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. abushaheer

    Can We Outrun a Moving Train? 🚆 Exploring Speed vs. Rotation

    if we fly over a moving train at the speed of train can we out run it?? it not, how come we fly at 255m/s when Earth is rotating at 460m/s and we reach from paris to america
  2. L

    What is the direction of friction on a plate on two rotating wheels?

    Homework Statement A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions. The separation between the wheels is L. The friction coefficient between each wheel and the plate is N. Find the time period of oscillation of the plate if it is...
  3. stipan_relix

    A homework assignment including rotation of a rigid body

    Homework Statement The problem is this: A car is evenly slowing down from 30 km/h to 0 in the time of 2 seconds. Radius of its wheels is 30 cm. What is its angular acceleration and what total angle will the wheel describe until it stops? How many turns does the wheel make and what is the length...
  4. T

    Determine speed needed to cause rollover of car hitting ramp

    Hello, So my issue is as follows: You have a car going at a constant speed and the right side of the car hits a ramp which causes that side to elevate and cause the car to rotate about its x axis. What I need to figure out is how fast does the car need to hit the ramp to cause a rollover...
  5. A

    Moment reaction with rotation and offset CG

    Hey folks, I created and verified a model with hand calculations, and decided to re-use my same logic.. Which now is giving me false numbers. Was wondering if you guys could help me out. Setup/Verification (See attached Reaction_Forces picture): Body in motion being held down by straps...
  6. Leonardo Muzzi

    Will Earth's Rotation Ever Synchronize with its Orbit Around the Sun?

    Will the Earth's rotation someday be synchronized with its revolution around the Sun (one rotation on the axis per revolution), such as the Moon around the Earth? If not, why?
  7. c3po

    Find matrix representation for rotating/reflecting hexagon

    Homework Statement Consider the set of operations in the plane that includes rotations by an angle about the origin and reflections about an axis through the origin. Find a matrix representation in terms of 2x2 matrices of the group of transformations (rotations plus reflections) that leaves...
  8. G

    Closest celestial object that has bound synchronous rotation

    Homework Statement What is the closest celestial object that has bound synchronous rotation with another object? Homework Equations - The Attempt at a Solution I am almost sure it's Moon.
  9. Q

    Direction cosine matrix of rolling disk on circular ring

    Hey all, I'm stuck on this problem and not sure how to proceed/if I'm in the right direction. Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below (A) find the direction...
  10. Z

    How to Calculate Rotation Curves for a Spiral Galaxy?

    I hope this is in the right forum. I'm trying to see how to calculate rotation curves for a spiral galaxy. The data I have is brightness profile (mag/arcsec^2) and observed rotation curve - to see how it fits. from what I found I need the total mass, and for that I need the surface mass density...
  11. S

    Rotation period of electron orbiting a proton

    Homework Statement An electron is rotating around a proton (at rest) in a perfect circular orbit. If the radius of the orbit is r=10^-10 m, how long is the rotation period [hint: the radial acceleration is entirely due to the electric force] k=9*10^9 q=1.6*10^-19 Homework Equations 1...
  12. T

    How Do You Calculate Turntable Rotation and Acceleration?

    I know this is not typical and you aren't suppose to solve the problem for the person just give hints, however my teacher has not taught this and expects us to know it. For whatever I cannot grasp how to do this any help would be great thank you! 1. Homework Statement The turntable of a...
  13. CaptCoonoor

    Rotational Motion - Disk-Disk Collision problem

    Hey Guys, Can you tell me how to solve this one, Need not give me direct answers but just take a look at this : Consider two disks A and B of equal radius, let m1 be the mass of disk A and m2 be the mass of disk B, Both are moving towards each other with Velocity v1 and v2 respectively, If they...
  14. AdityaDev

    Explaining Rotational Mechanics: Friction and Stationary Disc

    When you put o disc on top of a plank and if you pull the plank, the disc rotates but stays stationary. Here the friction between the plank and disk produces an unbalanced torque and hence it spins.But this friction should also cause an acceleration in the disc right? Then why does it remain...
  15. Pterosaur

    Has the Number of Galactic Revolutions Influenced Spiral Galaxy Formation?

