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. C

    Doubt with rotating body and force

    Hello. Let's image a bar. In one side is attached to a body so the bar can rotate over this axis. There is no friction between the two bodies. The system is at rest in t=0. A force acts forming a 90° angle with the bar. The bar moves and begin to rotates. The force dissapear. There is no force...
  2. Elroy

    Linear Algebra Problem: Solving for Euler between two ordered bases

    Homework Statement Linear Algebra Problem: Solving for Euler between two ordered bases I've got a problem I need to solve, but I can't find a clean solution. Let me see if I can outline the problem somewhat clearly. Okay, all of this will be in 3D space. In this space, we can define some...
  3. Danny Boy

    A Is the overlap of coherent states circular symmetric?

    What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...
  4. Datta108

    Rotation of a drum attached to a spring

    Homework Statement Rotation of a small drum of mass moment of inertia 0.44kg.m^2 and with frictional resistance torque 0.3 N.m is initiated by a string wound around its 20 mm diameter shaft and attached to a stretched spring, as shown in the figure. If the spring, which has a stiffness 2N/mm is...
  5. F

    Solving Motor Rotation: 0 to 1800rpm in 0.49s?

    Homework Statement The rotor of an electric motor weighs 10 pounds and is 4 inches in diameter. What is the length of time required for the motor speed to increase from 0 to 1800rpm, assuming a constant electrical torque of 20 in-lb and zero external load during this period? Assume the rotor is...
  6. J

    How does a ring laser detect Earth's rotation?

    This is my first time posting here so I hope I am in the right place. So I have read about some scientists who have built a ring laser that is sensitive enought to detec the Earth's rotation. I can get how a ring laser can detect the rotation of a missile say if the laser path is perpendicular...
  7. K

    Special relativity-analogy of rotation

    Homework Statement Analogy to rotation: $$(x')^2+(y')^2+(z')^2-c^2(t')^2=x^2+y^2+z^2-c^2t^2$$ It isn't Homework Equations Lorentz transformations: $$x'=\frac{x-ut}{\sqrt{1-u^2/c^2}}$$ $$t'=\frac{t-ux/c^2}{\sqrt{1-u^2/c^2}}$$ The Attempt at a Solution ##~(x')^2-c^2(t')^2~## must equal...
  8. bananabandana

    Rotation of spin projection different to general rotation?

    Homework Statement Prove, for the matrix ##S = exp \bigg(-\frac{i}{\hbar}\mathbf{\hat{n}}\cdot \mathbf{\hat{S}}\bigg)## (spin-rotation matrix), and for an arbitary vector ##\mathbf{a}## that: $$ S^{-1} \mathbf{a} \cdot \mathbf{\hat{x}} S = a(-\theta) \cdot \mathbf{x} = a \cdot...
  9. Jim Lundquist

    Solve 3D Rotation Problem: Help Needed

    Please help me solve a problem that has puzzled me for years. I am not a mathematician or a physicist, so please bear with me. Imagine the apparatus pictured to be a depiction of the x, y and z axes. The x is represented by the green stick. The y is represented by the yellow stick, and the z...
  10. JulianMau

    I Clocks ON a rotating disk: What happens?

    I was reading about the Ehrenfest Paradox and it got me thinking about something (that I think is) similar: Suppose we take a large, flat, and rigid disk, and we attach to various parts of it a number of clocks (some very close to the center of the disk, some along the edge, others in between)...
  11. G

    Rotation and balance of oil effecting Earth's rotation

    When oil is taken from the ground, it leaves a cavity that doesn't get backfilled. If material were taken from anywhere on a billiard cue ball, it would throw it out of balance. Trillions of gallons of oil have been displaced over roughly 100 years, shouldn't that affect Earth's rotation on...
  12. Mind----Blown

    General approach to find principal axes of rotation?

    Suppose i have an equilateral triangle and i want to find the principal axes of rotation passing through one of the vertex. How can i do that? I am thinking along the following lines but I'm not too sure: 1)Since the equilateral triangle has symmetry about a median, that definitely is one...
  13. E

    Instantaneous center of rotation

    <Mentor's note: ^Moved from a technical forum and therefore no template.> at the instant shown during deceleration, the velocity of the tire is 40 ft/s to the right and the velocity of point A is 5ft/s to the right. locate the instantenous center of rotation. Can the instantaneous center of...
  14. F

    Solve Inertia & Rotation Homework - Value of g = 10ms^2

    Homework Statement The question is uploaded. Value of g = ## \small \rm 10~ms^{-2}## Inertia of the individual square lamina = ## \rm \small \frac{1}{12}mr^2 ~kgm^{2}## The Attempt at a Solution $$\ C=Ia$$ $$\ Moment~of~Weight~of~Particle=1.594a$$ $$\ 0.3*2g=1.594a$$ $$\ 6=1.594a$$ $$\...
  15. S

    Angular momentum and when center of rotation is changed

    Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...
  16. S

    Can rotating shafts experience changes in deflection due to inertial effects?

