Rotating 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. C

    Transform a pde into rotating frame

    Hi, I have an equation of the form; \frac{d}{dt}(W) = \omega \left(x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) W + g \frac{\partial}{\partial y} W + k x \frac{\partial^2}{\partial y^2} W I want to change it into the rotating frame using the transform; x...
  2. A

    Mass-spring-mass system rotating about its centre of mass relativistically

    Homework Statement 2 equal masses 'm' are attached to a spring of spring constant 'K' and unstretched length 'L'. The system is rotating about its centre of with an angular velocity 'w'. The linear velocity 'v' of m is comparable to that of speed of light 'c'. Find a relation between the...
  3. N

    Force applied on a rotating disc

    I understand that if we apply a force on the axis of rotation of a spinning disc, the torque is in a different direction, and the axis is moved in a direction perpendicular to the direction in which the force upon the axis was applied, determined by the right-hand rule. But what if the force...
  4. snoopies622

    Geodesics in a rotating coordinate system

    In a uniformly rotating coordinate system the trajectories of freely moving objects are influenced by an apparent centrifugal and Coriolis force. Is there a coordinate system or metric (or both) in which these trajectories are geodesics instead?
  5. C

    Why should rotating black holes emit particles?

    In a brief history of time it says theft 'according to the uncertainty principle rotating black holes should emit particles'. However I do not understand why rotating black holes need to emit particles according to the uncertainty principle. I do understand why black holes emit particles it...
  6. J

    Rotating Object Transformation: Length/Circumference Change?

    If a disc-like object was rotating so that its outside edge was at about 0.86c (causing a factor of change of about 2) relative to an observer, then would it contract in length along the axis of rotation, or the circumference (relative to the observer)? in other words, would it get thinner or...
  7. J

    What causes angular momentum in rotating bodies

    Starting at BB everything moves outwards with linear momentum so unless the BB event was rotating where does the angular momentum come from, the Earth rotates, it orbits the sun, the galaxy is rotating and the sun orbiting within it. So it seems that angular momentum is the norm for bodies...
  8. binbagsss

    Angular acceleration direction, rotating rigid bodies

    The direction of rotating bodies about a fixed axis. I am confused on how you should regard the the direction of mg sin x, the angular acceleration and the force exerted on the body by the axis, perpendicular to OG ( where O is the fixed axis location and G is the centre of mass of the body)...
  9. binbagsss

    What are the equations of motion for a rotating disc on a fixed axis?

    -See attached diagram - A uniform disc of mass m and radius a is free to rotate in a vertical plane about a fixed smooth horizontal axis, the axis passes through the mp A of the radius of the disc. - It then asks you to dervie equations of motion for when AO makes an angle pheta with the...
  10. M

    What Are the Initial Angular Velocity and Angular Acceleration of the Flywheel?

    A flywheel makes 80 radians in 4 second and is rotating with constant angular acceleration during this time . It makes 60 radians in next 4 second with constant angular velocity . Find initial angular velocity and the angular acceleration ? my answer is form this equation Q= w0t +...
  11. M

    If a body is rotating at uniform angular velocity then in t sec , the angular displac

    1 ) If a body is rotating at uniform angular velocity then in t sec , the angular displacement is ... (complete ) my answer the angular displacement is increase . 2 ) If a body is making N revolutions in one second then its angular velocity in rad/sec is my answer the angular...
  12. A

    Find area of surface obtained by rotating the curve, ?

    Find area of surface obtained by rotating the curve, URGENT? Using Simpson's rule n=10, find the area of the surface obtained by rotating the curve y=x+sqrt(x), 1 less than or equal to x less than or equal to 2, about the x-axis. Include at least five decimal places in your answer. Area = ...
  13. M

    Questions in linear motion and rotating motion

    Hi please I want from you check my answer http://store2.up-00.com/May12/Ueu86896.jpg http://store2.up-00.com/May12/fkl86896.jpg
  14. I

    Rectangular coil rotating in magnetic field

    Homework Statement A rectangular coil of 80 turns has an area of 0.01m^2. It rotates @ 3000rpm about one of its in plane axes, in a uniform magnetic field having B=1.5T. Calculate the rms voltage generated. Homework Equations 1 Tesla= 1 Weber/m^2. Change in flux of 1 Weber per second...
  15. C

    How Does a Rotating Ball Affect Force Directions in a Box?

