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. T

    Solve Disk Rotation Problem: Conservation of Energy vs Momentum

    Ok here is the question that is being asked. Note that I know how to solve it one way, but when I go about trying to solve this problem another way that I think should give the the same result, I don't end up with the same result. Question: A disk of mass M and radius R rotates at angular...
  2. K

    Find the formula for X=tP+sQ under a translation and a rotation

    Homework Statement A group of American physicist works on a project where planar lines are in the form X=tP+sQ, where P and Q are two fixed different points and s, t are varying reals satisfying s+t=1. They need to know formulae for the images of the line X=tP+sQ in the following three cases...
  3. B

    How to measure angle of rotation of sucrose

    Hi all! Supposed I have my solution of sucrose, my light source, my polarizer. I shine my light source on my polarizer and plane polarized light passes through my solution, how then do I measure the how much my solution has rotated my polarized light by? And also, what kind of container...
  4. blintaro

    Rotation of a rod about a fixed end

    Homework Statement A 1 m long rod, 200g, is hinged at one end and held out horizontally, then released. What is the speed if the tip of the rod as it hits the wall?Homework Equations Initial energy = final energy rotational energy = .5Iω^{2} gravitational potential energy = mgh kinetic energy...
  5. BrainMan

    Rotation Motion Problem: Finding Acceleration and Tensions in a Pulley System

    Homework Statement A mass m1 is connected by a light cord to a mass m2, which slides on a smooth surface. The pulley rotates about a friction less axle and has a moment of inertia I and radius R. Assuming the cord does not slip on the pulley, find (a) the acceleration of the two masses, (b)...
  6. Entanglement

    Velocity uniformity of rotation in dynamos and DC motors.

    How can velocity uniformity in dynamos and motors be explained? What's the mechanism of that happening ? I'm aware that Newton's first law is involved in that situation where an equal and opposite torque must act on the coil during its rotation so the net torque is Zero and the coil keeps...
  7. E

    The Effect of Planets Rotation within its Galaxy?

    Hello All, A curious person here would like to know if a planet gains gravitational force as it rotates around the center of its galaxy. From what I understand this speed is quite impressive (the speed at which we travel around the center of our galaxy) so I'm wondering if the sheer mass of...
  8. C

    Rotation of coordinates (context of solving simple PDE)

    If you rotate your rectangular coordinate system (x,y) so that the rotated x'-axis is parallel to a vector (a,b), in terms of the (x,y) why is it given by x'=ax+by y'=bx-ay I got x'=ay-bx, y'=by+ax from y=(b/a)x. By the way this is from solving the PDE aux+buy=0 by making one of the...
  9. S

    MHB Arc Length and Rotation, Please Explain this problem

    EDIT: Okay now that the admin has cleaned up my mess, please scroll down to see the correct image and the question on the 3rd post in this thread.
  10. S

    Solve Rotation Matrix Homework: 60,892857 & 12,496875 -4,837500

    Homework Statement A have two points 60,892857 12,496875 -4,837500 70,714286 14,915625 -5,240625 I have to rotate for -0,067195795 radians. Homework Equations ##\begin{bmatrix} {x}'\\ {y}' \end{bmatrix}=\begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha...
  11. WannabeNewton

    Null geodesics and rotation

    Hi all. It is well known that in Schwarzschild space-time, a torque-free gyroscope in circular orbit at any permissible angular velocity at the photon radius (also known as the photon sphere i.e. ##r = 3M##) will, if initially tangent to the circle, remain tangent to the circle everywhere along...
  12. S

    Torque on shaft due to impact loading during rotation

    Hi All, I am trying to determine the correct equations to apply with a problem I have run into at work. Basically I have a shaft with a cutter with straight flutes, I am trying to find out the torque load on the shaft when the cutter flutes make contact with the material they are cutting...
  13. Adjoint

    Earth's Rotation: Questions & Answers

    I need some clarification here. We know that the Earth rotates about it's own axis and also around the Sun. Now my questions are: 1. In the geocentric model of Ptolemy the Earth was at the center of a circle while the planets (and sun) moved along epicycles and the centers of those epicycles...
  14. M

    Acc. due to earth's rotation - Thought Experiment

    Hi All, I have always been haunted by this basic question and will be grateful to anyone who can shed light on this! Please consider this experiment - A cube is kept on a plane horizontal surface on the equator (where the Earth's rotational speed is the maximum). If the friction between...
  15. V

    Rotation of Earth and falling objects

    Hello everyone! If a ball is released from the top of a very tall building, would it land ahead in the direction Earth is rotating (to the east) or would it lag behind i.e the Earth "moves out" from underneath it so it lands to the west? I think it should land ahead to the east since its...
  16. L

    What is the basis of Rotation Curve?

