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. A

    Newton's second law for rotation, when does it apply?

    I'm reading Halliday's chapter or rigid body rotation. In the derivation of Newton's second law for rotation, it is assumed that the object is hinged about some axis ( the connection would be a frictionless pin). The law is derived for such a connection, but is later applied to objects that...
  2. gracy

    How do these particles rotate about an x-axis?

    Can anyone explain how these two particles actually a complete molecule (given in the image)will rotate about x-axis?
  3. G

    Initial Gyroscopic Precession Using Forces

    I think I more or less understand how a gyroscope precesses--at least mathematically and in terms of torque/angular momentum. My question here is: how does the gyroscope start precessing in the first place? The external forces on the center of mass are entirely vertical. Given that Newton's...
  4. D

    Kinetic energy and direction of rotation

    Hi, I would like to study these two cases: Case A 1/ I turn counterclockwise the ring at w2, this need the energy \frac{1}{2}mr^2w_2^2 with m the mass of the ring 2/ I turn the ring with arm clockwise at w1, this need the energy \frac{1}{2}md^2w_1^2 with d the length of the arm 3/ I eject...
  5. D

    Why Do Spherical Balls of Different Sizes Roll at the Same Speed Downhill?

    Homework Statement Suppose two spherical balls roll down a hill without slipping. If both are released from rest, which one will roll the fastest? The answer is that both will roll at the same speed, even if they are of different sizes and weights, but I do not understand why Homework...
  6. T

    The cause of aerospace rotation

    Hi What is the cause of aerospace rotation whit the earth? May the gravity haves any roll?
  7. G

    Difference between a spinning sphere and rolling one

    Consider this: We have a sphere rolling down a slant, released from some height h with null velocity. At the end of the slant its potential energy will have been fully converted to kinetic energy, part translational and part rotational. Now consider this: at the end of the slant the ball enters...
  8. B

    MHB Matrix Rotation Query: Inertia Tensor D (+90y, -90z)

    I have an inertia tensor D in the old Cartesian system which i need to rotate through +90 in y and -90 in z to translate to the new system. I am using standard right hand rule notation for this Cartesian rotation. D=...
  9. M

    Force applied to dumbbell to CM and edge

    Today in class we learned about how if a force F is applied to a dumbbell on its center of mass and then separately applied to the edge where it gets its maximum torque, the dumbbell will have the same CM velocity after. It makes sense when you think about it in terms of momentum. F times T...
  10. H

    Faraday rotation and permittivity tensor

    Dear all, In textbooks about optics in magneto-optic materials, we often come across a Hermitian permittivity tensor with off-diagonal imaginary components. These components are relevant to the Faraday rotation of plane of polarization of light through the material. Now my question is: Is the...
  11. L

    Rotation angular velocity of a turntable

    I've spent at least an hour trying to figure this out, but can't seem to figure out how to solve this. 1. Homework Statement A 170g , 30.0-cm-diameter turntable rotates on frictionless bearings at 66.0rpm . A 25.0g block sits at the center of the turntable. A compressed spring shoots the block...
  12. A

    Why does the sun appear to move eastwards from Earth?

    Hello, I've been reading astronomy books for some time now but after leaving things for a while I seem to forget rotation directions. For example, I know that the Earth spins in the anticlockwise direction. That is easy to see why. They say that motion of the Earth is eastwards. Because of the...
  13. maxhersch

    Work and Rotational Kinetic Energy (Falling Chimney)

    Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...
  14. Q

    Are *two* external forces always required to cause rotation?

    As the title says, can there be any rotation if only one force is applied to an object at rest. For instance, if I had a rod laying flat on a frictionless surface, and I pushed one end, am I correct to say that Newton's second law says that all of that force goes into acceleration the center of...
  15. PcumP_Ravenclaw

    Derivation of mapping for isometric rotation about i

    Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...
  16. PcumP_Ravenclaw

    Doubt about rotation isometry on the complex plane

    Dear All, In the 2nd paragraph of the attachment can you please explain to me why we are trying to make ## r(z) = z ## and what does "As r is not the identity..." mean?? and how did the line ## L = 0.5*b + ρe^{θ/2} ## come about? Danke...
  17. PcumP_Ravenclaw

    Derivation of rotation isometry on the complex plane

    Dear all, can you please verify if my derivation of the algebraic formula for the rotation isometry is correct. The handwritten file is attached. The derivation from the book (Alan F beardon, Algebra and Geometry) which is succinct but rather unclear is given below. Assume that f (z) = az + b...
  18. B

    Coriolis Force and the Earth's Rotation,

    /* Last year, in first year I had problems with understanding the Coriolis Force. I asked the lecturer about it and he found a simpler way of explaining it. I thought I had understood. However, I've spent many hours this weekend trying to understand it and it keeps eluding me. That explanation...
  19. Aristotle

    Need assistance in Physics question relevant to Torque & Static equlibrium

    Homework Statement Homework Equations Static equilibrium: Net force & net torque = 0 The Attempt at a Solution Am i doing this correctly for part a? [/B]
  20. L

    The moment of inertia of a rod that is rotating off the end of the rod.

    Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...
  21. S

    What is an example of a proper rotation in physics?

    An example being its use in the beginning of this document: http://isites.harvard.edu/fs/docs/icb.topic1288789.files/Rotations-Lorentz-Transformations.pdf I haven't read the whole document yet so forgive me if it explains what it means later on.
  22. S

    Proof of disk moment of inertia using area density

    Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...
  23. V

    Double rotation, friction and sum of energy

    Hi, I posted my question on another forum: http://physics.stackexchange.com/questions/143377/one-disk-ring-in-double-rotation-and-sum-of-energy but it is "on hold" and nobody knows where is the error, so I try to post here if you are agree ? I can understand if you close the question...
  24. Logan Land

    MHB How to solve the following matrix rotation

    Find the standard matrix for the rotation of 60◦ about the axis determined by the vector v = (3, 4, 5). do I multiply each x,y,z by pi/3? doesnt seem like it should be that simple
  25. nicolauslamsiu

    Tides: Does Moon's Rotation Affect Earth?

    Apart from the the gravitational pull of the Moon and the Sun on the Earth, does the rotation of moon contribute to the tides?
  26. P

    B. What is the net force acting on the object?

    Homework Statement A uniform disk 0.3m in diameter and having a mass of 2 kg isfree to rotate about its horizontal axis on frictionless bearings.An object with a mass of 0.05 kg is attached to a string wound around the rim of the disk. The object is released from rest and descends with constant...
  27. P

    Torque vs Centripetal Force: What's the Difference?

    Torque causes a system to rotate about its axis while centripetal force causes a system to rotate about the axis of the separate system that exerted the centripetal force. So does this mean that torque specifically causes rotation and centripetal force causes revolution?
  28. F

    Rotation Problem - Constant Acceleration

    Homework Statement [/B] At t=0, a flywheel has an angular velocity of 3.4 rad/s, an angular acceleration of -0.42 rad/s^2 and a reference line at \theta_0 =0 A: Throigh what maximum angle will the reference line turn in the positive direction B: At what times will the reference line be at...
  29. L

    How High Must the Brass Ball Start to Complete the Loop-the-Loop?

    Hi everyone, I've been working on this problem for a while now, and I was hoping someone here could point me in the right direction. Here goes: 1. Homework Statement A solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight...
  30. S

    Measuring Motor Rotation with a Desktop Computer

    Hello all, A bit of background. We are communicating with a microcontroller through a desktop computer. The desktop computer controls direction of rotation of the motor, and it can prompt a step in the motor causing a rotation. However, what can I do in terms of feedback? I have not taken...
  31. T

    Unequal tension of a rope in a pulley system

    I am having a bit of difficulty with the concept of unequal tension in a rope. What are the conditions for unequal tension? I read that the tension is the same when there is no acceleration. Why is this the case? Can someone explain this concept to me? Thanks :)
  32. M

    Rotational motion: Find angular displacement when rotation speed is changing

    Homework Statement A torque acts on a wheel rotating at 19.8 rad/s and increases its angular speed to 23.5 rad/s in 11.2 s. Find the angle through which the wheel turns during this time. Homework Equations omega = theta/time The Attempt at a Solution 23.5 - 19.8/11.2 = .33rad/s/s --- this is...
  33. Chacabucogod

    Relation Between Electric Frequency and magnetic field rotation speed in a motor

    Hi! I understand that if you have a stator with a a three phase electric signal going into it, both the frqyency and angular velocity of the magnetic field and the electric entry will be the same. Now when you feed it with 2 groups of three phases electric signals you get four poles, or at least...
  34. K

    Understanding Neutron Star Rotation: Calculating Kinetic Energy

    1. The problem statement & given/known data A neutron star is a collection of neutrons bound together by their mutual gravitation. The density of such a star is comparable to that of an atomic nucleus (10^17 kg/m^3). a) Assuming the neutron star to be spherical in shape and of uniform mass...
  35. J

    Negative Poisson's Ratio in Rotated Orthotropic Material

    Hi all, I'm looking for physical and mathematical explanations for a phenomenon I've noticed when working with rotated material properties relative to an XYZ coordinate system. For certain rotations (~40 to ~50 degrees) about a single axis the S12, S13, or S23 components of the compliance...
  36. D

    Calculating Final Rotation of Spinning Wheel

    Hello, I am really struggling with calculating the final rotation of a spinning wheel. I am not even sure if my equation for changing the velocity of the spinning wheel given a coefficient of friction is even correct so I will post it here... change in angular velocity = angular velocity *...
  37. C

    How Is the Formula v=wr Derived in Vector Terms?

