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. Krushnaraj Pandya

    Inelastic collision of ball and rod - rotation problem

    Homework Statement A uniform rod of mass M and length l is hinged at the center. a particle of mass m and speed u sticks after hitting the end of the rod. find the angular velocity of the rod just after collision Homework Equations Energy conservation-0.5mu^2=0.5(m+M)v^2 Angular momentum...
  2. S

    Solving for Rotation in a Force & Torque Equation

    Homework Statement Homework Equations torque= F*r*sintheta total force on y= 0 The Attempt at a Solution how come it will rotate in this situation?? espicially that he is ignoring the weight force of the rod! i knew that i ignored the mass of the rod when he said total force on y= F -F. if...
  3. Krushnaraj Pandya

    Ring and solid sphere rolling down an incline - rotation problem

    Homework Statement A solid sphere, hollow sphere, disk and ring are released simultaneously from top of a incline. Friction is sufficient to prevent slipping of hollow sphere- what will reach the bottom first? Homework Equations a in pure rolling down an incline=gsinθ/(1 + I/mR^2) The Attempt...
  4. Abhimessi10

    Rotation of a Body: Frictional Force w/o Slipping

    Homework Statement A force is applied tangentially to a rigid body on a horizontal surface.if it doesn't slip find the frictional force https://ibb.co/m9sMEU Homework EquationsThe Attempt at a Solution The solution tells us to take axis about the bottommost point in contacy with the surface...
  5. C

    I How Does the Rotation Operator Affect Spin in Quantum Mechanics?

    for compute: $$e^{\frac{iS_z\phi}{\hbar}}S_x e^{\frac{-iS_z\phi}{\hbar}}$$ so, if we use $$S_x=(\frac{\hbar}{2})[(|+><-|)+(|-><+|)]$$ $$e^{\frac{iS_z\phi}{\hbar}}(\frac{\hbar}{2})[(|+><-|)+(|-><+|)] e^{\frac{-iS_z\phi}{\hbar}}$$ so, why that is equal to...
  6. X

    Turn the press of a button or pulling into a rotation?

    Here's some basic mechanical engineering question for you guys. How can one turn a press of a button (or pulling) into a rotation? My goal is to be able to have the button in any orientation and position and still be able to rotate a dial 360 degrees when fully pressed/pulled by 5mm. I suspect...
  7. J

    Rotational motion: Conservation of energy doesn't work....

    http://www.animations.physics.unsw.edu.au/jw/rotation.htm#rolling I have set up an apparatus similar to what the above link says (the first bit about brass object with shaft). So basically, the shaft is in contact when the brass is first rolling, then it suddenly accelerates when the edge of...
  8. sams

    I Explaining Coordinate Rotation in Arfken & Weber Chapter 1

    In Mathematical Methods for Physicists, 6th Edition, by Arfken and Weber, Chapter 1 Vector Analysis, pages 8-9, the authors make the following statement: "If Ax and Ay transform in the same way as x and y, the components of the general two-dimensional coordinate vector r, they are the...
  9. P

    I Is there some prediction of the speed of rings?

    From NASA page: The inner parts of the rings move around Saturn faster than the outer parts, all in accordance with Kepler’s third law for small objects revolving about a massive, larger one. They orbit the planet with periods ranging from 5.8 hours for the inner edge of the C ring, to 14.3...
  10. M

    I How to calculate angular rotation for a 2D line?

    For illustration purposes, I have attached an image of the line with the angle that I want to calculate. I am trying to determine the angle of rotation and the calculation that I am using currently is as below: angle = math.atan2(y,x) I use this formula to calculate the rotation for A and A'...
  11. R

    I Exploring Planetary Orbits and the Sun's Rotation

    Are there any good theories which can explain how the orbits of planets are not aligned with the rotation of the Sun? I gather there is about 6 degrees of differance, which is not small.
  12. Exath

    I Why is T+f=Ma in Cylinder Roll Without Gliding?

