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. LCSphysicist

    Masses, pulley, friction and rotation

    In summarize, i have four equations and five incognits. T2,T1,theta,a2,f Need to find one more equation, but i don't know how
  2. O

    I Rotate Functions with Derivatives: A Quantum Mechanics Homework

    I was solving a problem for my quantum mechanics homework, and was therefore browsing in the internet for further information. Then I stumbled upon this here: R is the rotation operator, δφ an infinitesimal angle and Ψ is the wave function. I know that it is able to rotate a curve, vector...
  3. M

    MHB Is the composition of the isometries a rotation?

    Hey! 😊 Let $\delta_a:\mathbb{R}^2\rightarrow \mathbb{R}^2$ be the rotation around the origin with angle $\alpha$ and let $\sigma_{\alpha}:\mathbb{R}^2\rightarrow \mathbb{R}^2$ be the reflection about a line through the origin that has angle $\frac{\alpha}{2}$ with the $x$-axis. Let $v\in V$...
  4. E

    Can Uneven Heating and Mechanical Rotation Generate Winds?

    I've had a question bugging me lately and no matter how much I google, I can't seem to find an answer. I'm sure this probably isn't possible, and my logic is probably flawed (Earth sciences isn't my forte), so I figured I'd ask you fine folks here. First, my understanding of wind, it's caused...
  5. J

    Rotation by matrix multiplication -- confirmation please

    The below matrix represents a rotation. 0 0 -1 0 1 0 1 0 0 Im trying to obtain the general point (x y z) when rotated by the above rotation matrix? So visited https://www.andre-gaschler.com/rotationconverter/ entered the above figures and not sure which entry would be x y z but assume it...
  6. Athenian

    Finding the Rotation Matrix for Vector Alignment

    Below is the attempted solution of a tutor. However, I do question his solution method. Therefore, I would sincerely appreciate it if anyone could tell me what is going on with the below solution. First off, the rotation of the matrix could be expressed as below: $$G = \begin{pmatrix} AB & -||A...
  7. Raimund Kempe

    How can the rotation of galaxies be explained?

    How did you find PF?: Google search How can galaxies rotate coming from a singularity? Raimund
  8. archaic

    Rigid body rotation problem: Mass on a cord spinning up a wheel on an axle

    (I know how to solve the problem, that's not what I am looking for.) I have a problem with how I ought to understand the moment of inertia. The only torque I see applicable on the wheel is that of the tension, and so I think that ##I## should be ##m_{\text{point}}R^2##, without including all the...
  9. S

    Do We Sense the Rotation on a Rapidly Spinning Planet?

    It's often said that you don't feel Earth rotation because the gravity acts against the centrifugal force. Of course this is true but also your body is turned around once each 24 hours. So I wonder on a planet which is rotating once each 3 seconds and has same g=9,81: Would you feel the rotation?
  10. G

    Confusion on the concept of point of rotation

    --no explanation as conceptual error--
  11. Adesh

    An isolated object can rotate only about its center of mass

    I was talking to someone about the equilibrium of fluids and we reached at some stage where we had to prove that in an external field the translational forces add to zero along with moments (torques) should also add to zero. The first one was quite easy but during the discussion of second...
  12. T

    A Algebraic proof that Euler angles define a proper rotation matrix

    I have asked this question twice and each time, while the answers are OK, I am left dissatisfied. However, now I can state my question properly (due to the last few responses). Go to this page and scroll down to the matrix for sixth row of the proper Euler angles...
  13. Ennio

    I Velocity correction´ formula for the rotation of the Earth

    Let´s suppose we are observing the sun and measuring some spectral lines. Does the velocity correction´s formula for the Earth include the rotational velocity components of the Sun as well? or rather are we basically measuring both velocity contributes of Earth and of Sun together (receeding...
  14. K

    Classical Rotation: Referencing Rotational Motion in Mechanics

    Hello! I am a bit confused by the reference frames used in derivations for rotational motion in classical mechanics (assume that there is no translation and the body rotates around a fixed point). As far as I understand there are two main frames used in the analysis: a lab frame, which is fixed...
  15. K

    I Rotating Molecules: Energies, Angular Momentum & Wavefunctions

    Hello! I am a bit confused about the rotational motion in molecules. Assuming the bond length is constant, the motion can be described as a rigid rotor. In the center of mass frame the energies are given by ##BJ(J+1)## and the wavefunctions are spherical harmonics. However when we measure the...
  16. K

    I Understanding Nuclear Rotation: Quantum Numbers and Wavefunctions

    Hello! I am a bit confused by the quantum numbers used to describe the rotation of a nucleus. In Wong's book these are J, M and K, which represent the rotational quantum number, its projection along the lab z-axis and its projection along the body intrinsic symmetry axis, respectively. However...
  17. Adwit

    I Rotation problem in Quantum Mechanics

    How do "sinϕ - cosϕ sinϕ" become 0 ?
  18. C

    Why Do Different Objects Share Similar Moments of Inertia?

    Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects. The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment...
  19. Prabs3257

    Is the angular acceleration of this rod constant?

    Please refer to the image
  20. M

    MHB Understanding Symmetry Maps and Rotations in the Plane

    Hey! :o Let $F\subseteq \mathbb{R}^2$. A map $\pi:\mathbb{R}^2\rightarrow \mathbb{R}$ is called symmetry map of $F$, if $\pi(F)=F$. A symmetry map of $F$ is a map where the figures $F$ and $\pi (F)$ are congruent. Let $\pi_1:\mathbb{R}^2\rightarrow \mathbb{R}^2$, $x\mapsto \begin{pmatrix}0...
  21. A

    Conservation of energy given the Earth's rotation?

    So Earth and everything is spinning around at 1000mph at the equator. From our perspective we are at a standstill. But let's say a fighter jets flies east to West against Earth at same speed, so now relative to someone in space, the Earth spins but the plane is at a standstill. Wouldn't that...
  22. M

    Understanding the Direction of Rotation for Stress State Equations

    Hi, The context for my question is: A thin plate, which lies in the x-y plane, contains a small hole of radius a . Consider a polar co-ordinate system r,􏰆 with its origin at the centre of the hole and 􏰆defined as the angle that a radial line makes with the x-axis. A uniform uniaxial tensile...
  23. rzyn

    Rate of fall depends on rotation?

    v1=460m/s×2, v2=0 m1=m2=5kg R=6378km a1=460m×460m/s/s/6378/km/1000/m×km=0.13m/s/s a2=0 F1=m1×a1=0.66kg×m/s/s F2=m2×a2=0 G=9.81m/s/s F3=(m1+m2)×G=98.1kg×m/s/s (F3-F1)/10/kg = 9.744m/s/s Where the heck did I go wrong?
  24. L

    Rolling without Slipping - axes of rotation and centripital acceleration

    Therefore, if someone were to ask what the magnitude of centripetal acceleration is at the top of the wheel at a given instant (relative to the ground): ##v_{cm} = v_{translational, center-of-mass/wheel}## ##ω = ω_{point-of-contact}## ##v_{top} = 2(v_{cm}) = 2(rω)## ##a_{c(top)} =...
  25. Hajarmq

    Rotation and spring force exercise

    Summary:: Calculating the inclination angle A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...
  26. R

    How can I use the right hand rule to find torque in bicycle wheel rotation?

    I tried to use the right hand rule to find torque but I’m not sure to go from there.
  27. S

    Invariance of a spin singlet under rotation

    I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...
  28. Athenian

    I Lorentz Boosts: Finding Speed, Coordinates & Rotation w/ Matrix Multiply

    Recently, I've been studying about Lorentz boosts and found out that two perpendicular Lorentz boosts equal to a rotation after a boost. Below is an example matrix multiplication of this happening: $$ \left( \begin{array}{cccc} \frac{2}{\sqrt{3}} & 0 & -\frac{1}{\sqrt{3}} & 0 \\ 0 & 1 & 0 & 0...
  29. sshanker

    Gear Rotation puzzle is confusing 50:10 GR but 6 rotations

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  30. P

    Drum rotation, lateral loads and point of pull

    I farm and have built water control devices for my rice operation that use a cable and drum setup. The moving part is a 24"water tight rotary union that we rotate with a cable that originates in a dual spool winch above the center line of rotation for the drum. The winch cables secure to the...
  31. M

    Find the volume of the solid formed by the rotation around the y=0

    Hi, I find this... Please tell me your opinion on this. Thanks.
  32. Wi_N

    Calculating the surface area of a solid of rotation

    For some reason I have become very unsure but my gut feeling says i can calculate y=(1-x^(a/b))^(d/c) I already know the formula for calculating the volume. but can transfer the whole thing as a function of y(x) and take the integral then as a single integral?
  33. W

    Effects of a Change of Direction of the Rotation of the Earth?