    Hello, I have a question about force produced by rotating ball. Let's say the ball rotates clockwise. The rotating ball is attached to the rotation axis with a rigid rod. The rotating ball is placed inside of the box. The box is placed on the very sensitive scale. The box is vibrating...
  16. A

    Variation of gravity in a Rotating SpaceStation

    This is very simple question, and i just need a 2nd opinion. We have a Space Station (preferably a torus) with angular velocity ω and radius r. We have a car inside which OPPOSES the angular velocity and moves with the speed ωr . So, will the gravity felt in this car be Zero? Or will it be...
  17. H

    Rotating the coordinates to coincide the principal axes

    Dear all, We can rotate the local coordinates of the element so that the stress tensor becomes diagonal. The new coordinate system would be the principal stress axes of which are in fact the eignevectors of the stress tensor. Once we have the eigenvectors ( which are generally orthogonal)...
  18. E

    Using rotating vector to draw sine waves

    We have met the idea that a radius of a circle rotating ANTI-CLOCKWISE can be used to draw a sine wave... I get that... it is a great idea but...why does it have to be rotating anti-clockwise. That seems so un natural to me. We were told it is a convention. Does that mean it is something...
  19. A

    Rotating drum being stopped dead by a pin

    I have a drum of radius of 1.375" with a wall thickness of .3025". It is rotating about its central axis at 2000 rpm. There are 6 holes drilled into the drum radially. I have a pin that slides in and out of those holes in order to release and stop the drum. I am trying to figure out the force of...
  20. A

    Detailed Windage losses calculations, rotating electric motors.

    Hi everyone, Long time reader first time poster. A little background on myself, 4th year in the field of ME mostly in simulation and analysis (FEA). I am currently working on a project of a high speed electric motor. I am putting together all the losses from the rotating motor (Copper...
  21. M

    Inelastic collision of ball with rotating beam (juggling robot)

    Homework Statement I'm trying to build a "juggling" robot but I'm getting stuck on the dynamics of catching. The robot follows the dynamics and terminology of a similar one presented in the attached paper (equation 1). Basically, there is a circular ball flying through the air which lands (and...
  22. B

    Rotating Usage of Shoes, Backpacks, to Extend Useful Life

    Hi, All: I know very little physics and/or materials engineering. I am just trying to see if there is something to the claim that alternating the usage of , say, backpacks/ shoes , will give an overall longer total life, i.e., if I will be able to get more useful days out of 2...
  23. R

    Lift of a Rotating Cylinder in Inviscid Flow

    Hi I am wondering why a spinning cylinder will produce lift in an inviscid flow. From: http://www.grc.nasa.gov/WWW/k-12/airplane/cyl.html one of the mechanisms for lift generation was the sticking of fluid particles to the wall of the cylinder. I thought that the no slip condition only...
  24. S

    Lagrangian in rotating space without potential

    Homework Statement I want to derive the centrifugal and Coriolis forces with the Lagrangian for rotating space. The speed of an object for an outside observer is dr/dt + w x r, where r are the moving coordinates. So m/2(dr/dt + w x r)^2 is the Lagrangian. The Attempt at a Solution...
  25. R

    Spring with 2 masses rotating and vibrating

    Homework Statement Consider an object consisting of two balls connected by a spring, whose stiffness is 400N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant the spring is stretched 0.3m, and the two balls at the ends of the...
  26. S

    Can a Rotating Magnet Create a Rotating Magnetic Field?

