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. S

    I How Does Electron Spin Affect the Partition Function in Saha's Equation?

    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}...
  2. 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...
  3. 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...
  4. 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?
  5. 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...
  6. TheSpectacularSpecs

    I Surface Differential Rotation by measuring the position of sunspots

    I am doing a University lab project where I measure positions of sunspots (using images from NASA's SDO) and use them to calculate the rotation of the Sun. Currently, all is going well: I have the angular velocity of several sunspots at varying heights. However, I want to be able to find the...
  7. S

    Engineering How to find the sense of rotation of a resultant moment?

    Hello, so I have a question about the sense of rotation of the body. I get the calculating part nd stuff like that. But what I don't understand is how we would determine the sense of rotation about the moment axis? Could someone explain this to me please? (to add to this, I know that it is...
  8. steveZ

    I Rotation of bike riding off cliff

    When a cyclist rides off a ‘drop’ (an abrupt step in topography, ranging from a curb to a cliff), the front wheel starts falling before the back wheel, so that by the time the back wheel comes off the drop, the bike will not be horizontal. The front wheel will be lower than the back wheel by...
  9. H

    Why is the angular momentum negative in a disk and stick collision?

    figure 11.12 I need someone to explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?p.s. ##\Delta\vec{L}_{total} = \vec{L}_{f} - \vec{L}_{i} = (-rm_{d}v_{df} +...
  10. A

    I Confused about the axis of rotation in rotational motion w/o slipping

    I'm now learning about rotational motion without slipping and it's really hurting my brain to think about. Imagine a cylinder rotating on a flat plane. I can accept that there is both translational and rotational motion. For example, a given point on the circumference of the cylinder follows a...
  11. Falgun

    I A Question on Spinors in a High school textbook

    While revising Rotational motion, I came across a qualitative question which blew me away. Meaning I couldn't even understand the question let alone answer it😅. It has to do with these objects called spinors which as I understand are evoked in quantum mechanics and Relativity. I am attaching the...
  12. genxium

    I Solving Sub-Problem for OpenAI Lunar Lander v2: Seeking Advice

    I'm currently working on a pet project which is similar to the OpenAI Lunar Lander v2 (hence the problem is in a 2D context), and seeking help for a sub-problem that's been blocking me for a while. At any instant of time, I'm to find Fe: magnitude of main engine thrust, must be >0 Fs...
  13. K

    A Take your time, and feel free to ask if something is still unclear.

    chapter 4.8 of Goldstein’s classical mechanics 3rd edition that deals with infinitesimal rotations, and the following is the part I got stuck: (p.166~167) : I'm not able to understand what the author is trying to say. How does "If ##d\boldsymbol{\Omega}## is to be a vector in the same sense...
  14. K

    A Ambiguity in sense of rotation given a rotation matrix A

    Goldstein 3rd Ed pg 161. Im not able to understand this paragraph about the ambiguity in the sense of rotation axis given the rotation matrix A, and how we ameliorate it. Any help please. "The prescriptions for the direction of the rotation axis and for the rotation angle are not unambiguous...
  15. K

    A Rotation matrix and rotation of coordinate system

    If we change the orientation of a coordinate system as shown above, (the standard eluer angles , ##x_1y_1z_1## the initial configuration and ##x_by _b z_b## the final one), then the formula for the coordinates of a vector in the new system is given by ##x'=Ax## where...
  16. jonas_biermann

    B Calculating the torque needed to rotate a drum

    Imagine this: You have a drum with a radius of 12cm, around that drum is a toothed belt which is connected to a motor. The drum weighs 10kg The motor should be placed under the drum How would I calculate the amount of torque needed to rotate the drum I don't have any idea how to calculate this...
  17. K

    A Matrix proof of Euler's theorem of rotation

    The question arises the way Goldstein proves Euler theorem (3rd Ed pg 150-156 ) which says: " In three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point"...
  18. Garlic

    I Cyclic rotation of the cross product involving derivation

    Dear PF, so we know that cross product of two vectors can be permutated like this: ## \vec{ \alpha } \times \vec{ \beta }=-\vec{ \alpha} \times \vec{ \beta} ## But in a specific case, like ## \vec{p} \times \vec{A} = \frac{ \hbar }{ i } \vec{ \nabla } \times \vec{A} ## the cyclic permutation of...
  19. A