    I am curious how the deflection of a shaft changes due to rotation. In the force diagram image the green arrows show the rotational fixture locations and the purple arrow show the location of the applied force. The second image shows the deflection during a static test. If the force is applied...
  17. E

    Does the rotation speed of a planet affect its gravitational pull

    For example let's a satellite was orbiting the moon which has no atmosphere. If the moon suddenly started spinning twice as fast would it effect the satellite's orbit even though the satellite is separated by the vacuum of space from the moon? Easier way to put it, if the Earth suddenly spun...
  18. Avimanyu Ray

    I What causes retrograde rotation in planets and moons?

    When I googled it, I wasn't satisfied with the answers from various sites...some sites like universetoday.com gave me a glimpse but it was totally theoretical and based on assumption. Also I would like to know why some planets have retrograde rotation; what might have caused them to and why do...
  19. O

    Torque Equation about a point other than point of rotation

    Hello all, These days I am studying rotation and rolling of bodies. We know a body can be made to rotate about any point. Let's assume that an external force is acting on the rotating body fixed about the point of rotation, and this force made the body rotates faster that is its torque produces...
  20. D

    Maglev Train and Earth's Rotation

    Homework Statement Will a maglev train beginning at rest slowly drift or accelerate due to the rotation of the earth? Homework EquationsThe Attempt at a Solution The Earth is a rotating reference frame, with points on the equator moving at approximately 1000 miles per hour. If the maglev is...
  21. akashpandey

    How can rotation with same phase be possible?

    How can we calculate the rotation without seeing change of phase of object like in case of moon,we see the same phase of moon but how it can be rotating. So rotation without change of phase is possible if yes or no than how and why ?.
  22. akashpandey

    I Have you ever wondered why we can't see the other side of the moon?

    We all know we see only one part of moon means part which is facing towards earth But moon rotates also so we should able to see its other part(dark part) but we cant. I know rotational period of moon is equal to revolutionary period of moon but if moon is having rotational motion So we should...
  23. CFurner

    Torsional strength at high temperature

    High school student here I am designing an experiment to test the effect of temperature on the torque required to twist a piece of metal, and need some advice on where to start researching. What I need help with is A) finding a table of the torque required to twist steel when cold, and B)...
  24. D

    Rotation of a ring pivoted at several points

    Homework Statement A rigid ring is fixed with three bearings evenly spaced around its circunference, which allow it to rotate but not to displace in the radial direction. An external force is applied in a fixed point P of the ring which moves with the ring. The bearings have friction. These...
  25. W

    Friction on a flat rotating surface

    If I push an object such as a cylinder of wood along a flat table (flat face of cylinder in contact with the table) through it's center of mass, the friction or energy required is not dependent of the surface area the block makes with the table, Friction = μ N, correct? And the energy required =...
  26. T

    I How is Graphene's Hamiltonian rotationally invariant?

    Graphene's Hamiltonian contains first order derivatives (from the momentum operators) which aren't invariant under simple spatial rotations. So it initially appears to me that it isn't invariant under rotation. From reading around I see that we also have to perform a rotation on the Pauli...
  27. J

    MHB Where does radius sin angle sin rotation come from?

    For calculating a new "x" point of rotation I found the formula: x' = radius * cos(angle + -rotation) which converts to: x' = radius cos angle cos rotation - radius sin angle sin rotation Where does "radius sin angle sin rotation" come from? Jerry D.
  28. K

    Analysis of tennis string tension

    I have a decent background in physics, but something that has always confused me is how to think about how the tension of the string in a tennis racquet affects how the ball leaves the strings. For example, the traditional lore in tennis is that tauter strings will give more control, whereas...
  29. VNV

    Spintropics and Magnetic Acceleration

    I have a rather odd question that delves outside of the realm of reality just a bit. Recently, I've had a bit of an obsession with designing ludicrous weapons. My current venture is a little bugger I call the 20MM Magnetic Accelerator Rotary Cannon. The MARC20 for short. It's an eight barreled...
  30. Arman777

    What is the solution to the spring and disk rotation problem?

    Homework Statement Overhead view of a spring lying on a frictionless surface and attached to a pivot at its right end.The spring has a relaxed length of ##l_0=1.00m## and a negligible mass.A small 0.100 kg disk is attached to the free end at left.That disk is then gvena velocity...
  31. OrlandoLewis

    What happens to the moment of inertia when a rod is folded?

    Homework Statement Consider one rod of length L which is spun at its center perpendicular to its length; it will have a certain moment of inertia. Now, if the same rod is folded in the middle creating a certain angle and still spun at its center, what happens to its moment of inertia? Homework...
  32. M

    Prove all Elements of O(2,R) have form of Rotation Matrix

    Homework Statement Show that every matrix A ∈ O(2, R) is of the form R(α) = cos α − sin α sin α cos α (this is the 2d rotation matrix -- I can't make it in matrix format) or JR(α). Interpret the maps x → R(α)x and x → JR(α)x for x ∈ R 2 Homework EquationsThe Attempt at a Solution So I know...
  33. Arman777

    Calculating Flywheel Rotations in Angular Speed and Constant Acceleration

    Homework Statement [/B] A flywheel with a D=1.2m is rotating at an angular speed of 200 rev/min (a) Whats the angular speed in rad/s ? (b)Whats v=? in the point on the rim ? (c)What const. ∝ ( in rev/min^2) will increase its angular speed to 1000 rev/min in 60 sec ? (d)How many...
  34. Y

    Rotational Mechanics Question.