    Summary: What if the Earth rotated about its axis in a N-S direction instead of doing so in an E-W direction. Hi, Just curious: What would be the effects/consequences if the Earth rotated about its axis in a North-South ( or South-North) direction instead of an East-West one as it currently...
  34. B

    I Questions about Rotation Groups in Physics

    I have questions concerning group theory, esprecially Rotation groups. The first is: Are rotations groups f.ex. SO(2) defined for rotations in the actual physical 2 dimensional plane or are general rotations in any 2 dimensional space included? Someone wrote that "the action of an element of...
  35. A

    What is the formula for calculating torque in a rotating pyramid?

    torque=Force*radius*sin(theta) center of mass x direction = ( 0(6 x 10^9 kg)+ (118m)(6 x 10^9 kg)+ (236m)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 118m center of mass y direction = ( 0(6 x 10^9 kg)+ (140m)(6 x 10^9 kg)+ (0)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 46.7 m radius = (118^2 + 46.7^2)^(1/2) =...
  36. J

    Translational and rotational velocity

    For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
  37. L

    Is rotation a relative property?

    I was recently trying to explain to a grandchild the relative nature of velocity (the different paths of a coin dropped by a passenger on a train, as seen by the passenger on one hand and a trackside observer on the other), and the invalidity of the concept of absolute velocity. For some reason...
  38. R

    Rotation of a roll by a driving wheel

    The bigger circle is a hollow cylinder (steel) with a length of 0.6m and a diameter of 0.133m and a mass of 8kg. The 2 smaller circles are rubber wheels with a diameter of 0.080 and mass of 0.2kg. Both the roll and the wheels have ball bearings and are mounted on a shaft. On both the shafts of...
  39. B

    Newton's Second Law for Translation and Rotation

    Answer choices: N2L for Translation, N2L for Rotation, Both, Either1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. My solution = N2L for rotation 2. You are asked to find the angular acceleration of a low-friction pulley due to a...
  40. K

    I Question about Galactic Rotation curves in the Milky Way galaxy

    The graph in Wikipedia, article Milky Way, section Galactic Rotation, shows the actual rotation speeds in blue and the calculated speeds due to observed mass in red. (The graph is to the right of the article.) At about 3 kpc the actual speed is about 205 km/s. To account for the decrease in...
  41. Kaushik

    A uniform rod allowed to rotate about an axis and then it breaks

    A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...
  42. brotherbobby

    Tension in a rotating rod at various places

    (The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite). I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...
  43. SpaceThoughts

    Is the Spinning Wheel's Rotation Maintained? | Investigating Kinetic Energy

    Hi. I searched and found no answer to this simple question: Is the spinning wheel in this videoclip keeping the same rotation (kinetic energy) when flipped upside down and back again? (if we forget about friction)
  44. deZordine

    Airplane flight and the rotation of the Earth

    If a plane departs from the North Pole (where the Earth's rotation speed around its axis is 0 Km / h) on the median line to Romania, around the 45th parallel (where the Earth's rotation speed around its axis is 1178, 80 km / h) would the plane reach its destination only by flying to *South* (...
  45. P

    I Measuring Galactic Rotation: How & What We Know

    How have we been able to measure galactic rotation? I have seen graphs showing the relation between the velocity of stars in a galaxy and their distance from the center. These graphs show that the observed velocities of stars are much faster than they are expected to be, particularly ones that...
  46. The Bizarre Behavior of Rotating Bodies, Explained

    The Bizarre Behavior of Rotating Bodies, Explained

    Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
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  47. S

    Yo-yo on an accelerating conveyor belt

    First off, I was wondering if the acceleration of the conveyor belt can be considered a force. And I'm not exactly sure how to use Newton's second law if the object of the forces is itself on an accelerating surface. Also, I don't know whether it rolls with or without slipping. I thought I could...
  48. Diracobama2181

    How to Determine the Axis of Rotation

    Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I...
  49. Manasan3010

    Linear momentum or Angular Rotation

    I think the answer is ##\frac{mV}{M}## but I am not sure. Won't the cylinder tries to rotate due to the collision at one end? Is this anything related to Angular Momentum? The Answers given were,
  50. Plat

    Radiometer rotation speed as function of pressure

    I am experimenting with using a radiometer as an approximate indicator of pressure in my homemade high vacuum system, running a small turbo pump. I am interested in the relationship between pressure and vane rotation speed, with light intensity being constant. I have only been able to find...
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