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. U

    Understanding Energy and Frequency in Rotation Spectra

    I don't really understand the explanation given in Binney's text about: Hamiltonian is given by: H = \frac{\hbar^2}{2} \left( \frac{J_x^2}{I_x} + \frac{J_y^2}{I_y} + \frac{J_z^2}{I_z} \right) Orient axes such that ##I_x = I_y = I##. H = \frac{\hbar^2}{2} \left( \frac{J^2}{I} +...
  2. M

    Calculating Solar Rotation Using Sunspot Observations

    Homework Statement Calculating solar of the sun through observing sunspots. We are given a series of photos of the sun over a period of time where we can see sun spots. I am assuming the way to calculate would be to work out the longitudinal angles of the sun spots in the different photos and...
  3. anorlunda

    Planes of Rotation in Solar System & Beyond

    I'm not sure if this belongs in Astronomy or Astrophysics. Todays APOD featured the rotation of the sun about its own axis. It seems to me that the axis of rotation of the sun should be aligned with the axis of rotation of the plane of rotation of the planets, i.e. the ecliptic, or more...
  4. Y

    Simultaneity, Rotation & Gravity: Agree?

    We have had a number of threads on how to synchronise clocks around a rotating ring. One method of doing this is to start all the clocks on the ring via a signal from the centre of the ring. This method has the advantage of being transitive, but has the disadvantage that the local one-way speed...
  5. J

    Why is a non-rotating object moving in a circle impossible?

    Why do celestial bodies follow different laws of physics than terrestrial bodies? A non-rotating object has a point on its axis, or axle, continually aligned with a point on the object. An axis is virtual, or imaginary; an axle is real and we live in a real physical world. In a real physical...
  6. M

    Nuclear Rotation: Electrons & Nucleus Vibration in Atom

    we know that an electron rotates about its own axis.similarly does the electron too rotates about its own axis? and does nucleus and electron vibrate in an atom?
  7. Q

    Does the rotation of an electron have any meaning?

    Does the "rotation" of an electron have any meaning? Not sure if this is the right subforum, but thinking of this was rather head-ache inducing. Is there any sensible meaning to claiming that an electron rotates 360 degrees? Intuitively I would initially say yes, but on second thought I would...
  8. V

    Conditional rotation in the bloch sphere with a 2-qubit system

    Homework Statement The problem is as follows. I have two spins, m_S and m_I. The first spin can either be \uparrow or \downarrow , and the second spin can be -1, 0 or 1. Now, I envision the situation as the first spin being on the bloch sphere, with up up to and down at the bottom. What I...
  9. Eagle9

    Rotation of DNA in electric field

    As known the DNA molecule has got negative electric charge. Imagine that linear (almost like a straight arrow) DNA is placed in water solution and we turn the electric field on. I would like to know if the DNA molecules can orientate/rotate so that they to stay along the field lines of the...
  10. J

    Rotation relative to an inertial frame

    Earth has a huge angular velocity regarding its rotation. Now let's imagine that the Earth has the velocity of 400 km/s relative to some inertial frame. What will be the velocity of Earth when we take the rotation into account combined with inertial motion? How do the 2 combine? Thanks in...
  11. C

    Expressing general rotation in terms of tensors

    Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...
  12. Z

    Deducir la Matriz de Rotación 2D y Encontrar Ayuda

    I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish). I don't understand the second line. How does he separate the matrix in two different parts? Thanks for your time.
  13. C

    MHB Rotation around a curve. Find the Volume.

    I am thinking about how to find the volume rotate around its function.Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volumeThank you CBARKER1
  14. A

    Axis of Rotation: Rotate About Other Axes?

    Does a body rotating about an axis also rotate about any other axis? Eg. Cars on a racetrack may be rotating about a vertical axis passing through the centre of the track but can they also be considered to be rotating about a vertical axis passing through the spectators' stand?
  15. J

    One way rotation into oscillating rotation, how can I do this?

    I know very little about mechanical systems, but what kind of small simple gear system can do this; I have a motor, it turns one way, I guess it would turn a spiral bevel, but it only goes into one direction since the motor turns continuously in one direction, what mechanical solution allows...
  16. C

    What is the surface area when a curve is rotated about the x-axis?

    Homework Statement Obtain the surface area when the curve y=ex, 0≤x≤1, is rotated about the x-axis Homework Equations Surface Area = 2∏a∫b x√(1+(dy/dx)2)dx The Attempt at a Solution I started with the the equation, Surface Area = 2∏0∫1 x√(1+e2x)dx. However, whichever way I try to...
  17. J

    Rotation Equations for 2 Angles: Combining Relationships for Easy Calculation

    Using http://www.mymathforum.com/download/file.php?id=6171 and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix} r'\\ z'\\ \end{bmatrix} = \begin{bmatrix} cos(\phi) & sin(\phi)\\ -sin(\phi) & cos(\phi)\\ \end{bmatrix} \begin{bmatrix} r\\ z\\ \end{bmatrix} and...
  18. N

