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. Manasan3010

    Linear momentum or Angular Rotation

    I think the answer is ##\frac{mV}{M}## but I am not sure. Won't the cylinder tries to rotate due to the collision at one end? Is this anything related to Angular Momentum? The Answers given were,
  2. Plat

    Radiometer rotation speed as function of pressure

    I am experimenting with using a radiometer as an approximate indicator of pressure in my homemade high vacuum system, running a small turbo pump. I am interested in the relationship between pressure and vane rotation speed, with light intensity being constant. I have only been able to find...
  3. S

    MHB Partially unpicking coordinate rotation

    I measured a vector many times, and then processed the data using a computer program. The program did a great many useful things, including rotate the coordinate system about all three axes. I have measured values for x, y, and z along the original axes. The program helpfully gave me the values...
  4. F

    What Is the Instantaneous Center of Rotation and How Is It Chosen?

    Hello, A force couple is compose of two forces of equal magnitude, opposite direction and parallel lines of actions separated by a distance ##d##. The moment due to a force couple is called a pure moment because its value does not depend on the point about which the moment is computed. The...
  5. J

    Auto/Motor How Can I Make My DIY Swirl Push Maker Create Perfect Spirals?

    Hi Everyone! I am trying to a DIY project to make a food maker. I am 50% succeeded with that and need help for the remaining 50%. The idea is to produce the output shown in the first image. That food is made with a flour. So I have the setup a pressing machine shown in image2. In this I was...
  6. J

    Energy required to change a sphere's axis of rotation OR pole location

    There is a disaster movie about a global cataclysm that results in Kilimantzaro becoming the north pole or something. Maybe this is plausible in terms of plate tectonics. Or maybe not. But I've got another question, a purely mathematical one: if the Earth were a solid sphere, no plates and such...
  7. C

    How Fast Can a Ring with Uneven Mass Distribution Roll Without Hopping?

    Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure. Find the maximum velocity the ring must roll so that it doesn't...
  8. N

    Rotating with slipping to rotating without slipping?

    It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.
  9. A

    How to stop a steering wheel using an electric motor?

    Problem Statement: i have a steering wheel mounted on an electric motor, and i want to stop the driver from going beyond a certain angle. i can read the torque applied by the driver, and the steering wheel angular velocity as well. how can i stop the steering wheel, without sending it harshely...
  10. Z

    I Pauli spin matrices under inversion and 180 degree rotation?

    How do the Pauli spin matrices transform under an inversion ? I think I mean to say the 3 dimensional improper rotation which is just in 3 dimensional matrix notation minus the identity - so exactly how are the 2 dimensional Pauli spin matrices changed. And under a 180 rotation do the 'y' and...
  11. cianfa72

    I Rotation or acceleration defined without relation to something else

    Starting from this post, we are able to define the concept of (proper) acceleration or rotation without any reference to something else About this definition which is the physical meaning of gyroscopes axes pointing in three mutually orthogonal spacelike directions ? In other words, from a...
  12. S

    Does mass distribution affect an object's ease of rotation?

    Say we have the moment of inertia of any object. If we removed the radius squared part of the moment of inertia and just leave mass, would heavier, further-from-the-axis mass on one end of the object be as easy to rotate as the lighter mass, maybe closer-to-the-axis of rotation on the other end...
  13. N

    How would we increase the rotation rate of very large structures in deep space?

    Imagine a 400-meter-long pipe with a 1600-meter diameter, floating in inter-planetary space. It is spinning at 0.5 gravity along its major axis and there are no secondary-axes spins. We need to increase rotation to 0.85 g. Its density is a uniform 2.3 kg/m³ and it weighs 49,120,056 kg. Thanks to...
  14. Curtiss Oakley

    Problem Concerning Rotational Kinetic Energy

    For parts A and B I used energy to find the vcom and omega, but that won’t work for C. I have an answer by combining the three formulas that use acceleration above. My answer for alpha=-5g/3r. The next two are easily solvable if you find C, but I still feel like I’m missing something. Any help...
  15. Lardos

    A Ideas for determining the volume of a rotating object

    Hello everybody, I am currently working on an experiment investigating the formation of planets. I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together). From the imagery I can see those agglomerates which are build up by smaller...
  16. H

    Find an expression for the power developed at the given rotation rate

    So for part (a), I used the fact that 1/N = the period = T. I solved for the velocity, where i got v=2πRN. I plugged that v into F=(m v^2)/R, which is the centripetal force, but also the force of friction. My answer to part (a) is 4(π^2)mR(N^2). I'm a bit confused on part (b). I know that...
  17. B