    I have been reading about rotation curves, and the I understand the basics, but I am trying to understand the basis / meaning of the curves? Are the findings based on redshifts of individual stars / "bins of light" at set distances from the centre of the galaxy? And given that the...
  17. S

    Understanding 3D Rotation Transformations

    Hello, First time posting to Physics Forums. I have been thinking about rotation transformations and am a bit confused on how trig works in 3D. In 2D, convention says the positive x-axis points to the right, the positive y-axis points upward, and positive angles are measured from the...
  18. U

    Rotation Spectra - Basic transition question

    Homework Statement In rotations of diatomic molecules such as HCL, the hamiltonian is found to be: \hat H = \frac{\hat L^2}{2\mu a^2} where ##\mu## is the reduced mass, a is the separation. (a) Find the energy levels and separation. (b) Explain why rotational spectra of HCl...
  19. J

    Rotation and circular motion under different simultaneity conventions

    A interesting question came up to my mind, and it's related to the concept of different synchonization methods. If we change the synchronization parameter from 1/2 to some other value, light will have different velocities in opposite directions, which implies that two velocities with opposite...
  20. AotrsCommander

    Tidal Acceleration and planetary rotation

    I'm struggling to get my head around tidal acceleration. I get what is IS, I know how to calculate it, but what I'm not sure is how to apply it in a way that's meaningful to me. So. If we took a stationary Earth (i.e. non rotating, tide-locked) and have the moon magically appear in orbit and...
  21. A

    Rotation of double and triple bonds

    Hi, My textbook does not really go into the details of rotation about a bond. I know single bonds can rotate easily. What about double bonds and triple bonds? The pi bonds would be broken. Does that mean new compounds are formed? My textbook says rotation around triple bonds is easy...
  22. G

    Earth Spin and Rotation: Effects of Fast and Heavy Objects

    If a fast moving and heavy object strikes earth,can it change its spin or rotation or both?
  23. Maxo

    Why is angular velocity perpendicular to the plane of rotation?

    Could someone explain how angular velocity points perpendicular to the plane of rotation? I mean what is a physical explanation of this? (not mathematical) I mean for a rotating object it's easy to see that is has a tangential velocity that always points tangential to the direction of...
  24. N

    Can something moving linearly without rotation have anguar momentum?

    I was doing a question in Taylor book (example 3.3) where a sticky putty is thrown at a stationary wheel. To solve it we use conservation of angular momentum. What I am confused about is that the wheel is initially at rest and has no angular momentum initially. But when the putty is thrown at it...
  25. A

    Calculating Volume of Rotation w/ Shell Method: Integral Difference

    calculate the volume obtained when the area bounded by y=e^x, x=1, y=1, is rotated around x=4. use shell method. Can I see your integral? My teacher gave me the first integral. I found the second one here: BUT: the two do not give the same numerical result: integral of pi((4-lnx)^2-9) FROM 1...
  26. N

    Rotation of PPL by opticaly active compounds (mathematical feeling)

    i read formulae in textbook : [α]λt°C = Θ/L*C ...(i) where Θ is rotation in light and L is length of tube and C is concentration in gm/litre if we consider tube of lenth L and cross section area 'A' then C= M/A*L M is mass of sample so (i) becomes [α]λt°C = Θ/[M/A] so are...
  27. C

    Rotation and translation of basis to remove cross terms

    So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...
  28. G

    Model Flow Over Bombs: Rotation & Drag Coefficients

    I'm working on a project that will find the coefficient of drag on bombs with various added drag features by modeling flow over the bomb at various angles of attack using CFD. The problem is that I'm not sure if bombs with fins rotate while they are falling due to gravity, and if so, how I...
  29. P

    Max Distance Up Ramp for Rotating Sphere

    A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if : 1- the ramp is frictionless...
  30. H

    Volume of Rotation around the y-axis for y=1/x+2 and x=1

    Homework Statement Hello! English is not my native language so I hope the terminology is right. Q: Find the volume generated by the curve y=1/x+2, positive x- and y-axis and the line x=1. Calculate the volume obtained by rotation around the: a) x-axis b) y-axis Homework...
  31. W

    Finding the angular velocity of a cube about different rotation points

    Homework Statement A homogeneous cube of sides l is initially at rest in unstable equilibrium with one edge in contact with a horizontal plane (θ = 45 degrees initially). The cube is given a small angular displacement and allowed to fall. What is the angular velocity of the cube when one face...
  32. H

    Rotation in a rotating superfluid

    Suppose you have a body floating in a rotating superfluid. Maybe a speck of dust. Would it rotate? What if you have two bodies connected in some way. Would this system rotate around its center of mass?
  33. W

    Rotation of a cone rolling on its side without slipping on a plane

    Homework Statement A uniform right circular cone of height h, half angle α, and density ρ rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time \tau. Find expressions for the kinetic energy and the components of...
  34. F

    Why Does the Moment of Inertia Change in Torque-Free Rotation?

    Torque Free Rotation...again... Hello Forum, I have read an old, but good, thread about torque free rotation: https://www.physicsforums.com/showthread.php?t=405781 I am still unclear on how, from the inertial (lab) frame of reference, the moment of inertia I, which is a tensor with 9...
  35. J

    Alternative to solids of rotation?