    So I'm looking at a problem that involves a situation that looks like this the cylinder rolls without gliding. And there are these following equations that apply to it (1) mg - T = ma (for the block hanging vertically) (2) T + f = Ma (for the cylinder f = friction force, T = String force) (3)...
  13. E

    How Does Earth's Slowing Rotation Affect Day Length Over Centuries?

    Homework Statement Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 61 centuries, what is the total of the daily increases in time (that is, the sum of the gain on the...
  14. Exath

    Rotation of Rigid Bodies: Rotating stick with disc on top

    Homework Statement [/B] A thin cylindrical rod with the length of L = 24.0 cm and the mass m = 1.20 kg has a cylindrical disc attached to the other end as shown by the figure. The cylindrical disc has the radius R = 8.00 cm and the mass M 2.00 kg. The arrangement is originally straight up...
  15. H

    What is the Instant Centre of Rotation for a Rotating Bar?

    Homework Statement Homework Equations orthogonality condition: that means that the point of ICR is orthogonal to the velocity Vb and Va The Attempt at a Solution the solution that i found with the problem is: The ICR of the bar is at infinity. the motion of the bar is translational. I think...
  16. A

    Fortran Rotation of the coordinates of a 3D function

    Hello, I come across a problem in programming and I do not find a lot of help on the internet, so I hope I can find an answer here. I have a 3D array representing a function, say f(i,j,k) and a basis function u(i,j,k). I would like to perform a general rotation of the basis function u so that I...
  17. K

    Understanding Rigid Body Rotation: Solving Problem 4A and B from a Physics Exam

    I am trying to solve problem number 4 part A and B from (http://people.physics.tamu.edu/kamon/teaching/phys218/exam/2003C/2003C_Exam3_Solution.pdf) but I am confused about certain aspects of it. In part A, I understand that since we are considering the person as a cylinder, the equation for...
  18. S

    Torque & Rotation: 2 Axes, Tilting Possible?

    I have some questions about torque and its role in gymnastics, or with anything that may rotate, possibly. First, is it possible for someone or something to use torque to rotate in two different axes of rotation at once? In a separate situation, is it possible to tilt using torque to tilt the...
  19. NatFex

    I Rotation of a point in R3 about the y-axis

    Hello, I'm having a visualisation problem. I have a point in R3 that I want to rotate about the ##y##-axis anticlockwise (assuming a right-handed cartesian coordinate system.) I know that the change to the point's ##x## and ##z## coordinates can be described as follows: $$z =...
  20. V

    How long would it take to stop the rotation of the Earth?

    Imagine a person is moving at the equator in the direction opposite of the Earth's spin. How long would it take them to stop the rotation of the Earth? Assume: the person's "weight" = 90.718 kg, they person's speed = 1m/s, The Earth's "weight" = 5.972*10^24 kg, the angular velocity of the...
  21. Krushnaraj Pandya

    What Force Keeps a Bar at a Constant Angle on a Smooth Plane?

    Homework Statement A uniform bar of mass m is being moved on a smooth horizontal plane by applying a constant horizontal force F acting at the lowest point. If the rod translates making a constant angle 'theta' with vertical, the value of F must be? Homework Equations 1) F=ma 2) Torque=Moment...
  22. F

    Rotation Measurment with Encoders

    I am trying to both design a code for Arduino and build a circuit connected with the Arduino which uses 3 anode 7 segment and 3 resistor arrays with 7 pins to connect to the Arduino Uno. The encoder is a rotary encoder. I have Pin A of the rotary encoder connected to pin 13 of the Arduino and...
  23. Igor Oliveira

    Describing the translation and rotation of a square frame

    Homework Statement Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...
  24. F

    Why does an artillery shell rotate when fired?

    An artillery shell is fired at, let's say, a 45 degree angle. The shell will rise to a maximun height and then fall back to earth, but the shell will also rotate considerably so that it strikes the ground with the nose forward. What accounts for the rotation? It would seem that the center of...
  25. M

    How does rotating a coordinate system affect vector direction and components?

