Rotation 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. sshanker

    Gear Rotation puzzle is confusing 50:10 GR but 6 rotations

    A gear A has 50 teeth and another B has 10 teeth, how many times does the small gear rotate around the big one? I thought 5 but its 6! Note: The gear is curved like 360 degrees.
  2. P

    Drum rotation, lateral loads and point of pull

    I farm and have built water control devices for my rice operation that use a cable and drum setup. The moving part is a 24"water tight rotary union that we rotate with a cable that originates in a dual spool winch above the center line of rotation for the drum. The winch cables secure to the...
  3. M

    Find the volume of the solid formed by the rotation around the y=0

    Hi, I find this... Please tell me your opinion on this. Thanks.
  4. Wi_N

    Calculating the surface area of a solid of rotation

    For some reason I have become very unsure but my gut feeling says i can calculate y=(1-x^(a/b))^(d/c) I already know the formula for calculating the volume. but can transfer the whole thing as a function of y(x) and take the integral then as a single integral?
  5. W

    Effects of a Change of Direction of the Rotation of the Earth?

    Summary: What if the Earth rotated about its axis in a N-S direction instead of doing so in an E-W direction. Hi, Just curious: What would be the effects/consequences if the Earth rotated about its axis in a North-South ( or South-North) direction instead of an East-West one as it currently...
  6. B

    I Questions about Rotation Groups in Physics

    I have questions concerning group theory, esprecially Rotation groups. The first is: Are rotations groups f.ex. SO(2) defined for rotations in the actual physical 2 dimensional plane or are general rotations in any 2 dimensional space included? Someone wrote that "the action of an element of...
  7. A

    What is the formula for calculating torque in a rotating pyramid?

    torque=Force*radius*sin(theta) center of mass x direction = ( 0(6 x 10^9 kg)+ (118m)(6 x 10^9 kg)+ (236m)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 118m center of mass y direction = ( 0(6 x 10^9 kg)+ (140m)(6 x 10^9 kg)+ (0)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 46.7 m radius = (118^2 + 46.7^2)^(1/2) =...
  8. J

    Translational and rotational velocity

    For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
  9. L

    Is rotation a relative property?

    I was recently trying to explain to a grandchild the relative nature of velocity (the different paths of a coin dropped by a passenger on a train, as seen by the passenger on one hand and a trackside observer on the other), and the invalidity of the concept of absolute velocity. For some reason...
  10. R

    Rotation of a roll by a driving wheel

    The bigger circle is a hollow cylinder (steel) with a length of 0.6m and a diameter of 0.133m and a mass of 8kg. The 2 smaller circles are rubber wheels with a diameter of 0.080 and mass of 0.2kg. Both the roll and the wheels have ball bearings and are mounted on a shaft. On both the shafts of...
  11. B

    Newton's Second Law for Translation and Rotation

    Answer choices: N2L for Translation, N2L for Rotation, Both, Either1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. My solution = N2L for rotation 2. You are asked to find the angular acceleration of a low-friction pulley due to a...
  12. K

    I Question about Galactic Rotation curves in the Milky Way galaxy

    The graph in Wikipedia, article Milky Way, section Galactic Rotation, shows the actual rotation speeds in blue and the calculated speeds due to observed mass in red. (The graph is to the right of the article.) At about 3 kpc the actual speed is about 205 km/s. To account for the decrease in...
  13. Kaushik

    A uniform rod allowed to rotate about an axis and then it breaks

    A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...
  14. brotherbobby

    Tension in a rotating rod at various places

    (The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite). I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...
  15. SpaceThoughts

    Is the Spinning Wheel's Rotation Maintained? | Investigating Kinetic Energy

    Hi. I searched and found no answer to this simple question: Is the spinning wheel in this videoclip keeping the same rotation (kinetic energy) when flipped upside down and back again? (if we forget about friction)
  16. deZordine

    Airplane flight and the rotation of the Earth

    If a plane departs from the North Pole (where the Earth's rotation speed around its axis is 0 Km / h) on the median line to Romania, around the 45th parallel (where the Earth's rotation speed around its axis is 1178, 80 km / h) would the plane reach its destination only by flying to *South* (...
  17. P

    I Measuring Galactic Rotation: How & What We Know

    How have we been able to measure galactic rotation? I have seen graphs showing the relation between the velocity of stars in a galaxy and their distance from the center. These graphs show that the observed velocities of stars are much faster than they are expected to be, particularly ones that...
  18. The Bizarre Behavior of Rotating Bodies, Explained

    The Bizarre Behavior of Rotating Bodies, Explained

    Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
    • Swamp Thing
    • Media item
    • moment of inertia rotation
    • Comments: 0
    • Category: Pop Science
  19. S

    Yo-yo on an accelerating conveyor belt

    First off, I was wondering if the acceleration of the conveyor belt can be considered a force. And I'm not exactly sure how to use Newton's second law if the object of the forces is itself on an accelerating surface. Also, I don't know whether it rolls with or without slipping. I thought I could...
  20. Diracobama2181

    How to Determine the Axis of Rotation

    Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I...
  21. 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,
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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...
  28. 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.
  29. 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...
  30. 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...
  31. 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...
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. I

    I Exploring Planar Rotation Commutativity via Direct Calculation

    Commutativity for planar rotations follows from a direct calculation. What does 'direct calculation' mean?
  39. 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 $$ R = \frac{1}{5}$$
  40. 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...
  41. 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.
  42. 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...
  43. ?

    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...
  44. K

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

    Is it difficult to show that a Fermi-Walker "rotation" happens only in the plane formed by a particle four-acceleration and four-velocity?
  45. 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...
  46. M

    Rigid Body Rotation relative velocity question

    This is a question about the concepts behind rigid body rotation when we use relative velocity. In general, let us say that we have a rigid body and on it are two points, A and B, which are moving with velocities vA and vB respectively. These velocities are in random directions. The theory...
  47. S

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

    If gear 1 fits into the internal gear and is made to rotate, will the internal gear rotate with gear 1? https://imgur.com/gallery/ELYZoRb
  48. 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...
  49. 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...
  50. 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...
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