matrix is given by ## \left[ \begin{array}{lcr} &\cos\phi \ \ \ &\sin\phi \ \ \ &0 \\ & -\sin\phi \ \ \ &\cos\phi \ \ \ &0 \\ &0 \ \ \ &0 \ \ \ &1 \end{array} \right]##...
  16. P

    Second Newton's law in rotation with pulley.

    Homework Statement The rope doesn't slide on the pulley, it's mass is negligible and it doesn't stretch .The pulley's moment of inertia is 0.00300 kg * m^2 with a radius of 10 cm. As the first mass goes down the rope's friction generates a moment of force of 0.150 N*m opposed to the angular...
  17. C

    Anti Rotation in Nut with low torque to start with

    Hi, i'm hoping to get a bit of assistance with stopping a nut from coming un-done if possible. I have an application using a load cell which is being inserted into metal rod, and then pulled under tension. The load cell is inserted into a hole drilled in the rod and screwed in at the bottom...
  18. Hoophy

    Possible webpage title: Understanding Multiple Axes of Rotation in Objects

    So I am having trouble with this one, I was wondering if an object could have more than one axis of rotation. More than one axis of rotation goes against what I think is possible until I thought about a coin, at which point I was stumped, if the coin was rotating in the way a coin rotates when...
  19. karush

    MHB W9.3.8 volume by rotation

    http://mathhelpboards.com/attachment.php?attachmentid=5579&stc=1 W9.3.8 Let $S$ be the region of the xy-plane bounded above by the curve $x^{3} y = 64$ below by the line $y = 1$, on the left by the line $x = 2$, and on the right by the line $x = 4$. Find the volume of the solid obtained by...
  20. RoboNerd

    Ratio of angular speed with conservation of energy

    Homework Statement A ball rolls down an incline plane without slipping. What is the ratio of its angular velocity at h/3 to its angular velocity at 2h/3? 1) 1:2 2) 1:sqrt(2) 3) 1:1 4) sqrt(2):1 5) 2:1 Homework Equations Conservation of energy with provisions for rotational and...
  21. RoboNerd

    Calculating Moment of Inertia for Rotating Objects: A Kinetic Energy Problem

    Homework Statement What is the moment of inertia of a spinning object of radius 0.5 m and mass 6 kg moving at 5 m/s, if it has a kinetic energy of 100 J? 1) 1 kgm22) 2 kgm23) 4 kgm24) 8 kgm25) 20 kgm2 Homework Equations K.E. = Kinetic energy of rotation + kinetic energy of...
  22. O

    Pure rotation under a point force and a distributed friction

    Hi guys, I was wondering if it is possible to have a pure planar rotation of a rectangular-prism shaped rigid body on a planar surface when it is subjected to a planar point force at the tip. Is there any range for the point force such that it can not break the static friction force (so no...
  23. K

    Schools Faraday rotation experiment for a high school student?

    Is it possible to replicate the Faraday rotation experiment for a high school junior? I am in honors physics (IB) and have been taught about waves, electromagnetism, energy transfers, etc. My physics teacher will guide me if I choose to do this. Is the experiment too ambitious?
  24. A

    Rotation of complex number

    Given A(2√3,1) in R^2 , rotate OA by 30° in clockwise direction and stretch the resulting vector by a factor of 6 to OB. Determine the coordinates of B in surd form using complex number technique. i try to rewrite in Euler's form and I found the modulus was √13 but the argument could not be...
  25. H

    I Understanding Wiki's Milky Way Galaxy rotation chart

    I was reading the wikipedia entry for Dark matter halo here: https://en.wikipedia.org/wiki/Dark_matter_halo And they have this graph for the Milky Way galaxy rotation curve: "Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the galactic center. Horizontal...
  26. J

    How does the rotation of a diver in the air conserve angular momentum?

    Homework Statement I am doing a report or physics homework where I have to talk about the rotation of an Olympic high diver and am slightly confused as to how it all works. I have a few questions which would help clarify. 1) So I know that in the air, angular momentum is conserved as in the...
  27. M

    Ansys Maxwell mechanical rotation problem

    Hie all. I want to implement an electromechanical system in maxwell. According to its sample projects,in order to define rotational movement, I should define a "Band" object that encloses all rotating parts. The problem is that in my problem the Band object can't be a non-hollow cylinder. I mean...
  28. D

    Angular Velocity and Acceleration

    Homework Statement If a bike wheel rotates 9.4 times while slowing down to a stop from an initial angular velocity of 8.1 rad/s, what is the magnitude of the angular acceleration in rad/s/s Homework Equations α = at / r α = ω / t α = Θ / t^2 ω = Θ / t ω = v / r Θ = ω t + 0.5 α t^2 v final = v...
  29. S

    Smooth rolling motion - conservation of energy?

    This isn't about a specific physics problem, but rather a question: Given I have a ball or cylinder rolling smoothly along some path, is it generally true that mechanical energy is conserved? I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##? I have been able to...
  30. i_hate_math

    Question on Moment of Inertia/Rotational Inertia

    Homework Statement In the figure, a wheel of radius 0.42 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.7 kg box that slides on a frictionless surface inclined at angle θ = 28 owith the horizontal. The box accelerates down the...
  31. D

    Angular Velocity and Acceleration

    Homework Statement A car is traveling at 27.8 m/s, it undergoes a negative acceleration of 2.6 m/s/s when the brakes are applied. How many revolutions will the tires go through before the car comes to a stop if the wheels each have a radius of 1.0 m? Homework Equations α = at / r...
  32. H

    Example of torque-free rotation with a fixed point

    What is an example of a rigid body rotating when one point is fixed and there are no net applied torques? And the fixed point is not the center of mass. I considered a cone rolling without slipping on a flat plane is such an example; the apex is the fixed point, but is there a net applied...
  33. S