    Calculating Average Velocity and Acceleration of the Singapore Flyer

    Homework Statement The Singapore Flyer is te world's largest Ferris wheel. It's diameter is 150m and it rotates once every 30 min. a) Find the Magnitude of the average velocity b) Find the average acceleration at the wheel's rim. The Attempt at a Solution a) |v→| = Δs/Δt=75m.2π/30mins =...
  19. Razorback-PT

    Artificial Gravity through Rotation BUT on a vacuum

    Hi everyone, here's the situation: Everyone knows that you can simulate artificial gravity by rotating a space ship. Usually these scenarios include an atmosphere with regular air inside. I know that the inclusion of air has an influence on the effects inside by way of friction. How different...
  20. E

    Expression of fields in Faraday rotation

    Hello! Talking about propagation of an electro-magnetic field in a non-isotropic medium, I've got some troubles with the expression in object, used to show the Faraday rotation of the polarization of a field. Homework Statement An electro-magnetic field enters a particular medium...
  21. G

    Understanding Rotational Mechanics: Finding Components of a Rotated Unit Vector

    Consider two cartesian coordinate system xyz and x` y` z` that initally concide. The x` y` z` undergoes three successive counterclockwise 45 rotations about the following axes: first, about the fixed z-axis;second, about its own x`-axis( which has been now rotated); finally, about its own...
  22. U

    How to Express the Angle of Rotation for a Rotated Electric Field

    Homework Statement Suppose an E-field is rotated by angle ø2. Express ø2 in terms of: Homework Equations The Attempt at a Solution I used the rotation matrix, and compared LHS and RHS but it led to nowhere: E'= RE \left ( \begin{array}{cc} E_1' sin (ky-ωt+ø_2) \\ 0 \\ E_2' cos...
  23. T

    Stress tensor transformation and coordinate system rotation

    Homework Statement Hi, I am not sure if this is the right place for my question but here goes! The stress tensor in the Si coordinate system is given below: σ’ij = {{-500, 0, 30}, {0, -400, 0}, {30, 0, 200}} MPa Calculate the stress tensor in the L coordinate system if: cos-1a33=45°, and...
  24. andyrk

    Understanding the Concept of Axis of Rotation: Definition and Explanation

    Homework Statement This is more of a conceptual doubt. Why does the axis being called as the axis of rotation of a rolling body have to be at rest with respect to some frame of reference? What is the definition of axis of rotation? When is an axis called an axis of rotation?
  25. K

    Does rotation of rigid body need a couple or only 1 force is sufficien

    Hi all, Suppose we go in space where no gravity and friction exists. If there is a bar, in say - horizontal plane and we apply a force at one end of the bar, in this plane and perpendicular to the bar. Will that bar rotate and translate or it will only undergo pure translational motion...
  26. Y

    Practical measurements of rotation in the Kerr metric

    In another thread WannabeNewton mentioned: and gave this reference: Until WBN mentioned it, I had never given any thought to the difference between these methods of measuring rotation, so I would like to explore those ideas further here, particularly in relation to the Kerr metric. Consider...
  27. I

    Could an eliptical galaxy exist with an axis of rotation?

    I was wondering if a galaxy could be perfectly orbiting to create a sort of axis of rotation, with a period being like 50 million years, or is it impossible because of some property that elliptical galaxies have? If it is possible, what is the probability that it exists in our observable...
  28. B

    What is the Formula for Acceleration in Rotation?

    Hi there, I am confused. I want to work out the acceleration that a body placed on a wheel of radius 10 mm going at a frequency of 3Hz would experience in the x y and z axis. The equations for rotation don't make this clear. They just give me one basic equation for acceleration Can you...
  29. T

    How Much Energy Is Lost When a Sledgehammer Hits a Stationary Merry-Go-Round?

    Homework Statement A merry-go-round is sitting in a playground. It is free to rotate, but is currently stationary. You can model it as a uniform disk of mass 220 kg and radius 100 cm (consider the metal poles to have a negligible mass compared to the merry-go-round). The poles near the edge...
  30. W

    On the clockwise rotation of the reflection coefficient with frequency

    It is well known that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must appointed that...
  31. R

    Rotational Inertia about Rotation Axis Through COM

    Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...
  32. J

    MHB Matrix transform- about origin, then angular rotation

    The problem asks to find the standard matrix for the composition of these two linear operations on R2. - A reflection about the line y=x, followed by a rotation counterclockwise of 60o. This is how I proceeded. y=x $\begin{bmatrix}0&1\\1&0 \end{bmatrix}$ counter clockwise 60degs...
  33. NATURE.M

    Conservation of Energy with Rotation

    Homework Statement A small circular object with mass m and radius r has a moment of inertia given by I = cmr^2. The object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 2.5 m that launches the object vertically. The object starts from a...
  34. C

    Show that +1 is an eigenvalue of an odd-dimensional rotation matrix.

    Homework Statement The probelm is to show, that a rotation matrix R, in a odd-dimensional vector space, leaves unchanged the vectors of at least an one-dimensional subspace. Homework Equations This reduces to proving that 1 is an eigenvalue of Rnxn if n is odd. I know that a rotational...
  35. F

    How do I measure the synodic rotation period using sunspots?