    Greetings all, First time poster and an absolute neophyte, please forgive my utter cluelessness in advance. So I was reading "Why does the Milky Way rotate?" (http://phys.org/news/2015-02-milky-rotate.html), and it brought to mind a question that's niggled at me every so often when my...
  16. Buckethead

    Need data for galactic rotation curves

    I'm looking for sources of data for galactic rotation curves but need not only the observed rotation curves but also the expected (Keplerian) curve data to load into a spreadsheet to experiment with. After extensive searching I found a few pockets of data for observed velocities but not for...
  17. H

    Relative Motion & Rotation of Axes of Reference

    I'm still very early on in my reading, so forgive me if this question isn't coherent. In the "historical introduction" section of the 1920 University of Calcutta translation of the original papers of Einstein and Minkowski available via the MIT online archive, mention is made of the fact that...
  18. P

    How do I arrest a rotation at any angle

    How would I go about creating something like a hatch, that could be arrested at any instance. I am looking for a solution for a 0-90, 90-180, and 0-180 degree range. A 360 degree solution such as a whiteboard, would work just as well. If you know how this can be made, or know a link that...
  19. R

    Rotation period of a space station

    Homework Statement To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of If the centrifuge diameter is 13.5m , what should be its rotation...
  20. T

    Volume of Rotation: Find Area Rotating Around Line

    Homework Statement Find volume when the area rotates around a line. Homework Equations x=y^2 x=1-y^2 about x = 3 The Attempt at a Solution Could someone please check my formula for Area? I have pi[ (3-(y^2))^2 - (2-(y^2))^2 ] which gives me the integral pi[5y-(2/3)y^3]. I think...
  21. R

    What do I need to learn in order to describe this?

    Hi! I'm new here, so I apologize on beforehand for any mistakes I may make (grammar/wrong thread etc.). Currently we are doing a project for our exam in my class, and in my group we chose to focus on the following scenario: On a spinning "plate" (you know, like a merry-go-around... sorry, I'm...
  22. T

    Volume Rot. Region: Find Vol. Bounded by Curve, Y=x^2 & x=y^2, Rotated about Y=1

    Homework Statement How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines? I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance...
  23. C

    Angle of rotation of a bead embedded in a support

    Hello Everyone, I want to explain my problem. I am quite starter in Ansys... I have modeled a simple bead embedded in a support as you will see in the screenshot. Then I apply a torque onto the bead to make it rotate a bit. I want then to calculate the angle of rotation the bead I have made...
  24. C

    Torque needed to mantain a disk rotating

    Hello, first post! I'd apreciate some help on finding out the calculus for knowing the motor's torque needed for mantaining 2 vertical disks ø46cm, 30kg each at 300rpm, taking into acount 3 generic bearings friction that hypotetically is 0.5Nm friction torque I'm having some trouble trying to...
  25. P

    Calculating change in linear position

    I would like to calculate the change in linear position of a point on a bar whose center of mass is changing as the bar rotates. Assume an angular velocity of pi-rad/s, a negligible mass for the bar, and a mass of 1-kg for the weight (which is what is moving and causing the center of mass to...
  26. davidbenari

    Prove to myself that rotation is a linear transformation?

    How do you prove that rotation of a vector is a linear transformation? It's intuitive (although not completely crystal clear to me) that it is a linear transformation at the 2d level, but how do I prove it to myself (that this is a general property of rotations)? For example, rotate vector...
  27. 2

    Why is kinetic energy due to a planet's rotation treated as negative?

    Homework Statement I am trying to answer the following question: Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain...
  28. A

    Rotation matrix multiplied by matrix of column vectors?

    Hey, let's say that in 2D space we have a 2x2 rotation matrix R. Normally you could multiply this rotation matrix by a 2x1 column matrix / vector X. In that case it would be XR to get the vector rotated in the way described by R. Now what I'm wondering is, what if I had 3 column vectors that I...
  29. T

    Could a Tidal Lock Cause the Earth to Stop Rotating?

    So my co-workers and I have had a dispute after hearing a podcast on NPR about Earth's rotation. One question was about what would happen if one side of the Earth always faced the sun (tidal locked) and another question was about what would happen if the Earth stopped rotating. From what I've...
  30. Amaterasu21

    Question about rotating reference frames

    Hello, I have a few questions about rotation and relative motion. Suppose we transport the proverbial spinning ice skater used to demonstrate conservation of angular momentum to beginning physics students to a universe with only her and two planets. She is now spinning in deep space...
  31. W

    Clockwise rotation of the reflection coefficient w/ frequency

    It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...
  32. W

    Rotation of the reflection coeff. at Smith Chart w/ frequency

    It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...
  33. AdityaDev

    Is the expression still valid for large differences in radius?

