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

    Rotating wind tunnel

    Why this wind tunnel rotate?
  2. R

    Question about torsional shear stress

    If a circular rod is allowed to rotate freely and a moment (M) is applied to one end of the rod. A moment acting in the opposite direction, with magnitude (M/3), is applied to the other end of the rod. What is the maximum moment in the rod that would be used to calculate the maximum torsional...
  3. K

    A Rotations on the Bloch sphere

    Hello! I am curious about how different rotations on the Bloch sphere are done in practice. For example, assuming we start in the lower energy state of the z-axis (call it |0>), a resonant rotation on the Bloch sphere by ##\pi/2## around the x-axis will take you to ##\frac{|0>-i|1>}{\sqrt{2}}##...
  4. S

    I Einstein - de Haas Effect

    This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod. Is there a classical thought...
  5. pedrovisk

    I Newton's second law for rotations

    EDIT: I forgot about Second Newton's law for rotations and this led to a mistake. Anyway, thanks for the people who answered it and remembered me about law of inertia. I was thinking about how to "make" things to move without rotate the object, then i tried to calculate the minimum force to...
  6. K

    I Anomalous contribution to galactic rotation curves due to stochastic s

    Anomalous contribution to galactic rotation curves due to stochastic spacetime Jonathan Oppenheim, Andrea Russo Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Theory (hep-th) another way to explain MOND in...
  7. P

    I Coriolis effect and the acceleration experienced in a rotating frame

    Is the reason behind coriolis acceleration is that as you move far from the centre of a rotating frame the tangential velocity increases?
  8. S

    Spinning a Bucket to measure gravity with the parabolic surface of the water

    I did (A) by balancing force on point p (in the figure). I found slope , tanθ = (w^2)x/g. I dont know what to do next. Pls help
  9. T

    I Velocity transformation between frames rotating relative to one another

    Good evening, I was wondering about how velocities transform when two successive rotations are applied. In other words, how is the transformation law between two frames which are rotating relative to another. Lets say some particle is moving with a velocity v in an inertial frame S. If we go...
  10. cianfa72

    I Is the Belt Trick Possible with Continuous Deformation in 3D Rotation Space?

    Hi, in the following video at 15:15 the twist of ##4\pi## along the ##x## red axis is "untwisted" through a continuous deformation of the path on the sphere 3D rotations space. My concern is the following: keeping fixed the orientation in space of the start and the end of the belt, it seems...
  11. Miles Behind

    "2001 A Space Odyssey" space station: Rotating or contra-rotating?

    I assume that a space station like portrayed in 2001 A Space Odyssey could either be fixed in rotation, or contra-rotating. Is there an advantage of one over the other?
  12. T

    I Is angular momentum perpendicular to fixed axis of rotation constant?

    So my book states torques perpendicular to the fixed axis of rotation tend to tilt the axis , however we assume sufficient restraints exist so these torques are simply ignored. It follows that angular momentum perpendicular to axis remians constant. (See image ) My question is that if a rod is...
  13. D

    B Why does a coin take 2 full rotations around another coin?

    This one baffles me, I still can’t get my head around it (no pun intended). Take 2 US quarters. Put them in contact side by side. Without slippage, roll one quarter around the circumference of the other until it returns to the starting point. It requires rotating the moving quarter 2 full times...
  14. apcosta

    What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?

    TL;DR Summary: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis? a) Consider two rigid bodies that have a relative motion characterized by a rotation and a translation with respect to the same axis (like a bolt and a...
  15. Codezero

    I Modeling Asteroid Rotation Using Quaternions: Seeking Guidance on Init

    Hello everyone, I am an International Baccalaureate (IB) student working on my extended essay, which is a mandated 4,000-word research paper. My chosen topic is Quaternions, a mathematical concept I find highly intriguing. The primary aim of my paper is to model the rotation of an asteroid...
  16. U

    I Do objects always rotate around center of mass?

    For example if airplane or boat move rudder, do they always rotate around center of mass? Or exist specific conditions when object rotate around center of mass?
  17. Sciencemaster

    B How to find the infinitesimal coordinate transform along a hyperbola?