    I Question about Earth's rotation

    The period of rotation of the Earth around itself is changed by seasonal winds, tides, and other factors. The exact amount changes daily(about nano second). Is there a website that shows this amount?
  20. T

    Choosing an Axis of Rotation for Equilibrium Analysis

    If I choose my axis of rotation for torque analysis to be the left-end of the plank, I can get the correct results. If I instead choose the com point -- I run into a dead end. Is there a way of a priori knowing this would happen? Thank you.
  21. N

    Compensating for Earth's Rotation With v = ωr

    We know that ##v = \omega r## where ##r = R_{\text{E}} + h##. To compensate for the motion, the plane must fly along the equator at the same speed as the Earth but in the opposite direction, i.e. from east to west, so $$\vec{v} = -\vec{ v}_{\text{E}}$$ $$v_{\text{E}} = \omega_{\text{E}}...
  22. K

    I A coordinate representing rotation about a variable axis and ##T##

    If a system is represented by a set of generalized coordinates ##q_i## in which one coordinate say ##\theta## is such that ##d \theta## represents a rotation of the system about a fixed axis( an axis whose orientation remains fixed in space) then the kinetic energy ##T## shouldn't depend on it...
  23. elcaro

    I Can magnetic fields explain anomalous galaxy rotation curves?

    Magnetic fields as an alternative explanation for the rotation curves of spiral galaxies ABSTRACT THE flat rotation curves of spiral galaxies are usually regarded as the most convincing evidence for dark matter. The assumption that gravity alone is responsible for the motion of gas beyond the...
  24. U

    Rotation of a photograph of an object due to relativity

    I came across an interesting question in the Hartle's textbook, "An Introduction to Eisntein's General Relativity". The question is as follows: Explain why a photograph of an object moving uniformly with a speed approaching the speed of light, parallel to the plane of the film appears not...
  25. L

    Mass m sliding without friction inside a rotating tube

    1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$ 2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this. 3) In ##R_0## the...
  26. crudux_cruo

    B Impulse and distance from the axis of rotation

    I'm trying to model the linear collision of a bat and a ball using the conservation of angular momentum. The ball is a point particle with at rest wrt the axis of rotation, and the bat is being treated as a rod of negligible radius. I have had to work through several problems involving a ball...
  27. july21

    I Where Are the Poles of the Integrand for Δ<0 in Wick Rotation?

  28. A.T.

    B Falling Cat - Rotation with Zero Total Angular Momentum

    I made a new version of the falling cat video, with narration. It explains how cats turn around while having zero net angular momentum during the fall:
  29. K

    I Rotation about two axes and angular momentum

    I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis. I've seen the following approach...
  30. Istiak

    How long does it take for the disk to stop rotating?

    Question : Solution attempt : for
  31. M

    Engineering Rotation around fixed axis (robot arm), dynamics

    Hello, Given the figure below, and the following statement: "The robot arm is driven by two hydraulic cilinders A and B which brings point D rotates CW. The gear in point D has a angular velocity of 5 rad/s. Calculate the velocity and acceleration of the part in point C." First I determined...
  32. snoopies622

    I How do I add "rotation" vectors (pseudo-vectors?)

    I'm tutoring an intro to meteorology pupil and learning about the conservation of potential vorticity, and realizing that I don't understand some basic rotational mechanics. For example, suppose I stand on the North Pole and hold a wheel such that the wheel's axis of rotation is parallel to the...
  33. F

    I Calculate Diameter of Quad Coil Array for Speed of Light Rotation

    I would like to know how to calculate, for any specified frequency in Hz, the required diameter of a 90 degree phased, quadrature coil array such that its generated EM field achieves rotation at the speed of light. Could someone please provide an example of the calculation using a specific...
  34. Ranku

    I Rotation curve with neutral hydrogen and dark matter

    Flat rotation curve in galaxies is determined by observing neutral hydrogen which is co-distributed with dark matter. What is the rotation curve profile of neutral hydrogen in galaxies where there is less dark matter?
  35. LCSphysicist

