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. greg_rack

    Rotation of the plane of polarization of light by glucose

    Hi guys, Online I found this really cool experiment that uses a glucose solution(e.g. in a beaker) to rotate the plane of polarization of a polarized light beam passing through it, of an angle ##\theta## which depends on the frequency of the EM wave. Then, for example, watching white light...
  2. Mr_Allod

    Rotation and Polarisation of Light using Jones Matrices

    Hello there I am having trouble with part b) of this exercise. I can apply the rotation matrix easily enough and get: $$ R(-\theta) \vec J= \begin{bmatrix} A\cos\theta + B\sin{\theta}e^{i\delta} \\ -A\sin\theta + B\cos{\theta}e^{i\delta} \end{bmatrix} $$ I decided to convert the exponential...
  3. P

    Conservation of energy in rotating bodies

    The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder. To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder). However, I viewed the cylinder as rotating...
  4. yucheng

    Two rotating coaxial drums and sand transfering between them (Kleppner)

    The solution is simple by noting that the total angular momentum of the system is constant. (Though I overlooked this) Instead, I went ahead analyzing the individual angular momentum of both drums. Let ##L_a## and ##L_b## be the angular momentum respectively. ##M_a##, ##M_b## be the...
  5. yucheng

    Incorrect derivation of tangential acceleration in polar coordinates

    I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...
  6. B

    Rotation within a vacuum vs rotation with a pressurized environment.

    common sense tells me that if an object can remain spinning in the vacuum of space for eternity, than placing that same object within a pressurised environment will cause the object to slow to a stop. is there a way for me to calculate the time in which it would take an object to stop rotating...
  7. PeterDonis

    I Does rotation in Gödel spacetime depend on the frame of reference?

    [Moderator's note: Thread spun off to allow discussion of this topic to continue since the previous thread was closed.] I have had something nagging at me about this for a while, and it finally hit me while looking through this paper about the Godel Universe...
  8. CallMeDirac

    Exploring the Behavior of Rotating Labels on Desmos: A Mathematical Perspective

    In desmos you can rotate a label by going into the settings. BUT the rotations get weird with large numbers: if you rotate by 360 nothing happens same for 3600 and 360000 but when you get to 360000000000000000 it starts changing from just being flat. It changes from a 0 degree tilt to a 332 or...
  9. Leo Liu

    Stability of rigid body rotation about different axes

    We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia...
  10. Leo Liu

    Finding the precession of a gyro using Euler's equations of rotation

    The rate of precession of this gyro ##\Omega## can be found by solving ##\tau_1=DMg=I_s\omega_s\Omega##. But when I apply Euler's equations to this problem, it fails. I first set the frame in the way shown in the diagram above. Then I wrote the first equation...
  11. S

    I Calculating Time Dilation & Galaxy Rotation Curve

    Hello, What I understood from multiple answers on different threads is that the effect of the time dilation is too small to explain the galaxy rotation curve. I was advised to do some calculations in order to see it myself. And this is what I would like to do but I need some help. - What is...
  12. A

    Engineering Finding the center of instantanous rotation

    [Mentor Note -- Improved versions of the two pictures are posted in a reply a few posts down] Good day and here is the solution I have a problem in finding the value of AC and BC, I couldn't figure it out? many thanks in advance!
  13. A

    Confusion about tidal locking and rotational kinetic energy

    Hello! I was reading two things: 1) tidal locking (as explained in the Wikipedia article:https://en.wikipedia.org/wiki/Tidal_locking where it is stated that, because of internal friction caused by the body of water being attracted to the moon and deforming, the kinetic energy of the system...
  14. R

    Rotation of a rod fastened to a wire

    Hi, I started with calculating the moment of inetria of the rod: I = ⅓ML^2 + M(3/2 * L)^2 = 31/12 ML^2 and I thought that the reaction force in the first case will be equal to centrifugal force: F1 = Mω^2*(3/2)L Angular velocity is calculated from the conservation of energy: Mg3/2*L=1/2 * Iω^2...
  15. sergiokapone

    I Rodrigues' rotation formula from SO(3) comutator properties

    Is any way to get Rodrigues' rotation formula from matrix exponential \begin{equation} e^{i\phi (\star\vec{n}) } = e^{i\phi (\vec{n}\cdot\hat{\vec{S}}) } = \hat{I} + (\star\vec{n})\sin\phi + (\star\vec{n})^2( 1 - \cos\phi ). \end{equation} using SO(3) groups comutators properties ONLY...
  16. mcas