    Hello everyone, I have a quick concept question for electrodynamics course. If a cylindrical magnet, axially magnetized, is rotated round its own central axis, axis of symmetry, will this create a rotating magnetic field in the vicinity of the magnet? what if the magnet was rotated around in...
  27. B

    Rotating mass connected to elastic spring (help needed)

    Homework Statement A mass m connected using elastic spring to the roof. the mass is rotating horizontaly. mass m= 0.6kg rate or spring constant (k) = 40 N*m-1 frequency= 1/2 sec-1 spring's equilibrium length is 0.8mThe question is: what is the length (L) of the spring while the mass...
  28. J

    Cuboid stability when rotating along different axes

    Homework Statement If we have a cuboid like this one *It won't let me upload the picture or include a link but if you Google cuboid its the first picture* We know that the mas moment of inertia through the centroid is different for each face. So the yellow has the greatest mass moment of...
  29. N

    What determines the speed of two balls on a rotating disk?

    Homework Statement Homework Equations I=mr^{2} L=ωI ω=\frac{L}{I} The Attempt at a Solution I thought that since the moment of inertia was larger for the ball on the outside its angular speed would be slower. So then it would take longer to hit the wall.
  30. 9

    Gravity of a Rotating Cylindrical Space Station: Confirmation Needed

    A cylindrical space station of radius r with thin walls and mass M rotates at angular velocity ω such that the apparent gravity on the inner surface of the cylinder is equal to g. 1) Radial spokes of negligible mass connect the cylinder to the centre of motion. An astronaut of mass m climbs a...
  31. A

    Accelerometer within a freely rotating sphere?

    Hi, Please could someone explain how they think an accelerometer would work if positioned within the center of a freely rotating sphere (e.g a kicked football)? If using triple axis accelerometer and the ball was kicked from a standstill but with no spin, I would imagine that the...
  32. W

    What techniques can be used to analyze a rod rotating about the edge of a table?

    A uniform rod of length 4x is rotating about the edge O of the table. (The rod does not fall off the table.) The centre of mass G of the rod is distance x away from O. The rod is making an angle θ with the horizontal. The only forces present are the weight W of the rod, the normal reaction N...
  33. S

    Relating radius and angular freq of an rotating object

    Homework Statement an ball of mass m is connected by a string with spring constant k, to a rotating shaft. Find a relation between the radius of the circle, and the angular frequency. Homework Equations The Attempt at a Solution Let: Natural length of spring = x0...
  34. A

    Rotating Square Loop in Constant B-field

    [SOLVED] Rotating Square Loop in Constant B-field Homework Statement Homework Equations \epsilon = - \frac{d\Phi}{dt} \Phi = BAcos(\theta) = BAcos(\omegat) d\Phi = -BA\omegasin(\omegat) The Attempt at a Solution I'm trying to study for an exam and I've got this practice...
  35. S

    Acceleration of an offset rotating point on a sphere

    Homework Statement I'm trying to sort out some equations for an academic paper I'm writing. I need to work out the acceleration of a point that rotates around another point that is moving on a sphere. In the attached figure the black dot lies on the surface of a sphere, with a fixed...
  36. R

    Velocities in inertial and rotating frames of reference

    Hi, I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation: \mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} = \left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} + \boldsymbol\Omega \times...
  37. C

    Induced current due to rotating coil

    I attached a problem from a practice exam. I'm stuck on part b). Part A, I'm assuming the answer is the standard equation for an infinite current sheet. How do I find induced current? I can only think of using Emf = NBA*ωsintωt Where Emf= I/R, but I don't have resistance. Only other equation I...
  38. R

    Find the Centripetal Acceleration at 2.5m from a Rotating Platform

    Homework Statement A person is on a horizontal rotating platform at a distance of 4.3 m from its centre. This preson experiences a centripetal acceleration of 56m/s^2. What is the centripetal acceleration is experienced by another person who is at a distance of 2.5 m from the centre of the...
  39. Peeter

