Rotation Definition and 1000 Threads

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. 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...
  2. 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...
  3. 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...
  4. 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?
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
  15. 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. Buzz Bloom

    I Tidal effects on Earth's rotation and moon's orbit

    Issues about two topics were discussed in another thread. https://www.physicsforums.com/threads/do-solar-tides-affect-Earth's-orbit.933073/ The topics are: how do the lunar tides (1) cause the Earth's rotation to slow down, and (2) cause the moon to move away from the Earth. This thread is...
  22. L

    Kinetic energy of rotation and parallel axis theorem problem

    Homework Statement A circular disc of radius 25 cm and mass 0.5 kg is revolving in its plane with an angular velocity of 4 radians per second. Find A) its kinetic energy of rotation, and B) its new angular velocity if a mass of 10 kg is suddenly fixed on the rim of the disc. Homework...
  23. E

    Rod swinging and hitting a ball

    Homework Statement There is a uniform rod of mass m = 1 kg and length L = 0.2 m fixed to the wall by an axis passing through its end. A uniform ball of mass M = 0.1 kg and radius R = 2.85 cm is on the ground, below the axis of the rod, such that the rod's unfixed end is at the height of the...
  24. C

    What is the Speed of a Falling Object Attached to a Rotating Spherical Shell?

    Homework Statement A uniform spherical shell rotates about a vertical axis on frictionless bearings. A light cord passes around the equator of the shell, over a light, frictionless pulley, and is attached to a small object that is otherwise free to fall under the influence of gravity. Calculate...
  25. T

    Understanding Rigid Body Rotation: Principles and Observations

    Just to confirm a few points: A body frame rotates with a body. It need not be aligned to the rotation axis. Angular momentum vector always aligned with rotation axis (not deviates from it). An observer on the body surface (body frame) observes no motion on a body. Principal axis of rotation...
  26. N

    Could we find enough mass to slow down the Earth's rotation?

    Hi, me and a friend were discussing calendars and how they go wrong. Apparently one orbit around the sun happens during, on average, 365.242189 rotations around Earth's axis. The persian calendar almost nails it, with a 1 sec per year error, because it is based on star observations rather than...
  27. E

    Rotating spool on table with friction

    Homework Statement I am referring to this thread and question: https://www.physicsforums.com/threads/rotation-of-a-spool-about-rough-ground.295666/ Here is the problem, restated: Homework Equations ##\tau_{net} = I\alpha## ##\tau = Frsin(\theta)## ##F_{net} = Ma_{cm}## ##\alpha = a_{cm} /...
  28. C

    Understanding Rotational Velocity and Its Significance in Physics

    As a student taking my first step into rotational physics in a classroom filled with students who have a year of this ahead of me I beg for help! :P So what is Rotational velocity? What does it define? How do signs work with rotation? What does its acceleration mean? Angular Velocity is...
  29. E

    Torque on Rod Due to Normal Force at a Hinge

    Homework Statement In this diagram, I wondered if there is any torque due to the normal force from the hinge, once the support stick is removed. I also want to know what the normal force would be at the hinge. The cup and ball are to be ignored here (essentially massless). Homework Equations...
  30. W

    B The bizarre rotation of galaxies

    The planets rotate around our sun faster and faster the closer they are.The Suns rotate around a black hole in a galaxy as if they were a record on a record player.Gravitational laws as we understand them don't seem to apply.Is it possible that a black holes gravitational pull not only freezes...
  31. ang__

    How Do You Calculate the Total Inertia Matrix for a Composite Object?

    Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework EquationsThe Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them to...
  32. C

    Rotation of a hoop about an off-center axis

    Homework Statement I am studying for a test and am struggling with this question on the practice exam. The answer is 9.9 I am not sure how she got to the answer though A hoop of mass 300 g. and a radius of 20 cm rotates about an axle at the edge of a hoop. The hoop starts at highest...
  33. Jamie_Pi

    Blocks falling while attatched to pulley

    Homework Statement The two blocks, m1 = 3.3 kg and m2 = 4.8, in the figure below are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.64 N · m. If the blocks...
  34. K

    Maths required for rotation point

    Hi The first thing to say about this is that I don’t have a clue where to start. What I’m looking for is somewhere (maybe a website or just a brief introduction) I can study – and learn – about the forces involved and the maths required. _______ Say I have an item/length/beam/weight/etc (C...
  35. H

    How Much Energy Is Needed to Move and Rotate a Weighted Tray Using Rubber Tires?