    If I move a coordinate system by an angle theta, why does the vector still have the same direction, but the components are different?
  26. G

    Why is the Gödel Universe Rotating

    Homework Statement Consider the Godel Metric in spherical coordinates as on page 6 here; ds^2=4a^2\left[-dt^2+dr^2+dz^2-(\sinh^{4}(r)-\sinh^{2}(r))d\phi^2+2\sqrt{2}\sinh^{2}(r)dt d\phi)\right] This is a solution to Einstein's Equations if we have ##a=\frac{1}{2\sqrt{2\pi\rho}}## and ##\Lambda...
  27. Japser Lu

    Collision and rotation problems?

    A cube with mass M and length 2a, move in the velocity v on the friction-less horizontal table, when it closes to the end of the table, it is stopped by the long block(the height can be ignored), ask what is the value of v to topple from the table? ( note: use one side of cube as the rotating...
  28. K

    Is There an Easier Way to Calculate 3D Rotation Matrices?

    While resolving a problem in mechanics I discovered a beautiful and easy way for finding out what the rotation matrices in 3 dimensions are! And I'm surprised that I do not find this method anywhere on the internet! Would it be because it's not technically correct? Anyways, here it is: It's all...
  29. K

    How does Newton's Law change with rotation between frames?

    If we have two frames related by ##x' = Rx## where ##R## is a rotation matrix and ##t'=t## Newton's law doesn't remain the same, for $$m \frac{d^2 x'}{dt'^2} = m \frac{d^2 Rx}{dt^2} = mRa$$ whereas it will be just ##ma## in the other frame. How do we solve this?
  30. Brilli

    What is the Angular Velocity Acquired by a Disk on a Rotating Platform?

    Homework Statement A horizontal platform rotates around a vertical axis at angular velocity ω. A disk with radius R can freely rotate and move up and down along a slippery vertical axle situated at distance d > R from the platform’s axis. The disk is pressed against the rotating platform due to...
  31. V

    Maximum torque on a rotating cylinder kept on a moving plank

    Homework Statement A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the x-y plane) with its axis along the y- axis and free to rotate about its axis. The platform is given a motion in the x-direction given by x= Acos(ωt). There is no slipping between...
  32. Ulle73

    Golf club "Swing Weight" and club head rotation

    for those Who Dont know golf. Swing weight is a measurment how Heavy the clubhead Feels. If i put on a heavier grip the swingweight falls. Heavier head swing weight goes up etc. If i Want to swing the Club with as little clubhead rotation as possible (i know forarm creats the rotation) Would i...
  33. Brilli

    An equilibrium problem -- Spinning a hinged rod and a ball

    Homework Statement This is a practice olympiad problem A light rod with length l is hinged in such a way that the hinge folds in one plane only. The hinge is spun with angular speed ω around a vertical axis. A small ball is fixed to the other end of the rod. (a) Find the angular speeds for...
  34. Buckethead

    B Spiral galaxies: Multiple axies of rotation?

    Spiral galaxies of course rotate around one axis perpendicular to the plane, but has anyone measured if any spiral galaxies are also rotating about an axis through the plane or about any other axis?
  35. T

    I Macroscopic rotation from spin flipping?

    There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.) I...
  36. Jay1298

    Motor combination to drive multiple tyres

    If I need 50,000 Nm of torque to rotate a wheel, and I am rotating it about its rim (like the London eye), would 5 10,000 Nm motors each connected to a set of tyres to rotate it (the motors are not connected to each other), or would these motors first need to be connected to each other and then...
  37. lc99

    Friction and Rotation: Understanding the Ratio of Forces on a Rotating Disk

    Homework Statement A phonograph record is whiring around at 103 rpm. Two balls of mass 1 kg are sitting on the disk and are at rest with respect to disk. The first ball (1) sits at a radius 5 away from center. The second ball (2) sits at a radius of 10 away from center. What is the ratio of...
  38. JTC