    Angular acceleration in rigid body rotation due to a torque

    For the rotation of a rigid body about a fixed axis z the following holds. $$\vec{\tau_z}=\frac{d\vec{L_z}}{dt}= I_z \vec{\alpha} \tag{1}$$ Where \vec{\tau_z} is the component parallel to the axis z of a torque \vec{\tau} exerted in the body; \vec{L_z} is the component parallel to the rotation...
  34. M

    MHB Applying rotation matrix to make inclined plane flat again

    I want to rotate an inclined plane to achieve a flat surface. I think I can use the Euler angles to perform this operation. Using following data: and following rotation matrix I think you can make the plane flat by following rotations: 1: rotation around x-axis by 45° 2: rotation around...
  35. A

    Sphere rolling with slipping on a movable platform

    Homework Statement A sphere (of radius r and mass m) rotating with angular velocity ω0 is lowered onto the edge of a floating platform of length L and mass M. The platform can move freely on water. The platform is rough and the sphere rolls all the way from one edge to the other edge of the...
  36. P

    Proving that net torque isn't reliant on point of rotation.

    Homework Statement So we have a horizontal bar. Distance = r Forces = F All numbers remain constant with the exception of the distance, denoted as r(set)() Length of bar = 1m F1 = 10N r1-1 = 0m r2-1 = .25m (behind the point of rotation) F2 = 5N r1-2 = 0.5m...
  37. S

    Component of angular momentum perpendicular to rotation axis

    Homework Statement Consider the rigid body in the picture, rotating about a fixed axis z not passing through a principal axis of inertia, with an angular velocity \Omega that can vary in magnitude but not in direction. Find the angular momentum vector and its component parallel to z axis (...
  38. S

    Component of angular momentum perpendicular to rotation axis

    Consider the rotation of a rigid body about a fixed axis z, not passing through a principal axis of inertia of the body. The angular momentum \vec{L} has a parallel component to the z axis (called \vec{L_z}) and a component perpendicular to it (called \vec{L_n}). I have some doubts on...
  39. S

    Rotation of a block when not in equilibrium

    Homework Statement Consider a block placed on a surface, in two different configuration, a and b. Explain the condition for which the mass is in equilibrium and describe qualitatively the rotation it follows when it falls. Homework Equations Center of mass theorem \sum F = M a_{cm} The...
  40. cidadao

    Control the rotation of several discs along the same axis

    Hi everyone, I have an engineering background, I'm an EE, but I know almost nothing about mechanics and that's why I'm writing here. This is the challenge: how to control the rotation of multiple discs along the same axis? Assume you have a sliced cylinder. The ideal scenario would be to...
  41. Ben Wilson

    I What are the necessary trig functions for finding the rotation formula?

    I have a function of a 3 vector, i.e. f(+x,+y,+z) [ or for conveniance f=+++] this function is repeated 4 times where: f1 = + + + f2 = + - + f3 = - - + f4 = - + + I need a formula where i have a different vector for each function in a summation, to obtain the superposition of all 4...
  42. S

    Torque on rigid body when angular momentum is not constant

    I 'd like to clarify some doubts about the rotational motion around a fixed axis of a rigid body, in the case the angular momentum vector \vec {L} is not parallel to the angular velocity \vec {\omega} . In particular, consider a horizontal barbell with two equal masses m , forced to rotate...
  43. A

    I What are the irreducible representations of point groups and how do I find them?

    As part of physical chemistry I am reading up group theory for molecular symmetries. I realize the way chemistry textbooks treat this must be very different from what mathematicians do. So I want to know how I take a point group, find the matrix operations and get the character table.For an C2...
  44. Josephthe2

    Calculating deflection with rotation about center support

    I am preparing for a qualifying exam for my PhD program and am looking at some of the old tests from previous years (as supplied by the school for study/prep material). I have come across a deflection problem that has me stumped, and I might just be overthinking it. The problem:
  45. S

    Rubber on a rotating disk (angular velocity, forces)

    Homework Statement We place a rubber on the edge of a rotating disk. What forces act on the rubber? At what angular velocity, why and in what direction will the rubber fly off the disk? Homework Equations http://images.tutorvista.com/cms/formulaimages/83/angular-speed-formula111.PNG The...
  46. RicardoMP

    Rotating Cone and instantaneous axis of rotation

    Homework Statement Hi! I'm trying to solve a simple problem of mechanics, but I'm getting the wrong results and I suppose I don't yet grasp the concept of instantaneous axis of rotation very well. So, a cone (see attached picture) is rolling without slipping on a plane. Vp is point P linear...
  47. C

    MHB Math Problem: Rotation on z Axis

    I currently have a math problem that i am so thoroughly stuck on that my brain is coming out of my ears. I am given z1 θ = 600 and R10 = [2 -2 -1] [1 2 -2]...
  48. FruitNinja

    ORBIT: change in orbital distance

    Homework Statement we know the mass of the moon, Mm, and the Earth's, Me, and also the initial distance between their centers as the moon orbits the earth, Rem. Now if the earth’s angular velocity about its own axis is slowing down from a initial given angular velocity, ωi to a final angular...
  49. V

    Is Angular Momentum Conserved in Circular Motion?

    Homework Statement A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension : (1) angular momentum changes in direction but not...
  50. A

    Calculation of Kinetic Energy in Rotation Motion

    Homework Statement Respected Physics Gurus/experts...! I am confused in the application of Kinetic energy Expression, i.e, KE = (1/2)MVCM2+(1/2)ICMω2 I had been trying out this question actually(it's pretty simple though:-p)...--- "A rigid body is made of three identical thin rods each of...
Back
Top