    Solving Steady Flow b/w Rotating Cylinders

    Homework Statement Consider the steady flow between two long cylinders of radii R_1 and R_2, R_1 > R_1, rotating about their axes with angular velocities \Omega_1, \Omega_2. Look for a solution of the form, where \hat{\boldsymbol{\phi}} is a unit vector along the azimuthal direction...
  40. H

    Rotating a Curve & Line Around the X Axis: A Math Problem

    Homework Statement The curve x=y^(2) and the line x=4 is rotated about the x axis. Homework Equations pi* integral from a to b of Radius^(2) The Attempt at a Solution pi* integral from 0 to 4 of (square root of x)^(2) dx. My teacher has this answer as 8pi but I think that that...
  41. C

    Vertical speed of a point attached by two rods to a rotating hinge.

    Homework Statement Not exactly homework, but an interesting problem I found for which I have some questions about the answer. A rod of length r is rotating around a point O with constant angular velocity w. Distance r away to the right from the point O is a rail. The end of the rod with...
  42. R

    Two grids, one rotating, share equivalent x-y coordinates with different values.

    I’m a woodworker, a math idiot, my trig hasn’t improved since I flunked it 40 years ago and I need help making a Christmas toy for my grand-kids. The values that follow are arbitrary, were extracted using eng graphics software and should be solid. Problem: I have one 2D surface (that...
  43. H

    Rotating y=x^(3)+1 about x=-1 Using Washer Method

    Homework Statement y=x^(3) +1, x=1, y=1; rotated about x=-1 Homework Equations Washer Method. Pi * Integral from a to b of [Outer radius]^2-[inner radius]^2 The Attempt at a Solution I understand the shell method version but I wanted to learn the washer way for this one. Pi*...
  44. P

    Volume of solids rotating about two axises

    Homework Statement Find the volumes of the solids revolution obtained by rotating the region about the x-axis and the y-axis. y=2x-x^2, y=0 The Attempt at a Solution I know how to get the volume of a function that is rotating around one axis, but the "y=0" is confusing me. Because...
  45. K

    Velocity distribution of particles in an arbitrary-arrangement of rotating gases

    If we have a "quasi-rigid" rotating convective cell where the gas overall rotates at the same angular velocity, we could establish a non-inertial frame of reference co-rotating with this convective cell such that the particles of the gas (seen from that frame of reference) may follow a...
  46. K

    Comsol - Balancing of the rotating propeller

    Hi, I am new in comsol. I currently doing a simulation on rotating propeller. I need to obtain vibration magnitude of the rotating prop.. can anyone tell me which type of analysis and how i can get the data? I have been working on this and search over the google for past two week didnt...
  47. L

    Kinetic energy of a rotating disc

    if KE=1/2mv^2 and you have a circular object rotating, with it's mass uniformly distributed through the object (ie each part of the disc weighs the same) then obviously certain parts of the disc will be moving faster than others. therefore closer to the middle of the disc, you have more KE...
  48. X

    Calculating Average Tangential Stress for Non-Uniform Rotating Disk

    Assumed a disk loaded with external pressure Po, internal Pressure Pi and rotating at the speed ω. I'm sure that average tangential stress for uniform thickness rotating disk can be calculated using equation below : σ avg = (PiRi/Ro-Ri) - (PoRo/Ro-Ri) + (ρω^2) / 3(Ro^2+RoRi+Ri^2) Ro = outer...
  49. P

    Rotating and Nonrotating Rods Superposed

    Homework Statement A uniform disk turns at 3.7 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk . They then both turn around the spindle with their centers superposed. What...
  50. K

    Understanding Rotational Stability of Long Axles: Theory and Analysis

    Does anyone know the theory behind rotational stability of a (long, thin) axle? I would like to know the maximum allowable rotational speed of a 5 meter long axle. I suppose its something in line with the theory of column stability, but I can't find anything about it. I have made a FEM...
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