    So I was doing my calc homework when I stumbled upon this thought: lets say you were trying to find the solid of rotation of y=x^2 around the x-axis over the interval [-2,2]. the traditional method would entail pi * integral from -2 to 2 of (x^2)^2 dx while this is easier for a simple...
  36. D

    Is a reaction moment/force created in off-center constrained rotation?

    Assume that the arbitrary-shape object shown has a torque applied at the black X with a circle, and is free to rotate about the X axis. Assume that the object is also constrained by a pin at this torque input point, parallel to the X-axis. The CG of the object is the blue plus sign, and there...
  37. K

    Rotation problems - Torque & Angular Momentum

    I'm having trouble with two review questions: 1) Julie has been hired to help pain the trim of a building, but she is not convinced of the safety of the apparatus. A 5 m plank is suspended horizontally from the top of the building by ropes attached at each end. Julie knows from previous...
  38. Saladsamurai

    Rigid Body Rotation: Proving/Disproving \vec{R'} Direction

    Homework Statement This is not a HW problem, but something I am trying to prove/disprove for my own knowledge. I have a tube pinned at both ends and inclined in the x-y plane. The pin locations can both move freely in space but subject to the constraint that the tube will not stretch or...
  39. M

    Rotation of Rigid Bodies HW

    Homework Statement PS:The compound gear to the right is located inside a truck, whose engine rotates the driving gear with torque of 816 N*m. Assume that in the figure to the right, each of the smaller gears have a radius of 5.0 cm, and the larger gears have a radius of 25cm. Also, assume...
  40. A

    Rotation dynamics, dealing with impulse and oscillation

    Homework Statement A homogene rod with length "l" is placed vertically, and a nail is stabbed on the top of the rod (now the rod has an axis). And then an impulse is given on the rod with the separation between the impulse given to the rod's axis is "d". Earth gravitational acc is represented...
  41. A

    Rotation dynamics, dealing with impulse and oscillation

    A homogene rod with length "l" is placed vertically, and a nail is stabbed on the top of the rod (now the rod has an axis). And then an impulse is given on the rod with the separation between the impulse given to the rod's axis is "d". Earth gravitational acc is represented as g, the mass of the...
  42. N

    Rotation linear transformation

    Homework Statement Given below are three geometrically defined linear transformations from R3 to R3. You are asked to find the standard matrices of these linear transformations, and to find the images of some points or sets of points. a) T1 reflects through the yz-plane b) T2 projects...
  43. S

    Rotation: Speed of an object as it slips off a rotating disk

    Homework Statement A 75g mass sits 75cm from the center of a rotating platform undergoing a uniform angular acceleration of 0.125rad/s . The coefficient of static friction between the mass and the platform is 0.250. What is the speed of the mass when is slides off? A. 0.889 m/s B. 1.26...
  44. U

    Understanding Energy and Frequency in Rotation Spectra

    I don't really understand the explanation given in Binney's text about: Hamiltonian is given by: H = \frac{\hbar^2}{2} \left( \frac{J_x^2}{I_x} + \frac{J_y^2}{I_y} + \frac{J_z^2}{I_z} \right) Orient axes such that ##I_x = I_y = I##. H = \frac{\hbar^2}{2} \left( \frac{J^2}{I} +...
  45. M

    Calculating Solar Rotation Using Sunspot Observations

    Homework Statement Calculating solar of the sun through observing sunspots. We are given a series of photos of the sun over a period of time where we can see sun spots. I am assuming the way to calculate would be to work out the longitudinal angles of the sun spots in the different photos and...
  46. anorlunda

    Planes of Rotation in Solar System & Beyond

    I'm not sure if this belongs in Astronomy or Astrophysics. Todays APOD featured the rotation of the sun about its own axis. It seems to me that the axis of rotation of the sun should be aligned with the axis of rotation of the plane of rotation of the planets, i.e. the ecliptic, or more...
  47. Y

    Simultaneity, Rotation & Gravity: Agree?

    We have had a number of threads on how to synchronise clocks around a rotating ring. One method of doing this is to start all the clocks on the ring via a signal from the centre of the ring. This method has the advantage of being transitive, but has the disadvantage that the local one-way speed...
  48. J

    Why is a non-rotating object moving in a circle impossible?

    Why do celestial bodies follow different laws of physics than terrestrial bodies? A non-rotating object has a point on its axis, or axle, continually aligned with a point on the object. An axis is virtual, or imaginary; an axle is real and we live in a real physical world. In a real physical...
  49. M

    Nuclear Rotation: Electrons & Nucleus Vibration in Atom

    we know that an electron rotates about its own axis.similarly does the electron too rotates about its own axis? and does nucleus and electron vibrate in an atom?
  50. Q

    Does the rotation of an electron have any meaning?

    Does the "rotation" of an electron have any meaning? Not sure if this is the right subforum, but thinking of this was rather head-ache inducing. Is there any sensible meaning to claiming that an electron rotates 360 degrees? Intuitively I would initially say yes, but on second thought I would...
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