    A Example of how a rotation matrix preserves symmetry of PDE

    Good Day I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc. But I am making a lot of progress. There is, however, one issue that continues to elude me. I often read how Lie developed Lie Groups to study symmetries of PDE's May I ask if someone...
  39. L

    Simple Harmonic Motion of Meterstick

    Homework Statement Homework Equations ##\tau = rFsin(\theta)## ##\tau_{net} = I\alpha## ##F = -kx## ##kx = mg## The Attempt at a Solution I don't understand how the restoring force from the bending of the ruler behaves (so I have no idea how to apply torque here). I also don't understand how...
  40. Richie Smash

    Determine matrix for reflection followed by rotation

    Homework Statement Hi good morning to all. The problem at hand states, that the points A (3,0) and B (5,0) are reflected in the mirror line y=x. Determine the images A' and B' of these points. I've done that using the reflection in the line y=x which i know to be \begin{bmatrix} 0 &1 \\ 1 & 0...
  41. Z

    What is the torque required for a track to climb over a step

    I'm trying to figure out whether it is best to use a multi-wheel or track system to get an object over a step, however I'm having a bit of trouble finding the torque needed for a track to pull itself up and over. Diagram of course is not to scale, but I've drawn up something of the situation...
  42. L

    Elastic Spring / Simple Pendulum Lowest Point

    Homework Statement A perfectly elastic spring swings in a vertical plane as a simple pendulum with a mass m suspended at the bottom of the spring. The force constant for this spring is ##k## and the unstretched length is ##L##. The spring is carefully held in the horizontal position so that the...
  43. L

    Marble rolling on ramp harmonic motion

    Homework Statement A perfectly solid marble of radius R rolls without slipping at the bottom of a spherical bowl of a radius 6R. The marble rolls back and forth in the vertical plane executing simple harmonic motion close to the lowest point. How long does it take the marble to go down one side...
  44. JTC

    Calculating power from a prescribed rotation

    Hi, Forgive me for this trivial question. I am confused. Let's say I have a gyroscopic device in which the rotor is set to spin at a prescribed angular velocity. Next, put it on an ocean surface in which the ocean waves induce a precession. These two rotations, then induce a moment (induce a...
  45. D

    Instantaneous center of rotation

    In absence of any other forces, if you push a free object not on the center of mass, during the application of the force (not after) should it only rotate around its instantaneous center of rotation (also called pole or center of oscillation/percussion)? Or it can also be subjected to...
  46. V

    Gravitational Effects on a Pendulum in a Moving Ship

    Homework Statement A pendulum having a bob of mass ##m## is hanging in a ship sailing along the equator from east to west. If the ship sails at speed v what is the tension in the string?. Angular speed of Earth's rotation is ## \omega ## and radius of the Earth is ## R ## Homework Equations...
  47. A

    Will a sphere rotate on a frictionless inclined surface?

    Well, my physics teacher taught us about rotation the other day and I came across a scenario where a sphere and a ring roll down a friction-less inclined plane from a point of absolute rest. I found it counter-intuitive as I started to think about why would they start rolling in the first place...
  48. Ventrella

    B Complex products: perpendicular vectors and rotation effects

    My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces? As I understand it, the product of complex numbers x = (a, ib) and y = (c...
  49. Biker

    Instantaneous axis of rotation

    I studied statics but I thought I can figure out the dynamics part. In a rectangular shape that is tipping, Usually we take the center of mass as an axis of rotation however the center of mass is accelerating with centripetal force so taking it would make the problem complex and we just take...
  50. C

    Unlocking Realistic Rotational Collisions with Physics & Graphics Engines

    Hi all! I'm currently working on a graphics/physics engine. The following Wikipedia page was extremely helpful in making rectilinear collisions look natural: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional Specifically, the very general vector form of the equation on the bottom...
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