    A question about magnetism that causes a wheel-loop to rotate

    This question is from 1977 AP Physics C so I suppose it would be clear enough, but I am confused about question c. Question a is easy (it rotates counterclockwise), question b too (Στ=6*rxF=6*r x (I*i x B)=0.06). Question C is where I am stuck. The diagram provided with the question looks like...
  18. I

    I Exploring Planar Rotation Commutativity via Direct Calculation

    Commutativity for planar rotations follows from a direct calculation. What does 'direct calculation' mean?
  19. F

    Calculating Centripetal Acceleration in a Vertical Loop

    $$mg(0.45) = mg(R + R \cdot cos(\frac{π}{3})) + \frac{1}{2}mv^2$$ $$v^2 = g(0.9 - 3R)$$ The centripetal acceleration during the "flying through air" will be given by gravity $$mg \cdot cos(\frac{\pi}{3}) = \frac{mv^2}{r}$$ $$R = \frac{1.8}{5}$$ But my book says $$ R = \frac{1}{5}$$
  20. Romain Nzebele

    How to calculate angular speed?

    Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...
  21. R

    Pump rotation to provide pressure or volume flow

    how much rotation needs to start volume flow for a adjustable variable pump?.I get it 5pi from the book. Is there any rule that it needs such rotation to start volume flow. From where I get it?I think that pump designer does not give the information on the manual.
  22. J

    What Forces Affect the Rotation of a Submerged Disc?

    1. A 20-lbf disc with diameter 18" and thickness of 3" is held static while completely submerged in water. Upon release of a lock, the disc experiences a torque from a torsional spring that causes rotation about its center of mass along the x/y axis (think coin toss, not wheel). If the spring is...
  23. ?

    Rotating sphere which separates into hemispheres

    Hi all, The scenario I'm considering is a solid sphere (of uniform density) rotating with constant angular velocity when it abruptly splits into two hemispheres along a cut which contains the rotation axis. The hemispheres will begin to separate; if, for example, we consider the rotation to be...
  24. K

    I Fermi-Walker: Showing Rotation in Plane of 4-Accel & 4-Vel

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  25. mohammed othman

    Force due rotation about axis parallel to centroidal axis

    in the case of a disc rotating about the centroidal axis and having an unbalanced mass we used the formula F(force)=m x r x w^2, where r is the distance from the center to the center, m mass of the unbalanced, w rotational speed in the case of a disc rotating about axis parallel to the...
  26. M

    Rigid Body Rotation relative velocity question

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  27. S

    Will the Internal Gear Rotate with Gear 1? - Gear Rotation Question

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  28. brotherbobby

    How Does Adding Masses Affect the Angular Velocity of a Rotating Cylinder?

    Problem : A cylinder of mass ##M## and radius ##R## rotates with an angular velocity ##\omega_1## about an axis passing through its centre of symmetry. Two small masses each of mass ##m## (small in comparison to the radius of the cylinder) are glued to either of the two circular faces of the...
  29. J

    Formulas for Rotation and Translation

    Given the coordinates ##P = (3,4)## , find the coordinates of ##P"(x',y')## when the origin is shifted to (1, –2), and the axes are rotated by 90° in the clockwise direction. I attempted to solve this problem using the following formulas : ##x = X + h## and ##y = Y + k## for translation of the...
  30. Spinnor

    I Set of possible rotations of a 3D object and the rotation history

    I am trying to understand the picture below which is of a contractible and uncontractible loop in what I would call (proper name?) "rotation space", where "rotation space" is a solid ball of radius π with opposite points on the surface of the ball identified, each point of the ball representing...
  31. A

    I Dark energy and the rotation curve of spiral galaxies

    Recently I have studied that from the rotation curve of spiral galaxies, the nearly constt. behaviour of velocity of the stars situated far away from the central core suggests mass(r) ~ r ,rather than 1/√r as expected. Are there any other theory which proves the existence of dark energy ??
  32. G

    Calculating angles of rotation for 2 interconnected levers

    Hi all, This isn't really "homework" - it's a personal project I'm working on. I'm attempting to animate some mechanical controls of a turbine engine in Adobe After Effects. Having a hard time with the math for "rotating two interconnected points". Here is a photo for visual aid: It's...
  33. A

    I Integration being unchanged after rotation

    This question is about the general 1 loop correction to the propagator in QFT (this is actually not important for this question). Let's say we have an integral over an integration variable x, and this x ranges from ##-\infty## to ##\infty##. If we look at this integration contour in the complex...
  34. E

    Coriolis force and the Earth's rotation

    Homework Statement A body is thrown as shown in the picture (0°<x<90°). In what direction the body will the body move in relation to the point it was thrown from - east or west (assume the distance between the point the body was thrown from and the point it lands at is no more than a few...
  35. F

    Rigid body kinematic motion and rotation

    Hello everyone, A rigid body is a system whose points, pairwise, always keep a constant mutual distance. Let's say the body is in a certain configuration ##C_0## at time ##t_0## (which means that each point has a specific velocity and position relative to a fixed lab reference frame) and the...
  36. F

    Deriving the Matrix for a 3 dimensional rotation

    Homework Statement [/B] The problem consists of deriving the matrix for a 3 dimensional rotation. My approach consisted of constructing an arbitrary vector and rewriting this vector in terms of its magnitude and the angles which define it. Then I increased the angles by some amount each. I...
  37. JGHunter

    B What factors influence the flattening of planets in our solar system?