    How to derive the formula: v=wr where v is the tangential velocity, w is the rotational velocity, and r i the radius vector? From the attached image, it can be concluded that (each quantity is a vector): w=r x v, also v=w x r, and r= v x w. All three vectors are perpendicular to each other...
  38. X

    Calculating torque required to rotate objects

    I don't have any background in any physics past high school, so I was wondering if someone could help me figure something out. I'm trying to build a robot that involves shooting off a foam bullet from a Nerf gun at different angles. I want to have a motor attached to the center of the gun...
  39. Fizzios

    Gyroscope- Angular Momentum and Torque

    I was reading on gyroscopes, and everything seemed to make sense: the spin angular momentum along the axis of the gyroscope changes due to the torque by gravity, causing precession. However, I can't understand why we are measuring angular momentum (the spin of the gyroscope) from the center of...
  40. R

    Spider Gear Rotation: What Causes It & How Does It Work?

    Whenever the car goes about a differential comes into action.This action generally starts with the spider gear starts to rotate about its axis,this causes increase in speed in one wheel and decrease in other.I want to how this spider gear starts to rotate about its axis what causes it to rotate ?
  41. L

    Newton’s law of motion for rotation clarification

    Hey guys, I'm trying to work through a question but the solution we have been given is extremely vague. I can't seem to figure out what any of the values such as Beta or Tmax are. If I knew how to work those two out, I'm sure I'd be fine from there... See attached image. Thanks in advance
  42. M

    Find the critical rotation rate

    Homework Statement The tumbler in an upright clothes dryer rotates at a critical angular velocity so that clothes passing over the top briefly experience weightlessness. If the radius of the drum is 0.30 m, what is this critical rotation rate? (Express your answer in both radians per second...
  43. P

    Gravitational Field Strength of a Neutron Star: Rotation & Heat Impact

    So let's say we have a neutron star. A neutron star is very massive and very dense therefore it has a very strong gravitational field. But also it is rotating very fast and it really hot. This means it has more energy than if it was stationary and cold. Of course if this neutron star has more...
  44. R

    Calculating rotation based on multiple accelerations

    Hi, I would like to ask you If you could help me with a (I guess quite simple) problem I have to solve. To put it into context: I want to program a helicopter for a videogame with a physical model. So the player controlls throttle, pitch, ... and the game calculates the correct response...
  45. D

    Instantanious center of rotation problems

    Homework Statement [PLAIN]http://i61.tinypic.com/10dwmtv. what is the instantaneous center of rotation for the rigid body. OA = 16 AB = 25 AD = 60 BC = 35 ωOA=2s-1 Homework Equations Vb=ωCB*BC The Attempt at a Solution I am assuming the values angles and vectors from red...
  46. L

    Rotation of Axes: Homework Statement & Equation Solution

    Homework Statement THe x and y axes have been rotated about the origin through a 45 degree angle to produce the X and Y axes.. Thus, a given point P (x,y) has coordinates in the first coordinate system and (X,Y) in the new coordinate system The orignal equation is y=10sech(x). What is...
  47. L

    Rotation of Axes: 5x^3+10x^2+20x+15

    Homework Statement 5x^3+10x^2+20x+15 is rotated through the angle 45 degrees to new xy coordinate system.Whats the equation to the coordinate system? Homework Equations The Attempt at a Solution New X= xcos(theta)+ycos(theta) New Y=-xsin(theta)+ycos(theta)
  48. B

    Calculating Angular Velocity and Energy Dissipation After Collision and Rotation

    Hi there, right now I am making my first steps towards physics, and I would appreciate your help to solve some of my problems. As you surely have already noticed, I'm not english and I guarantee I'll make thousands of errors. Should I make any, please, try to always advise me, and if it's not...
  49. A

    Free Energy from the Earth's Rotation

    Is it possible to generate energy from the Earth's rotation? Imagine a Foucault Pendulum attached to a dynamo shaft? http://www.google.com/patents/US8299636
  50. E

    Time dilation due to changing the speed of rotation of the earth

    I was wondering about how to speed up time because I was bored, so I considered rotating my body clockwise (in the northern hemisphere) in order to speed up the rotation of the Earth by creating angular momentum opposite to that of the earth. I was thinking that this would then speed up the...
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