    Hi, The goal here is to increase/decrease the angle x by 5 degrees. the black circles represent a rubber tire (same as car tires, only smaller), 5cm in diameter, rotating on it's center, powered by a motor. each wheel has 40 psi (2.76 bar) of air in it. the yellow tray on both diagrams are...
  36. Alexanddros81

    A package of mass m is placed inside a drum

    Homework Statement 13.69 A packege of mass m is placed inside a drum that rotates in the vertical plane at the constant angular speed ##\dot {θ} = 1.36 rad/s##. If the package reaches the position θ = 45deg before slipping, determine the static coefficient of friction between the package and...
  37. A

    What is the angular acceleration of the rod?

    Homework Statement A thin, uniform, 18.5 kg post, 2.10 m long, is held vertically using a cable and is attached to a 5.00 kg mass and a pivot at its bottom end (as shown below). The string attached to the 5.00 kg mass passes over a massless, frictionless pulley and pulls perpendicular to the...
  38. A

    Number of rotation till the drum comes rest

    Homework Statement A solid cylinder rotates till it comes to rest. It has inititial angular velocity. To stop the drum a mass m ishung the belt which has a friction coefficient with the drum material as u we have to find no of rotationd all the data is known and correct Homework Equations...
  39. Q

    I Coordinate transformation - Rotation

    How author derives these old basis unit vectors in terms of new basis vectors ? Please don't explain in two words. \hat{e}_x = cos(\varphi)\hat{e}'_x - sin(\varphi)\hat{e}'_y \hat{e}_y = sin(\varphi)\hat{e}'_x + cos(\varphi)\hat{e}'_y
  40. Alfredo Tifi

    B Relative Rotation: Physics Approach for Newton's Bucket in Empty Universe

    Is there any physics approach useful to establish what should happen to a Newton's water bucketful rotating in a hypothetically empty universe (but for the bucket)? What the bucket would be rotating respect to in that one-bucket-universe? Everything rotating seems to have absolute (not relative)...
  41. redtree

    I Galaxy Rotation Curves and Mass Discrepancy

    I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to ##\mu(x)## (from https://arxiv.org/pdf/astro-ph/0403610.pdf). The mass discrepancy, defined as the ratio of the gradients of the total to baryonic...
  42. JTC

    I Left translate back to I in SO(3)

    Hello I am hoping someone can explain a sentence to me. Unfortunately, I do not even recall where I read it. I wrote it down years ago and long since lost the source. (Now I think some of it is making sense, but I don't remember the source.) Consider R(t) as an orthogonal rotation matrix...
  43. Z

    Rotation Operator: Interaction between Two-Level Atom in {|g>, |e>} Basis

    Hi, I'm working on the interaction between a two level atom (|g>, |e>) In my exercise we have to use the rotation operator : R(t)=exp[i(σz+1)ωt/2] with σz the pauli matrix which is in the {|g>,|e>} basis : (1 0) (0 -1) If i want to represent my rotation operator in the {|g>,|e>} basis. Then...
  44. K

    Relationship between translation and rotation

    Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...
  45. E

    Door Rotation: The Influence of Attached Rods and Forces

    If I were to put attach a long rod to the side of a door (the exact opposite of the side where it is hinged, the slim part) And then I apply a force to the the right side of the rod I attached, would the door rotate to the right, or would the hinge completely oppose the force and the door...
  46. E

    Why do we fall forward when walking and rotating?

    When we push off with with our foot on the ground and accelerate, why do we fall forward and catch ourselves with our swinging leg, while when push forward the inertia of our body must actually tilt it backwards, how do we fall to the front?
  47. arpon

    Two successive rotation (Goldstein problem 4.13)

    Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...
  48. E

    Me, A Rod and A Table With Little Friction

    Lets say I have a massive rod laying on a table with little froction, screwed into the table on one side to become our pivot point, and I lay next to it with my feet pointing towards the rod. First scenario: I position myself very close to the pivot point and push, the rod rotates and I move...
  49. saadhusayn

    I Matrix for transforming vector components under rotation

    Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...
  50. kostoglotov

    Viscous drag parallel to the axis of rotation: Control Systems

    Homework Statement https://i.imgur.com/WPAKuf4.png seeking G(s) = \frac{\theta_2(s)}{\tau(s)} Homework EquationsThe Attempt at a Solution What does it mean when the viscous drag is parallel to the axis of rotation?[/B] It also turns out that this system needs two equations. I can sort...
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