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. Mazin Nasralla

    Effect of Rotation on the Earth and Planetary Disk(s)

    Hello, This problem has probably been done before in different guises but I am struggling, and hoping for help. I am struggling to understand a phenomena which I am assuming is one and the same: Equatorial Bulge of the Earth Flat Plane in which the Planets rotate Protoplanetary disks are flat...
  2. J

    Translational Motion Vs. Rotational Motion

    Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's...
  3. O

    Rotation from Oscillating Axis Of Rotation

    Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin. Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move...
  4. Ookke

    Two Lorentz Boosts Causing Rotation - Measurable w/ Gyroscope?

    It seems that combining two Lorentz boosts cause rotation: https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer...
  5. freutel

    What is the speed when a disk has reached maximum extension?

    Homework Statement Two identical disks with mass m and radius r are connected via a massless wire of length L which is winded up around both disks. Disk B is connected to the ceiling and is free to rotate around its axis. Disk A is besides disk B and will fall due to the gravitational force...
  6. C

    Hubble redshift and calculation of galactic rotation curves

    I am interested in whether it is necessary to account for the effects of the Hubble Redshift in determining the rotation velocities of galaxies exhibiting keplerian motion and, in particular, whether the associated spatial expansion of the Universe is known to result in spectral shifts that...
  7. M

    Analytical continuation by contour rotation

    Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...
  8. S

    Commutator of the matrices of the rotation group

    Consider the rotation group ##SO(3)##. I know that ##R_{x}(\phi) R_{z}(\theta) - R_{z}(\theta) R_{x} (\phi)## is a commutator? But can this be called a commutator ##R_{z}(\delta \theta) R_{x}(\delta \phi) R_{z}^{-1}(\delta \theta) R_{x}^{-1} (\delta \phi)##?
  9. W

    Orthogonality from infinitesimal small rotation

    Hello buddies, Could someone please help me to understand where the second and the third equalities came from? Thanks,
  10. S

    Acceleration of object at constant velocity in rotation?

    I have some questions about acceleration that I'd like for someone to explain to me. As far as I know, acceleration depends on either change in velocity or change in direction (or both). So if I'm going 1m/s North constantly I'm not accelerating. However, what would be the acceleration if I walk...
  11. Aafia

    Crop rotation and inter planting?

    How interplanting and crop rotation helps to control the pethogenic diseases and parasitic weeds and also explain what are parasitic weeds ? What is crop rotation ? What is interplanting ? Thanks :-)
  12. minimario

    Why is the Instantaneous Speed Zero in this Rotational Motion Problem?

    Homework Statement Homework Equations ##v = r \omega ##?? The Attempt at a Solution The answer is 0...why?
  13. Z

    Translational Acceleration with No Rotation

    Hello Everyone, Let us think about a rod whose length is L and end points are A and B. The road is parallel to the ground therefore the weight of the rod is perpendicular to the line between A and B. The weight of the rod is F and two forces with the magnitude of F are exerted on both ends and...
  14. C

    Wheels linked by belts: find the one with the least rate of rotation

    Homework Statement See Diagram Homework Equations See Diagram The Attempt at a Solution I have been looking for hours for the correct formula but do not know what to use or where to start. If you can point me in the direction of the right formula if one is needed, and I would be very...
  15. mlipscombmtl

    I'm wondering about air travel and the rotation of the earth

    It would seem to me that if you fly from point a to point b following the rotation of the earth, you'd have to go faster than this rotation to move forward. For example, if the Earth spins at 1,040/mph, then wouldn't a plane have to go faster than this just to escape the spin of the earth? I get...
  16. T

    Understanding Rotation Matrices: A Journey of Mistakes and Lessons Learned

    I'm working through Meisner Thorne and Wheeler (MTW), but have been temporarily sidetracked by a problem with rotation matrices. I've worked through the maths and produced the matrices by multiplying the three individual rotation matrices, (no problem there) but I have been trying to work out...
  17. B

    Calculating Rotational Volume for Enclosed Area by Revolution Around Y-Axis

    Homework Statement An area is enclosed by y=1/x, the positive x-axis and x=1 and x=2. Determine the volume of the rotational body that is created around the y-axis. Homework Equations The formula is pi*integrate from d to c for x^2 dx. The Attempt at a Solution Take a look here...
  18. B

    Rotation around an axis

    Homework Statement The curve y=1/x and the line y=2.5-x enclose an area together. Determine the exact volume of the rotating body that is formed when this field rotates about a) The x-axis and b) The y-axis Homework Equations The formula for rotation around the x-axis is pi*integrate from b to...
  19. moenste

    Mechanics. Circular motion and rotation

    Homework Statement An aeroplane loops the loop in a vertical circle of radius 200 m, with a speed of 40 m s^-1 at the top of the loop. The pilot has a mass of 80 kg. What is the tention in the strap holding him into his seat when he is at the top of the loop? Answer: 160 N. Homework...
  20. R

