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. 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...
  2. 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]...
  3. 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...
  4. 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...
  5. 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...
  6. Z

    Gravitational Force/Earth Rotation Question

    The force of gravity is what makes things on the Earth rotate with it, instead of flying off. Doesn't this mean, however, that if you were to apply an upward force on something exactly equal in magnitude to the gravitational force on the object (so the net force on it is 0), it would cease to...
  7. Shailesh Pincha

    I Rotation curve of galaxy Keplerian method

    There are 2 unknowns in the formula. The time period of rotation and the mass enclosed by orbit is Star. So how could we calculate the expected time period of rotation of stars in a galaxy and thus velocity of stars.
  8. AndresPB

    Coordinate Rotation: Find Transformation Matrix for 120° Rotation

    Homework Statement [/B]Hello, I am seeking help solving the following problem: find the transformation matrix that rotates a rectangular coordinate system through an angle of 120° about an axis making equal angles with the original three coordinate axes.Homework Equations none, we need to find...
  9. F

    Rotation speed for a satellite

    Homework Statement A geostationary satellite is located at 0'N 0'E (degrees), 36000 km above a spherical Earth with radius R(earth) = 6370 km. To scan the fieldof view, the satellite rotates around its own axis(oriented parallel to the Earth's rotation axis). It records one (constant latitude)...
  10. evinda

    MHB Finding the Rotation Vector $\omega$ of a Sphere

    Hello! (Wave) A sphere with radius $10 cm$ and center $(0,0,0)$ turns around the $z$-axis with angular velocity $4$ and with such a direction that the rotation has counterclockwise direction, being seen my the positive semi-axis $z$. I want to find the rotation-vector $\omega$. Is this equal...
  11. vishnu kumar

    I Earth rotation different in hemisphere

    Why Earth rotates from West to East in southern hemisphere and East to West in northern hemisphere?? Is this true,if yes then explain please.
  12. S

    Insight/Intuition into rotations in R²

    I've been using rotation matrices for quite some time now without fully grasping them. Whenever I tried to develop an intuitive understanding of... x' = x\cos\theta - y\sin\theta \\ y' = x\sin\theta + y \cos\theta ... I failed and gave up. I've looked at numerous online texts and videos, but...
  13. T

    Rotation and vibration of 2 particle spring system

    Homework Statement Homework EquationsThe Attempt at a Solution Is it possible to solve this problem without using Hamiltonian Mechanics (just by Newtonian). My instructor expects use to solve this problem without any knowledge of any advanced classical mechanics. I tried to solve this...
  14. Mr. Rho

    Mathematica Rotation of 3D Plot using Euler angles

    So, I'm trying to plot a 3D "dipole" (an arrow with a small torus around it basically) in mathematica, and want to rotate it according to Euler angles... I use this code for the rotation matrix: rot[a, b, g] := RotationMatrix[g, {1, 0, 0}].RotationMatrix[b, {0, 1, 0}].RotationMatrix[a, {0, 0...
  15. Eric V

    Rotational Vs Linear Acceleration

    Hi guys, I'm having a debate with a mechanical engineer friend of mine, and I was wondering if you could help me solve it. I'm not much of a physicist, but honestly I think he might have this one wrong, I just can't remember my old physics classes well enough to calculate and be sure. The...
  16. B

    Physics Centripetal Force problem?

    1. At what rate a space station 200m in diameter would have to rotate to create gravity equal to 0.7 that at the surface of earth. How fast does it spin, and how long would it take to make a complete rotation? 2. a2 = v2 / 100m T = 2pi(r) / v 3. so far: 6.867m/s2 = v2 / 100m = 26.2 m/s T =...
  17. Rotation in Space - Professor Carolin Crawford

    Rotation in Space - Professor Carolin Crawford

    Public lecture on aspects of rotating astronomical objects. Covers planetary and stellar rotation, protoplanetary discs, accretion discs and galactic rotation curves. Mechanisms and observation methods.
    • Bandersnatch
    • Media item
    • astronomy rotation
    • Comments: 0
    • Category: Astronomy and Cosmology
  18. K

    Conservation of Angular Momentum; angle of rotation

    Homework Statement A block of mass m slides down a frictionless ramp from height h above the floor. At the base of the ramp it collides and sticks to the lower end of a uniform rod, length L, mass 2m, that is suspended about a pivot at point O, about which it is free to rotate. Express...
  19. S

    Why do spheres roll easier than cubes?