    I've been told that the infinitesimal change in coordinates x and y as you rotate along a hyperbola that fits the equation b(dy)^2-a(dx)^2=r takes the form δx=bwy and δy=awx, where w is a function of the angle of rotation (I'm pretty sure it's something like sinh(theta) but it wasn't clarified...
  18. S

    Translation and rotation of quadric surface

    I want to ask how ##Ax^2+By^2+Cz^2+Dxy+Eyz+Fxz+Gx+Hy+Iz+J=0## can be brought to ##Ax^2+By^2+Cz^2+J=0## or ##Ax^2+By^2+Iz=0## using translation and rotation. There is no explanation in the book. What kind of translation and rotation are needed? Thanks
  19. yashboi123

    The velocity of a satellite rotating around the Earth

    Not sure what r would be in this scenario. I tried adding the radius of the earth to the altitude but that wasn't correct either.
  20. xkcda

    Combined Rotation and Translation of a Rectangular Plate

    I tried to solve it using the work-energy theorem.The work done to make it stand on its one vertex should be equal to the change in its kinetic energy. I am confused what will be the value of radius here? I have seen formula of kinetic energy for rolling of circular objects.Can anyone please...
  21. Mohmmad Maaitah

    Net torque on a cylinder by multiple applied forces

    Why did he give torque number 4 zero? It's not touching the axis of rotation and the angle 90 degrees between them. I get this: ##\tau## = 1 - 0.8 - 0.4 + 0.4 = 0.2 (C.C.W)
  22. I

    Evidence that the Earth rotates in Space

    I was wondering if the Foucault pendulum experience was an evidence that earth does rotate on itself.
  23. D

    Translating reciprocating motion into a 45 degree rotation

    I'm trying to design a mechanism to translate reciprocating motion into a 45 degree rotation. Here's the idea: A pin will push against the part marked in red, causing part of the desired rotation. Then, when the pin is pulled back, its interaction with the blue part will complete a 45 degree...
  24. S

    B Homopolar motor rotation in Vacuum

    Hi again, I've found interesting video. Roller homopolar motor : Roller Motor Do you think the motor from 1:08 min Will self rotate in Vacuum/Space (No other forces : Gravitational or Other type.) Thank you in advance.
  25. P

    I Finding the Axis of Rotation with Given CoG and Force Point

    [Mentor Note: See post #10 below for an updated problem statement using LaTeX and with a better drawing] what i want is to find the axis of rotation when the centre of gravity and point on which external force is acting is given along with the magnitude and direction of force. In the example...
  26. Like Tony Stark

    Rotation of spherical harmonics

    I tried using the Wigner matrices: $$\sum_{m'=-2}^{2} {d^{(2)}}_{1m'} Y_{2; m'}={d^{(2)}}_{1 -2} Y_{2; -2} + {d^{(2)}}_{1 -1} Y_{2; -1} + ...= -\frac{1-\cos(\beta)}{2} \sin(\beta) \sqrt{\frac{15}{32 \pi}} \sin^2(\theta) e^{-i \phi} + ...$$ where $$\beta=\frac{\pi}{4}$$. But I don't know if...
  27. Trysse

    B Invariant under rotation: Banal, obvious, or noteworthy?

    Given a cartesian coordinate system with a fixed point of origin and three axes, it is a fact, that the coordinates of a point P change, when the coordinate system is rotated around its point of origin. The distance between the origin and point P is of course unaffected by such a rotation. What...
  28. HauTo

    Help to calculate rotation speed of rotor

    Hello everyone, i have a question, how to find wind turbine rotor rotation speed based on freewheel rotation speed of rotor (RPM)(torque = 0)? Thanks for your attention.
  29. K

    I Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

    Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves this paper A. N. Lasenby, M. P. Hobson, W. E. V. Barker, "Gravitomagnetism and galaxy rotation curves: a cautionary tale" arXiv:2303.06115 (March 10, 2023). Directly comments on Deur's theory of self-interaction...
  30. bakerjay

    A Data on galaxy rotation curves vs visible matter

    I'm after some raw data for testing theories of dark matter in galaxies. Basically what I want is table showing visible mass vs total mass within different radii (or, observed rotational velocity vs expected rotational velocity without dark matter). Plus error percentages. And ideally, for...
  31. G

    I What Could Cause the Earth's Rotation to Dramatically Slow Down?

    Hi everyone, I’ve been thinking about this for a while and have done a bit of research but can’t seem to get a straight answer. Aside from collision with another object in space, is there anything that could cause the Earth’s rotation to dramatically slow down? If a sufficiently massive object...
  32. chris25

    Rotation and torque about an accelerating point

    A solution was provided: We take torques about point B. Note that τ = MgL/2 = Iα so α = (3g)/2L. Everything from here is straightforward. I don't understand why in this step, you can take torque about B without accounting for a fictitious force due to the acceleration of the Rod.Thanks for...
  33. LadiSilverfox

    Questions about a habitable second moon

    Good afternoon, I am working on writing a story that is set on a habitable second Moon. I suppose I could easily say it's a mild planet that splits into three main seasons and make up some story about how the first Moon appears every so often for a month of phases and then vanishes. As a...
  34. J

    B Rotation is absolute, linear motion is relative?