    Check invariance under rotation group in spacetime

    I started by inserting ##ds=\sqrt{dx'^{\mu} dx'_{\mu}}## and ##p'^{\mu}=mc \frac{dx'^{\mu}}{ds}##. So we have: $$\frac{dp'^{\mu}}{ds}=mc \frac{d}{dx'^{\mu}} \frac{d}{dx'_{\mu}} (x'^{\mu})$$ Now I know that ##dx'^{\mu}=C_\beta \ ^\mu dx^\beta## and ##dx'_{\mu}=C^\gamma \ _\mu dx_\gamma## where...
  17. M

    Rotation angle measurement of pedal with ball and socket joint

    the device that I have is the same as the mirror of this truck.
  18. ricles

    Cylinder rotating on a support

    This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...
  19. E

    Rolling 3 objects on an inclined plane

    Hello there, I have a question regarding this problem. I have no problem with part A. However, in part B, my solution manual states that the hollow cylinder will reach the bottom last. Why is it? I mean shouldn't the solid cylinder and the hollow one reach the bottom at the same time? you know...
  20. J

    Angular Momentum Problem: Rotation Rate

    First I found the moment of inertia, I=1.8(5.5^2+3.9^2+4.9^2) =125.046 Then I tried to find the rotation rate using the equation L=rotation rate*I rotation rate=3773/125.046=30.173 But the answer is suppose to be 21.263?
  21. WonderKitten

    Conservation of angular momentum

    Hi, I have the following problem: A homogeneous disc with M = 1.78 kg and R = 0.547 m is lying down at rest on a perfectly polished surface. The disc is kept in place by an axis O although it can turn freely around it. A particle with m = 0.311 kg and v = 103 m/s, normal to the disc's surface at...
  22. J

    Exploring Motion in Physics: Beyond Translation, Rotation, and Oscillation

    In high school I learned about three kinds of motion in classical mechanics - translation, rotation, and oscillation. Are there any other kinds of motion in the physical world?
  23. jaumzaum

    Is Newton's third law valid for rotation / Torque?

    Is third Newton law valid for rotation / Torque? I mean, can we say that for every torque there must be another torque with equal magnitude and opposite direction? This can only be true for contact forces or radial forces, as these forces will create a reaction that will cancel the torque...
  24. G Cooke

    Questions About Highly Coupled Magnetic Resonance

    This is one of very few in-depth sources of information I can find online about Highly Coupled Magnetic Resonance...
  25. Butterfly41398

    Rigid body rotation -- A person walking around a merry-go-round

    This one is challenging for me. Can anyone give me a hint?
  26. T

    I Earth's Rotation & Orbit: Effects on Space Objects?

    Hi. I don't know what prefix this question belongs in so I just chose advanced at random. What's the physical effect called when the Earth orbits around the sun at extremely fast speeds and also rotates around itself every 24 hours at the same time? Does that force cause anything in space...
  27. F

    Calculate a specific boost and rotation

    Let's begin with the first point. a.I) Apply a generic boost in the y-z plane (take advantage of the arbitrariness in deciding the alignment of the y and z axes). \begin{equation*} B_{yz} = \begin{pmatrix} \gamma & 0 & -\gamma v_y & -\gamma v_z \\ 0 & 1 & 0 & 0 \\ -\gamma v_y & 0 &...
  28. Y

    Equilibrium for a rotation lab

    So for the first one on the left is it T= 2g*20=40Nm ? Our professor said it is clockwise I just don't understand how she gets that conclusion.
  29. H

    I Is this something like a Wick rotation?

    Please look at this YDSE with two orthogonal polarizers...
  30. Gh778

    B Energy to increase the radius of a circle composed of several disks

    Hi, I take a big number of disks to composed a circle of a radius of 1 m, the blue curved line is in fact several very small disks: I take a big number of disks to simplify the calculations, and I take the size of the disks very small in comparison of the radius of the circle. The center A1 of...
  31. J

    I Rotation rates of planets seem odd?

    Ok, I know there are a lot of strange things in our solar system. Can anyone explain why the small planets spin so slowly? and why does Jupiter spin so quickly? It seems like a ball of debris, getting smaller and smaller, would increase its speed like an ice-skater pulling their arms in...
  32. Sabertooth

    I Elliptic Function Rotation Problem

    Hi all:) In my recent exploration of Elliptic Function, Curves and Motion I have come upon a handy equation for creating orbital motion. Essentially I construct a trigonometric function and use the max distance to foci as the boundary for my motion on the x-plane. When I plot a point rotating...
  33. dontknow

    Constraints in Rotation Matrix

    In Rigid body rotation, we need only 3 parameters to make a body rotate in any orientation. So to define a rotation matrix in 3d space we only need 3 parameters and we must have 6 constraint equation (6+3=9 no of elements in rotation matrix) My doubt is if orthogonality conditions...
  34. P

    Forces at the bottom of a rotating U-tube filled with water

    So when the rotation starts some water will move upwards and in the vertical part of tube. I know hat centripetal force will be given by F=mv²/r Now I though of taking r as centre of mass of the water system but I don't know what to take the value of m as? Should I only consider the water...
  35. burian

    How can I find the velocity of a point on a disk rotating in a disc?