    New coordinates from the rotation of an axis

    Homework Statement There is a point P(x,y) and now I rotate the x-y axis, say by θ degree. What will be the coordinates of P from this new axis. I have google but found formula for new coordinates when the points is rotated by θ degree. So I tried my own. So is there other simplified formula...
  21. Quantioner

    The Wick rotation in position space

    The Feynman propagator is $$ G_{F}(x) = \int d^4p \, \frac{e^{-ip x}}{p^2 - m^2 + i\epsilon}. $$ I want to understand why the directions of Wick rotation in position space and momentum space are contrary. Every book I find says something like "we should keep ##xp## unchanged", but why? As we...
  22. AakashPandita

    Question on gravitation and rotation of the Earth

    Homework Statement A body is suspended on a spring balance in a ship sailing along the equator with a speed ## v' ## . If ## \omega ## is the angular speed of the Earth and ## \omega_0 ## is the scale reading when the ship is at rest , the scale reading when the ship is sailing, will be very...
  23. AdityaDev

    Finding acceleration of block connected to pulley with mass

    Homework Statement Homework Equations a=Rα The Attempt at a Solution Free body diagrams: For larger pulley, TR=Iα ⇒ T=½MRα If this pulley rotates by some amount suchat x length of rope becomes free, and if I hold the smaller pulley at rest, then this extra length of rope comes bellow the...
  24. Y

    Instantaneous axis of rotation

    Homework Statement Two hoops are fastened together as shown below. Smaller hoop mass m, and larger hoop mass 3m. The system is now placed on the table and the system is released from rest in the position shown below. There is sufficient friction between the large hoop and the table so that it...
  25. P

    How to find the total acceleration (magnitude and direction) of a rotating disk?

    Homework Statement A disk of radius 16 cm rotating around a fixed axis at its center is accelerated from rest to an angular velocity of +13rev/min in +0.27 rev. (A )Find the angular acceleration (in rad/s^2), which is assumed to be constant, during this time interval. (B) what is the total...
  26. M

    Flat galaxy rotation curves without dark matter

    I need someone with more experience in the field who has knowledge of excel to check over my work. Given the gravitational attraction between two bodies is F = (GMm)/r^2, and the centripetal force required to keep a body in orbit is F = (mv^2)/r, therefore (mv^2)/r = (GMm)/r^2 therefore...
  27. C

    Calculate Torque for 8N Forces on 0.6m Beam

    Homework Statement Two 8.0N forces act at each end of a beam of length 0.60m. The forces are parallel and act in opposite directions. The angle between the forces and the beam are 60 degrees. What is the torque of the couple exerted on the beam? 1. 2.4Nm 2. 4.2Nm 3. 4.8Nm 4. 9.6Nm Homework...
  28. S

    Scaling the parameter of the SO(2) rotation matrix

    For the distance function ##(\Delta s)^2 = (\Delta r)^2 + (r \Delta \theta)^2##, the rotation matrix is ##R(\theta) = \begin{pmatrix} cos\ \theta & - sin\ \theta \\ sin\ \theta & cos\ \theta \end{pmatrix}##. That means that for the distance function ##(\Delta s)^2 = (\Delta r)^2 +...
  29. E

    Helicopter Rotation, Torque and Angular Momentum

    The direction of the torques in the following working will be found using: \vec{\tau} = \vec{r} \times \vec{F}. When viewed from above, the counterclockwise rotation of the blades produces a torque out of the page: As the angular momentum (right-hand corkscrew rule) is also out of the page...
  30. R

    Drumstick Rebound: Physics Behind Stick Stroke & Rotation Point

    Hello, I'm trying to figure out what effect does the rotation point where you choose to hold a drumstick have on the rebound of the stroke. Drummers usually find this point by feel, or by fiding out at which rotation point the stick produces the most rebounds. I'm curious to know what are the...
  31. ognik

    Derive infinitesimal rotation operator

    Homework Statement Derive the infinitesimal rotation operator around the z-axis. Homework Equations My book gives this equation (which I follow) with epsilon the infinitesimal rotation angle: $$ \hat{R}(\epsilon) \psi(r,\theta, \phi) = \psi(r,\theta, \phi - \epsilon) $$ but I just don't get...
  32. W

    Decomposition of Rotation into Forward Motion and Turn Motion

    Hi, just curious: I was able to simulate rotation motion in Alice software , as a combination of two motions: 1)Moving forward 2)Turning left (I can choose the rate at which each of these happens , in terms of meters and revolutions respectively.) Done simultaneously, at just the right rate...
  33. V

    Precession of Mercury and period of rotation

    HI - we know that the orbit of mercury precesses (I hope I am using the right terminology here). Which basically means that the orbit seems to undergo some sort of rotation in the ecliptic plane. Does this also mean that the period of Mercury's orbit as seen from the Earth is not uniform but...
  34. H

    Earth's rotation related to atmospheric motion

    How much affect does the rotation of the Earth (such as drag friction) have on the motion of the atmosphere (if any). Respectfully, Hagar
  35. mooncrater

    Two discs' rotation question

    question - Consider the cobination of two discs(attached) , then what will be the velocity of falling disc centre as a function of h. Both discs are identical and string doesn't slip relative to disc. Relevant equations - Conservation of energy . Torque=r×F Force=ma An attempt to the question...
  36. J

    Can Increasing a Spool's Diameter Boost a Motor's RPM?