    I Unit Norm Axis Rotation in R3: Exploring Representation & Algebra

    Now, i am extremelly confused about all this thing. More preciselly, i can't understand how 1.29 was obtained. It was used the A representation? How do he uses it? There is something to do with the canonical basis?
  36. E

    MHB Creating a Number Rotation: Step-by-Step Guide

    Someone help me write a number rotation ,pleae. 1= filled ,2,3=every 14 seconds ,4=every 15 seconds,5=x 6,7=every 18 seconds,8=every 16 seconds,9=every 12 seconds,0=evrey 10 seconds, roration 300 seconds total. my bad expamle: 26783 01194 /11111 20136/ 78914 10111/ 21139 10678/41111 25031
  37. D

    Rotation: inertial frame vs. body-fixed frame

    Hi Angular momentum L is related to the moment of inertia (MOI) , I by L= Iω In the body-fixed frame , ie. rotating with the object then ω = 0 and so the angular momentum is zero in the body-fixed frame. Is that correct ? If i have a thin circular ring then the MOI about the centre is given by...
  38. I

    Polar Ice Caps and the Earth's Speed of Rotation

    Is it correct to say that the melting of the polar caps due to climate change may increase Earth's speed of rotation?
  39. imotta

    Earth's Rotation & Global Agriculture: Impact & Possibilities

    How much will this phenomenon affect the Earth's rotation? Is it possible that the change in the Earth's rotation movement will significantly affect agricultural production on a global scale, for example?
  40. H

    A Wick's rotation on a complex vector space

    I read this in the wiki article about Wick rotation: Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no...
  41. M

    MHB The product γ is a rotation or a translation

    Hey! :giggle: For $p\in \mathbb{R}^2$ let $\delta_{p,\alpha}=\tau_p\circ \delta_{\alpha}\circ\tau_p^{-1}$. Let $p,q\in\mathbb{R}^2$ and $\alpha,\beta\in \mathbb{R}$. (a) Show that $\gamma=\delta_{p,\alpha}\circ\delta_{q,\beta}$ is a rotation of a translation (or both). Give the center of...
  42. R

    How Earth's rotation is changed by the change in inertia when you get out of bed

    Don't understand from where should I start?
  43. greg_rack

    Volume of a solid of rotation, obtained rotating a function around x=2

    At first, I inverted the function(##f^{-1}(x)=g(x)##) and calculated the volume through the integral: $$V=\pi\int_{0}^{4}[4-(2-g(x))^2]\ dx$$ but then I questioned myself if the same result could have been obtained without inverting the function. To find such a strategy, I proceeded as follows...
  44. SAMAHIR

    Analytical question: circular rotation

    Can a point P on the smaller wheel trace a straight line path inside the circular road (like the walls of a well)
  45. R

    Earth's rotation slows down slightly over time -- How much energy is lost?

    Inertia I = 2/5 mr² m=5.98* 10^24 kg. r=6.38* 10^6 kg. I= 9,736 * 10^37 kg. Earth rotation is V= (2 * pi* R)/T = (2*pi*6.38*10^6m)/(24*3600s)=463 m/s angular velocity w= V/r =463m/s/(6.38*10^6m)=7.27*10^-5 rad/s Enerrgy, E= 0.5* I*w²=2.57*10^29 j I get the...
  46. SJay16

    How would one estimate the rotation period of a star from its spectrum

    The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
  47. E

    Observation about the rotation of a disc

    Someone that I tutor asked a simple but pretty good question today which I thought I'd share the answer to. In a tidied up form: a disc with centre at the origin and central axis parallel to a unit vector ##\mathbf{n}## in the ##xy## plane rotates with a constant angular velocity...
  48. H

    Calculating Rotation Rate from Change of Angle

    If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?
  49. Kaushik

    Find the frictional force acting on a solid cylinder

    This was the answer key provided: My questions are the following: if the force required for rotational equilibrium is more than the limiting static friction, then the body will rotate aka slip over the surface. When it slips, the frictional force will be kinetic and not static, right? If I...
  50. warhammer

    Motion involving Translation & Rotation |Kleppner and Kolenkow

    My doubt is with Method 2 of the given example in KK. I'm unable to understand why the torque around A (where we have chosen a coordinate system at A) becomes zero due to the R x F in z direction with a minus sign {Photo Attached} I have tried to reason out that one way to formulate that term...
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