    I was looking at the numbers regarding the planets in our solar system, their bulge, their flattening ratio and their rotational speed. I know that rotational speed plays a role in this flattening, however what else is at play? For example, Earth's flattening ratio is nearly 1:300, whilst Mars...
  38. R

    Why does the axis of rotation pass through the metacentre?

    When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is called the...
  39. F

    I Rotation profile for radiative zone of Sun - convection

    I am exercising on Stellar Physics topics and in particular the questions below: 1) First of all on the rotation profile for the radiative zone: I know that unlike the convective zone, where the rotation varies mainly in latitude (faster at the equator than at the poles), the radiative zone...
  40. J

    Maximum and minimum speeds in a moving cube

    Homework Statement A rigid cube in the figure moves in space. At a certain time ##t## its front face ##ABCD## is vertical and the velocity of vertex ##A## is vertical down ##v## while the velocity of its vertex ##D## makes an angle with the vertical and has magnitude ##v_{2}## while lying on...
  41. P

    How to find the normal force of a car jack lifting a car

    Homework Statement A car is lifted vertically by a jack placed at the car's rear end 40cm off the central axis, so that the weight of the car is supported by the jack and the two front wheels. The distance between the front wheels is 1.60m, the distance from the axis connecting the two wheels...
  42. R

    A Integration with Euler angle of rotation matrixes

    Hello, I was struggling with solving a specific integral. I know that I can rewrite the exponential matrices and the range of the three Euler angles. However, I am not sure I should I write in terms those three Euler angles.
  43. S

    Moment of inertia of door rotation

    Homework Statement A 23 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge? Homework Equations I = I_cm + MR^2 The Attempt at a Solution I = I_cm + MR^2 I = (1/12)(23kg)(0.95m)^2 +...
  44. wolram

    B Why does MOND fit rotation curves so exactly?

    I have been reading this article https://tritonstation.wordpress.com/2018/10/05/it-must-be-so-but-which-must/ so why does Mond fit so well over dark matter models?
  45. S

    Center of mass and rotation question

    Homework Statement A 100 g ball and a 250 g ball are connected by a 34-cm-long, massless, rigid rod. The balls rotate about their center of mass at 150 rpm . Homework EquationsThe Attempt at a Solution I solved by first getting the center of mass, then converting rpm into m/s I treated rigid...
  46. omega_minus

    Rotational dynamics of mono-domain magnetic nanoparticles

    Hi, I have a question about the rotation of a single-domain magnetic nanoparticle that is suspended in a ferrofluid immersed in an external field. Specifically, I am trying to work out the path that a normal vector on the surface of the sphere traces out in time. There are 2 ways the...
  47. J

    What is the magnitude of the acceleration of cylinder's com?

    Homework Statement In the figure below, a constant horizontal force app of magnitude 18 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 19 kg, its radius is 0.11 m, and the cylinder rolls smoothly on the horizontal surface. (a)...
  48. Krushnaraj Pandya

    Inelastic collision of ball and rod - rotation problem

    Homework Statement A uniform rod of mass M and length l is hinged at the center. a particle of mass m and speed u sticks after hitting the end of the rod. find the angular velocity of the rod just after collision Homework Equations Energy conservation-0.5mu^2=0.5(m+M)v^2 Angular momentum...
  49. S

    Solving for Rotation in a Force & Torque Equation

    Homework Statement Homework Equations torque= F*r*sintheta total force on y= 0 The Attempt at a Solution how come it will rotate in this situation?? espicially that he is ignoring the weight force of the rod! i knew that i ignored the mass of the rod when he said total force on y= F -F. if...
  50. Krushnaraj Pandya

    Ring and solid sphere rolling down an incline - rotation problem

    Homework Statement A solid sphere, hollow sphere, disk and ring are released simultaneously from top of a incline. Friction is sufficient to prevent slipping of hollow sphere- what will reach the bottom first? Homework Equations a in pure rolling down an incline=gsinθ/(1 + I/mR^2) The Attempt...
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