    Hi all, I have a small DC motor which turns at 20 rpm. The shaft diameter is 6mm, giving a circumference of 18.85 mm. What I want to do is get an effective rate of 30 rpm. Can I do this by simply attaching a spool or spindle to the motor output shaft with a larger diameter? If so, would it...
  37. A

    Center of rotation of a free rod

    Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM. What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation? If not, are the 3...
  38. P

    Collapsing sun, new average rotation

    Homework Statement the sun collapses to the size of the Earth (approximately 1/100 the original diameter), The current average rotation of the sun is approximately 30 days. Homework Equations what would be the new rotational period (time to spin once)? The Attempt at a Solution I know that in...
  39. F

    A question on the commutativity of finite rotations

    I was reading a section in my book discussing the commutativity of infinitesimal and finite rotations. In the book the authors try to set up a scenario to explain why finite rotations are not commutative. The following is an excerpt from the book regarding this language: "The impossibility of...
  40. H

    Rotation matrix about an arbitrary axis

    Suppose a position vector v is rotated anticlockwise at an angle ##\theta## about an arbitrary axis pointing in the direction of a position vector p, what is the rotation matrix R such that Rv gives the position vector after the rotation? Suppose p = ##\begin{pmatrix}1\\1\\1\end{pmatrix}## and...
  41. C

    Equilibrium Question: Arbitrary Axis of Rotation?

    Ok, I solved the question posed in the attached image. I did so by using the car's center of mass as the location of my axis of rotation, generated torque and force equilibrium equations, and solved for all unknowns. When I try to use another location for my axis of rotation, e.g., the point...
  42. J

    Rotation operators on Bloch sphere

    Can anyone explain to me why the following operators are rotation operators: \begin{align*}R_x(\theta) &= e^{-i\theta X/2}=\cos(\frac{\theta}{2})I-i\sin(\frac{\theta}{2})X= \left(\!\begin{array}{cc}\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\ -i\sin(\frac{\theta}{2})&...
  43. R

    How do I calculate the angle of rotation?

    Homework Statement We consider Rectangle Parallelepiped on a board and a=1m ; b=2m and c=3m. The face a and b is considered touching the board. there’s no sliding; we tilt the board so a is horizontal. Q: Starting from which angle we can see a rotation? Homework Equations I want to know how...
  44. blue_leaf77

    2pi rotation of angular momentum eigenket

    Homework Statement Prove that ## e^{2\pi i \mathbf{n\cdot J}/\hbar} |j,m\rangle = (-1)^{2j}|j,m\rangle ##. This equation is from Ballentine's QM book. The term in front of the ket state in the LHS is a rotation operator through ##2\pi## angle about an arbitrary direction ##\mathbf{n}##...
  45. C

    Magnetic field rotation or not?

    Suppose for a moment you had a circular copper disc placed concentrically in the air gap between the poles of an upper and a lower circular magnet, the outer faces of the upper lower magnet being connected by a pole piece so as to complete the magnetic circuit. The edge of the copper disc is...
  46. M

    A cuboid on an inclined plane - based on an Olympiad problem

    Homework Statement Let's suppose we have a [cuboid](http://en.wikipedia.org/wiki/Cuboid) of dimensions ##a \times b \times c##. We put it on an inclined plane of an angle ##\alpha## so that only one edge of length ##c ## touches the plane. In time ##t = 0 ## the cuboid doesn't rotate. Let the...
  47. M

    Understanding use of accelerometers

    Homework Statement Imagine this: A rod is attached at one end to a rotating shaft. So, as the shaft rotates from 0 to 90 degrees back-and-forth (in the xy plane), so does the rod. My goal is to measure the instantaneous acceleration of the rod while its moving. I have a few 3-axis...
  48. abushaheer

    Can We Outrun a Moving Train? 🚆 Exploring Speed vs. Rotation

    if we fly over a moving train at the speed of train can we out run it?? it not, how come we fly at 255m/s when Earth is rotating at 460m/s and we reach from paris to america
  49. L

    What is the direction of friction on a plate on two rotating wheels?

    Homework Statement A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions. The separation between the wheels is L. The friction coefficient between each wheel and the plate is N. Find the time period of oscillation of the plate if it is...
  50. stipan_relix

    A homework assignment including rotation of a rigid body

    Homework Statement The problem is this: A car is evenly slowing down from 30 km/h to 0 in the time of 2 seconds. Radius of its wheels is 30 cm. What is its angular acceleration and what total angle will the wheel describe until it stops? How many turns does the wheel make and what is the length...
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