    From a freebody analysis I got, $$ \vec{r} \times \vec{F} = |r| |F| \sin( 90 - \theta) = (R-r) mg \cos \theta$$ and, this is equal to $$ I \alpha_1$$ where the alpha_1 is the angular acceleration of center of mass of small circle around big one, $$ I \alpha = (R-r) mg \cos \theta$$ Now...
  36. Sagittarius A-Star

    B Explaining Galaxy Rotation Speed Discrepancies with GR & Gravitic Fields

    The speed of the ends of the galaxies is higher than what it should be. Current solution: This could be explained by hypothetical "dark matter", which was not found up to now, or by a MOND theory (MOdified Newtonian Dynamics). Can this be explained instead with rotational frame-dragging...
  37. B

    Confusion About Rotational Motion

    I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
  38. P

    Minimum force required to rotate a lamina

    When the lamina rotates about A, FA must act on B (because it is the farthest away) perpendicular to AB (so that all of FA contributes to rotation). Same argument is valid for rotation of lamina about B as well. Having noted that, I tried two approaches: Approach 1- If I assume that the...
  39. E

    Direction of an infinitesimal rotation?

    I had a question from the magnetic dipole thread that was posted earlier today, but it's a bit more mundane. The torque on a magnetic dipole, using a right handed cross product is ##\vec{\tau} = \vec{\mu} \times \vec{B}##. The work done during a rotation is $$W = \int \vec{F} \cdot d\vec{r} =...
  40. brotherbobby

    Independent parameters of the rotation tensor ##R_{ij}##

    I am afraid I had no credible attempt at solving the problem. My poor attempt was writing the matrix ##\mathbb R## as a ##3 \times 3## square matrix with elements ##a_{ij}## and use the matrix form of the orthogonality relation ##\mathbb R^T \mathbb R = \mathbb I##, where ##\mathbb I## is the...
  41. T

    Rotation around a non fixed axis + linear motion of a system

    I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...
  42. brotherbobby

    On the orthogonality of the rotation matrix

    Let me start with the rotated vector components : ##x'_i = R_{ij} x_j##. The length of the rotated vector squared : ##x'_i x'_i = R_{ij} x_j R_{ik} x_k##. For this (squared) length to be invariant, we must have ##R_{ij} x_j R_{ik} x_k = R_{ij} R_{ik} x_j x_k = x_l x_l##. If the rotation matrix...
  43. J

    Wheel moving in rotation and translation

    Hi :) 1/ First case A wheel with a mass ##m## and a radius ##r## moves in horizontal translation and rotates around itself. The wheel is just above the ground, doesn't touch it. The wheel rotates CW if the wheel moves in translation to the right. The ground is horizontal and there is no...
  44. P

    Rotation of two cylinders inclined at an angle

    A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal. Say the final angular velocity of Q is ωq. The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...
  45. K

    What was Newton's insight on rotational motion in Principia?

    mgR = d(mvR + MvR + ½M(R^2)v/R)/dt mgR = ma + Ma + ½Ma mg = a(m + 3/2M) v = mgt / (m+3/2M) My answer is incorrect. The right answer is v = mgt/(3m+M), but I have no idea what I'm doing wrong.
  46. J

    Energy of translation compared to the energy of rotation

    I use an example with a rack and a pinion. I suppose there is no losses from friction. I suppose the masses very low to simplify the study, and there is no acceleration. I suppose the tooth of the pinion and the rack perfect, I mean there is no gap. There is always the contact between the rack...
  47. karush

    MHB APC.5.2.01 AP Volume by Rotation

    $\displaystyle\pi\int_{0}^{\infty} e^x \ dx = \pi$ Ok I looked at some of the template equations but came up with this.
  48. K

    I Rotation and Boost of Tensor Components: Meaning?

    If two coordinate systems are related by a rotation or a boost, does it make sense to say the tensors components are rotated or boosted with respect to their components in the original coordinates? For vectors, I think it is standard to say that, but what about general tensors?
  49. O

    Angular Rotation and Acceleration

    [Mentor Note -- OP deleted his posts after receiving help. His posts are restored below] @ocean1234 -- Check your messages. Deleting your post is not allowed here, and is considered cheating. Problem was given: ##\theta(t) = at - bt^2 + ct^4## a) calculate ##\omega(t)## b) calculate...
  50. 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
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