    If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R is this expression correct? (When ball reaches lowest point) ##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2## where...
  34. H

    Circular motion in planets and satellites

    Homework Statement A spaceship in outerspace has a donut shaped with a 500 m outer radius. The inhabitants stand with their heads towards the center and their feet on an outside rim. Over what time interval with the spaceship have to complete one rotation on its axis to make a bathroom scale...
  35. C

    Perpendicular force with a spiral

    Homework Statement A red Archimedean spiral is fixed to the ground. An external motor turns a grey support clockwise at w, the support can only turn around itself. On the support there is one orange disk that doesn't turn around itself at start. A stem is on the support. That stem: - turns...
  36. J

    Mounting a small ultrasonic sensor to a continuous rotation servo

    I'm an Arduino electronics hobbyist I'm not a professional electrical engineer. How would I mount a small ultrasonic sensor on a continuous rotation servo, without tangling the wires? How would I fix this problem easily and what's the most common way to mount electronics in a rotating object...
  37. E

    Rotation in the Kerr metric?

    I understand the Kerr metric has an off-diagonal term between the rotation and the time degrees-of-freedom? That a test mass falling straight down toward a large rotating mass from infinity will begin to pick up angular momentum? Is that what’s called “frame dragging”? Did the Gravity Probe B...
  38. M

    Centripetal force and rotation

    I noticed that if you swing a ball around attached to a string with a centripetal force. The ball also rotates. What causes this rotation? Is there always rotation when there's a centripetal force? does an object orbiting the Earth always face the same way as it orbits?
  39. D

    Does Particle Spin Refer to Rotation?

    Does spin for particles actually refer to spin as in rotation? Or does it mean something else. Do all elementary particles rotate? Without a magnetic field can you have rotation or does the rotation create the magnetic field?
  40. P

    Having trouble understanding General moment

    On the website http://www.real-world-physics-problems.com/physics-of-billiards.html they take this equation ∑Mg = IG∝ where ∝ = -agx/r for the rotation of a rigid body where there is no slipping They then change the equation to F⋅(h-r) = IG(-agx/r) why is ∑MG = F⋅(h-r) when ∝= -agx/r?
  41. E

    Rotation formula Complex numbers

    Homework Statement If arg(\frac{z-ω}{z-ω^2}) = 0, \ then\ prove \ that\ Re(z) = -1/2 Homework Equations ω and ω^2 are non-real cube roots of unity. The Attempt at a Solution arg(z-ω) = arg(z-ω^2) So, z-ω = k(z-w^2) Beyond that, I'm not sure how to proceed. Using the rotation formula may also...
  42. CaptainSiscold

    Angular kinematics: determining satellite orbital radius

    So, I'm working on my semester finals for my high school physics class, and I've run across a problem that has me stumped. I've included the pertinent material below. Homework Statement A rocket with a mass of 2kg and traveling at 14,008.34 meters/second loses 10% of its velocity as finishes...
  43. C

    Rotation of two motors and two disk with friction

    Homework Statement I changed the problem, because I understood my error I forgot a force. It's the same problem with one motor. A motor drives two disks on a support. The support is turning clockwise at w1. Disks turn at w at start. The motor M gives a force F and a counterclockwise torque...
  44. M

    Rotation and centrifugal force

    what is the cause of the centrifugal force from the perspective of the rotating observer? Also is rotation relative like linear motion?
  45. Z

    Rotate System: Polar vs Tangential & Normal

    how do we know which system of coordinates to use whether (polar) or (tangential and normal) in case of a rotating system ??
  46. ellipsis

    Earth's rotation having effect on sub-orbital trajectory

    If you throw a ball obscenely high (ignoring air resistance, etc), and the Earth is rotating, the ball will land in a different spot. Relative to an observer on the Earth, the ball has a sub-orbital trajectory across the surface. If we attach thrusters onto that ball, and have it burn at its...
  47. L

    Entropy of translation and rotation of a molecules

    Homework Statement Hi all, There is a question from the course book: Homework Equations S=k_B ln W The Attempt at a Solution My solution: So first of all, for each molecule, there are 2 motions: translational and rotational. For rotational I get: W_1 =\Omega \left ( \theta \right ) For...
  48. S

    Angular acceleration of a yo-yo pulled with constant force

    Homework Statement A yo-yo is pulled with a constant tension T. The string is horizontal and parallel to the table and unwinding from the bottom of the spool, as shown. The yo-yo's outer radius is R and the spool radius is r. The mass of the yo-yo is m and the moment of inertia of the yo-yo...
  49. B

    How Does a Moving Particle Affect the Rotation of a Spherical Top?

    Homework Statement A solid sphere of mass M and radius R rotates freely in space with an angular velocity ω about a fixed diameter. A particle of mass m, initially at one pole, moves with constant velocity v along a great circle of the sphere. Show that, when the particle has reached the other...
  50. L

    Naive Question regarding Galaxy Rotation Curves

    Many apologies in advance if this question is ridiculous or if it has already been answered on another thread. I've searched and searched through the forums and haven't found the answer - please do direct me accordingly if that's possible. If not - please help! Preamble: We know from...
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