    I am aware that this could be the wrong section for this, but I wish to ask this here if you all don't mind. You all know how a sphere rolls along the ground easier than a cube, right? Well, how are the physics of motion involved in why a sphere rolls easier than a cube, or an irregular object?
  20. FrancescoS

    Performing Wick Rotation to get Euclidean action of scalar f

    I'm working with the signature ##(+,-,-,-)## and with a Minkowski space-stime Lagrangian ## \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi ## The Minkowski action is ## S_M = \int dt d^3x \mathcal{L}_M ## I should obtain the Euclidean action by Wick rotation. My...
  21. S

    How much could the Earth's rotation speed up?

    I've noticed there are a lot of documentaries and youtube videos about what would happen if the Earth stopped spinning. However, I would like to know what would happen if the Earth kept speeding up, what would happen if it did, and the approximate maximum rotational velocity before the Earth...
  22. S

    Venus' Synodic Year: Why Does It Take Longer Than Earth's?

    Why do venus take more number of days for one complete rotation around sun than Earth when the gravitational pull towards venus is higher than Earth ?
  23. M

    Rotations in differential geometry

    Simple and basic question(maybe not). How are rotations performed in differential geometry ? What does the rotation matrix look like in differential geometry? Let us assume we have orthogonal set of basis vectors initially. I am looking to calculate the angle between two geodesics. Can this...
  24. H

    Rotation in a cylindrical cylinder (fluid)

    Homework Statement what's the difference between zs and hc ? in the pictuire , they are both drawn from the bottom of water to the free surface ... Homework EquationsThe Attempt at a Solution [/B]
  25. P

    Ellipse Rotation: Solving with Normal Rotation Matrix

    Hello! Okay- This is a relatively simple problem, but for some reason I'm having huge difficulty with it. So I have the equation of an ellipse, x^2-6sqrt3 * xy + 7y^2 =16, which I have converted into quadratic form to get (13, -3sqrt3, -sqrt3, 7) and I need to rotate it using the normal...
  26. M

    Euler angles in latitude longitude space

    In most physics introductions Euler angles(pitch, roll, yaw) are defined with respect to Cartesian coordinate system. If I chose not to use a Cartersian coordinate system but instead use a latitude, longitude and a proprietary vertical coordinate(and no back transformations to Cartersian...
  27. S

    Rotation transformation by poisson brackets

    Homework Statement Can anybody suggest hints on how to show that x'=xcosΘ-ysinΘ, y'=xsinΘ+ycosΘ by using the infinite string of poisson brackets? Homework Equations ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+... The Attempt at a Solution Sorry, I just can’t think of any way, substituting doesn’t work.
  28. M

    Spherical vectors and rotation of axes

    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...
  29. L

    Why Do Different Definitions of Rotation Matrices Exist in Mathematics?

    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...
  30. R

    Proving Spin Coefficient Transformation for Null Rotation with l Fixed

    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
  31. Shailesh Pincha

    Galaxy centre and rotation curve

    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?
  32. G

    Understanding Rotational Acceleration and the Role of Normal Force

    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 ) ...
  33. M

    Vector Rotation About Arbitrary Axis

    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 : $$T (v_{\perp}) = \cos(\theta) v_{\perp} + \sin(\theta) w$$...
  34. A

    Difference between Rotation Inertia of Rod V.S Cylinder

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

    Rotation in Space: Rod, ISS, Yoyo Motion

    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...
  36. R

    Load rotating device - will it slide?

    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...
  37. vetgirl1990

    Finding angular acceleration of pulley attached to a mass

    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...
  38. B

    Rotation of wheel between two non-slip surfaces

    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...
  39. (Ron)^2=-1

    Rolling without slipping over a plank

    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...
  40. K

    Flat Rotation Curve Astronomy Question

    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...
  41. ognik

    MHB Exploring the 3-D Rotation Matrix with Euler Rotations and Net Angle of Rotation

    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...
  42. A

    Increasing speed by decreasing intertia?

    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...
  43. N

    How does rotation have vectors?

    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...
  44. S

    Query on the Euler Theorem for Rigid Body Rotation

    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...
  45. artriant

    Calculate Wire Tension in Zero Gravity Circle | Rotating Wire

    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...
  46. Conservation

    Understanding Rolling Without Slipping

    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...
  47. Alettix

    Angular velocity of a rod - translational KE?

    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...
  48. hackhard

    Rotation of line about rotating axis

    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...
  49. hackhard

    Rotation of a rigid body about external axis

    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...
  50. Chrono G. Xay

    Finding Optimal Axis of Rotation with Constraints

    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...
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