    Homework Statement A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping. Homework Equations Since the shell is rolling, friction does not act at the bottom. So equating the torque, F*R= I*α The...
  35. Arman777

    Flywheel Rotation Question

    Homework Statement A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop.Assuming a constant acceleration,find the tme for it to come to rest. Homework Equations ##w-w_0=∝t## The Attempt at a Solution In Δt secon the change in w...
  36. quantumSpaghetti

    I Rotational excitation of quantum particle

    I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I $$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$ n^2 * ħ^2$$ was...
  37. Konte

    I Internal rotation kinetic energy operator

    Hello everybody, My question today is: Given a molecule that has an internal degree of liberty ( let's take the ethane molecule with its internal rotation as an example), how to write the kinetic energy operator by means of the corresponding internal coordinate? Thank you guys. Konte
  38. C

    Ball Doing a Loop Min Kin Energy: Find Angle θ

    Homework Statement A ball with radius ##r## is inside a hollow cylinder with radius ##r+R##. In the first part of the assignment, one has to calculate the minimum kinetic energy the ball has to have at the bottom in order to complete a full loop in the cylinder. It turns out to be...
  39. S

    Torque and rotation around a fixed point

    This isn't a real homework problem (i.e. I made this problem up myself for my own purposes), but I figured this is the correct forum to post. 1. Homework Statement In the following figure we have two rods connected to each other, and the bottom rod is connected to the blue structure (G), and G...
  40. Clubbes

    Does Earth's Rotation Affect Gravity?

    Homework Statement I do not know if this is the right forum to be asking this, but it is the best i have found. A classmate of mine came with the statement that if the Earth stopped spinning we would all float off to space because the Earth's mass is to small to able to hold everyone down. I...
  41. doktorwho

    Find the position of equlibrium

    Homework Statement From the diagram below find the position of the man (##x##) if the system is in balance. Total length is ##L## and the man is distance ##x## from one end. Homework Equations 3. The Attempt at a Solution [/B] I know that the system must be in balance if all the torque and all...
  42. B

    Thoughts on Newton's Bucket and the relativity of rotation

    Isaac Newton imagined a bucket of water suspended on a fine (ideally torsionless) rope, set spinning. Friction eventually causes the water to rotate along with the bucket. The surface develops a dip in the middle and rises at the edges owing to the water's inertia. (You see this effect every...
  43. R

    Torque and forces parallel vs perpendicular to the axis of rotation....

    why force parallel to the axis of rotation do not make any torque.
  44. F

    Angle of rotation in fixed end of beam

    Homework Statement In the first photo , i was told that the fixed end moment is zero when the far end is pinned or roller supported . Why in the example in the second and third photo( both end are fixed) , the angle is zero ? Homework EquationsThe Attempt at a Solution I think it's wrong ...
  45. E

    I Rotation operators on a sphere, around x and y axis

    I need to start by saying that I'm not a physicist, nor a student of physics. I'm a translator, and my text is about rotations around the azimuthal nodal lines on the sphere. I need to find a name for a particular type of a rotation operator, which rotates the sphere around the x and y axes...
  46. Vitani11

    Finding the period of rotation of this system....

    Homework Statement Three identical stars, each with mass m, form the verticies of an equilateral triangle with side length d and rotate in a circular orbit due to their mutual gravitation. What is the period τ of their rotation? I set up the FBD for each star and am now trying to figure out...
  47. R

    2 astronauts near a space station (no rotation)

    Homework Statement You have a space station in space far from any planets or stars in form of a hollow cylinder with inner radius R1 outer R2 length L and density Rho. On a symetric axis z are 2 astronauts, 1 at the middle and the second at distance H=2L from the center of the bottom of the...
  48. L

    Linearly-damped rotational motion

    http://imgur.com/a/8QjoW http://imgur.com/a/8QjoW Hello- I am trying to determine the dynamics of this linearly-damped hinge. Assuming that: v(0) = 0 damping constant = b door has mass = m I was able to determine that: ∑Fx = -Fd * cos(45-θ/2) + Rx = m*dvx/dt ΣFy = -Fd * sin(45-θ/2) - Fg +...
  49. cheapstrike

    Angular momentum conservation.

    Homework Statement A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ωo, meets a rough inclined plane of inclination θ=60°. The sphere starts pure rolling up the plane with an angular velocity ω. Find the value of ω. Homework...
  50. cheapstrike

    What are the effects of impulse and kinetic energy on two identical spheres?

    Homework Statement Two identical spheres A and B are kept on a smooth surface. They are given the same impulse I. The lines of action of impulses pass through the center of A and away from the center of B. Then: (A) linear kinetic energy of B will be less than that of A. (B) B will have...
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