    Ok so I have a project and I have to measure the sidereal synodic rotation period of the sun using sun spots. I have included a diagram of what to do. but I will explain it too. you take 5 images with a common sunspot and track it's movement on those 5 days (on the diagram, the sunspot is...
  36. M

    Archived Rotation with String Slipping & Not Slipping

    Homework Statement Block's 1 (460g) & 2 (500g) are mounted on a horizontal axle of negligible friction (R = 5.00cm). When release from rest, block 2 falls 75.0 cm in 5.00s without the cord slipping on the pulley. a) What is magnitude of acceleration of blocks? b) Tension of T2 c) Tension...
  37. G

    Angular rotation of a wheel that slips

    A wheel spinning clockwise on its axis at with angular velocity ω0 drops to the horizontal ground. It initially has no center-of-mass velocity. The coefficient of kinetic friction between the ground and the barrel is µ. The radius of the wheel is R, and it is a solid disc of mass M. Express your...
  38. W

    Angular velocity when mass is added at center of rotation

    Homework Statement A guy is spinning on a chair with his hands at rest on his lap. As he is spinning, a large mass drops into his hands/lap. Does the guy continue spinning at the same rate, a slower rate, or a faster rate? This video demonstrates what happens when the guy drops mass...
  39. J

    What Is the Maximum Speed of a Hollow Shaft Given Specific Shear Stress Limits?

    Homework Statement A hollow shaft has an internal diameter of 72 mm and wall thickness of 24mm is to be used to transmit a power of 90 kW. what would be the maximum speed of shaft rotation if the shear stress must not exceed 150 MPa ?? Homework Equations...
  40. W

    Newton's Second Law and Rotation

    Homework Statement A 0.70-kg disk with a rotational inertia given by MR^2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip, then as the mass falls and the...
  41. R

    How Can I Apply a Quaternion Rotation on a Local Axis After an Initial Rotation?

    Hey, Once again, I got a question about quaternions. Say I have an initial rotation Q1. I now want to rotate Q1 on the X and then on the Y axis. BUT: The Y rotation should apply to the local Y axis which was given in Q1. The problem is: If i rotate Q1 by the X-rotation Q2, then the Y...
  42. Q

    Conservation of ang. momentum for paths reaching a rotation axis

    Hey everyone. My question is the following: if we had the trajectory of a particle eventually reaching a point of a rotation axis \vec{u} ((take that as being the z-axis for convenience) by an angle s , would Noethers Theorem still give a conserved quantity? More specifically (let me...
  43. Avi Nandi

    Yo-Yo Homework: Find Average Force on String

    Homework Statement A Yo-Yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR^{2}/2 and the thickness of the string can be neglected. The Yo-Yo is released from rest. The center of the Yo-Yo descends distance h before the string is fully...
  44. Avi Nandi

    How Do You Relate the Accelerations in a Disk and Pulley System?

    Homework Statement A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley and mass m is suspended from the other end. Assume that the disk drops vertically. a. relate the accelerations of mass m and disk ,a and A, respectively to...
  45. S

    Rotation of Earth relative to a distant star

    Homework Statement On the Earth the Sun appears to rise and set about 365 times in one year. During the same 365 days, how many times does the Earth rotate on its axis relative to a distant star (a star beyond the Sun and out of our solar system)? Homework Equations The Attempt...
  46. L

    K of Rotation vs Rotational Momentum

    Homework Statement A space station has the form of a hoop of radius R = 15 m, with mass M = 1000 kg. Initially its center of mass is not moving, but it is spinning with angular speed ωi = 4 rad/s. A small package of mass m = 22 kg is thrown at high velocity by a spring-loaded gun at an angle θ...
  47. S

    Why is there more than 1 value for load W where there is no rotation?

    Homework Statement The problem along with its solution is attached as TheProblemAndSolution.jpg. Here is the textual part of the attached image: “In Fig. 1 a 20 ft-frame PQ is supported at two points L and M, 6 ft and 4 ft respectively from the edges. If a 300 lb load is attached to edge...
  48. AakashPandita

    Rigid Body Rotation: Axis Points Stationary?

    In rotation motion do points through which the axis passes also rotate or are they stationary?
  49. K

    Conservation of Energy applied to A system with Rotation and Translati

    Problem Statement: The system consists of a 20-lb disk A, 4lb slender rod BC, and a 1-lb smooth collar C. If the disk rolls without slipping, determine the velocity of the collar at the instant theta=30 degrees. The system is released from rest when theta= 45 degrees. Above I attached a photo...
  50. AakashPandita

    Relation between r ,ω and θ for rotation around fixed axis.

    relation between r ,ω and θ for rotation around fixed axis. \frac{d\textbf {r}}{dt} = \textbf {ω} \frac{dθ}{dt} = ω \lvert\frac{d\textbf {r}}{dt}\rvert = \frac{dθ}{dt} bold means vector. Is this right?
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