    Can you explain with example what mean rotation is absolute and linear motion is relative?
  35. A

    I Measuring the rotation curve of galaxies

    What should I learn to make astrophysical measurements from open data? Suppose I want to measure the rotation speed of galaxies to generate galactic rotation curves like these: https://en.wikipedia.org/wiki/Galaxy_rotation_curve What should I do and what should I learn? I think I should get...
  36. FEAnalyst

    Gear teeth force from the rotation angle

    Hi, in books about machine design fundamentals, one may easily find the formulas for forces acting on the teeth of paired spur gears. They require torque as input. For example, for the tangential force: $$F=\frac{2T}{d}$$ where: ##T## - torque applied to the driven gear, ##d## - pitch diameter...
  37. S

    Spin-1 particle states as seen by different observers: Wigner rotation

    Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...
  38. C

    I Steering a Car: Investigating the Forces of Rotation

    In a car we turn the wheels to steer. The wheels however are spinning about their axis of rotation when the car is in motion. Does the revolving motion of the wheels cause a force that opposes trying to rotate the wheels around the other axis to steer? How much opposition is created? Here's...
  39. Ranku

    I Rotation curve and dark matter

    Do all galaxies with dark matter halo have flat rotation curve?
  40. Vladimir_Kitanov

    Rotation about a Fixed Axis

    Answer should be (c) 32,7 ##\frac{m}{s^2}## My attempt: ##\omega_{2\pi}## -> ##\omega## after 1 revolution ##\omega_{2\pi} = 0,2 * (2\pi)^2## ##\omega_{2\pi} = 7,9 \frac{rad}{s}## ##\frac {d}{dt}\omega = \alpha = 0,2*2*\theta## ##\alpha_{2\pi}## -> ##\alpha## after 1 revolution...
  41. C

    I Summing linear momentum in circular rotation

    Hello everyone! I was wondering why can't we take a rotating body and see the linear movement that each particle moves to find the 'total linear momentum,' I imagine this quantity would be conserved, and furthermore couldn't you write the total linear momentum as a function of angular velocity...
  42. F

    I Can you detect the Earth's Rotation Using a Hockey Puck on Ice?

    If you put a hockey puck on a flat Ice rink, will it move due to the Earths rotation? For example, if I make a mark and measure the distance moved with a caliper, would I notice a change?
  43. A

    I Rotation of a vector along two axes (of which one is angle-dependent)

    I have been trying to determine an expression for a unit vector in the direction of F for hours now. I think the expression is supposed to look something kind of like this, But I don't understand at all how to arrive at this expression. Any help?
  44. S

    I Partition function rotation

    Hey, I have a question about proving Saha's equation for ionizing hydrogen atoms. The formula is \frac{P_{p}}{P_{H}} = \frac{k_{B} T}{P_{e}} \left(\frac{2\pi m_{e} k_{B}T}{h^2} \right)^{\frac{3}{2}}e^{\frac{-I}{k_{B} T}} with P_{p} pressure proton's, P_{H} pressure hydrogen atoms, m_{e}...
  45. V

    Finding tension as a function of distance from the center of rotation

    I'm not too sure how to account for both the mass and the rope at once. I think the following are true for the two individually: For the mass at the end, ## T = m ω^2 L ##, following from ##a = v^2/r##and ##v=ωr##. For the rope, ##dT = ω^2 r dM##, where ##dM = λ dr## and λ is the mass per unit...
  46. Rikudo

    Tension between two rigid bodies

    Ok. So, I already worked on this problem, and get ##m_c## = 2m/3, which is correct according to the book. However, I also want to know the value of the tension (T) between rod A and B. Note: Before we start working on my modified question, I want to point out that the force exerted by the...
  47. A

    B Rotation of Galaxies: Mass vs Dark Matter?

    Is it possible that galaxies are spinning faster than expected due to a particular configuration of the moving mass and not due to dark matter?
  48. V

    Forces when car wheels "lay rubber"

    Suppose the car is moving to the right, so if the wheels roll without slipping, they are rolling clockwise. To get the wheel to slip, a counterclockwise torque would need to be applied to cause the wheel to have some angular acceleration. If the wheel was slipping, then the bottom of the wheel...
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