Rotating 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. P

    Conservation of energy in rotating bodies

    The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder. To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder). However, I viewed the cylinder as rotating...
  2. yucheng

    Two rotating coaxial drums and sand transfering between them (Kleppner)

    The solution is simple by noting that the total angular momentum of the system is constant. (Though I overlooked this) Instead, I went ahead analyzing the individual angular momentum of both drums. Let ##L_a## and ##L_b## be the angular momentum respectively. ##M_a##, ##M_b## be the...
  3. B

    What is the angle between the acceleration and velocity when rotating?

    ##ω = \frac {k} {\sqrt{φ}}## What is the angle between acceleration and velocity after 1spin (2π radians)? First I decided to find out what is the angular acceleration: ##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = -...
  4. A

    A charged conducting ring rotating B field -- referece frames

    Admittedly I found similar threads here already but due to my rather lacking math skills I wanted to go through this myself. As for the math side, I see various different equations with which this is treated can someone please provide the formulas for calculating B field from a rotating charged...
  5. Leo Liu

    Is Mach's Principle truly a paradox in rotational frames?

    I have been reading Kleppner's An Intro to Mech recently and have found an interesting discussion on the nature of rotational motion in the book. The authors wrote: Newton described this puzzling question in terms of the following experiment: if a bucket contains water at rest, the surface of...
  6. Leo Liu

    Confusion about the derivation of acceleration relative to rotating frames

    This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...
  7. A

    Engineering How to find the angular velocity of a rotating drum?

    Good day here is the exerciceThe only velocity I do have is the velocity v os the center of pulley 5, I tried to find the center of instantaneous velocity to find the angular velocity of pulley 5 but I couldn't, any hint would be highly appreciated! Best regards!
  8. S

    How to Measure Torque Required for motor to spin a rotating shaft?

    I've harvested a motor from a cordless drill and connected it to a belt which turns a rotating shaft. The motor pulley and the pulley on the other side of the belt are roughly the same size, which a fairly small radius (5 mm maybe?). The issue I'm running into, which I don't fully understand...
  9. S

    Tension connecting two collinear rotating objects

    Tangential speed of 4 kg object is 8 m/s At the top of the trajectory, there will be two downwards forces acting on 4 kg object, which are tension of string 2 (T2) and weight ##F=m.a## ##W + T_2=m.\frac{v^2}{r}## Putting all the values, I get negative value for T2. Where is my mistake? Thanks
  10. Leo Liu

    Why Is Torque Calculated Differently in Rotating Hoop Problems?

    Problem (a only): Solution: My questions: 1. The official solution gives no information about the point at which the torque is measured. I thought it was the CM of the hoop, but the torque should be ##\tau=RT\cos(\alpha-\beta)##; the angle was given by a geometric proof. I would like to know...
  11. E

    What is the Constant of Motion in a Rotating Potential Field?

    I'm getting a bit stuck here, the Lagrangian and equation of motion is$$\mathcal{L} = \frac{1}{2} m \dot{\mathbf{x}}^2 - V_0(R^{-\omega t} \mathbf{x}) \implies m\ddot{\mathbf{x}} = -\nabla_{\mathbf{x}} V_0(R^{-\omega t}\mathbf{x})$$as expected. To try and verify that the quantity ##E - \omega...
  12. ricles

    How to Find Linear Acceleration Without Cylinder Radius?

    This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...
  13. ricles

    Tension in a rotating ring under gravity

    I know the solution for the problem of the tension on a rotating ring without gravity (tha is, ##\frac{mR\omega^2}{2\pi}##) - that I find simple enough. But I'm at a loss how can I change it to do with gravity :/ Any help is appreciated! (and apologies for the bad drawing)
  14. E

    Two rotating masses balanced by a third mass (rotational dynamics)

    Here's a diagram of what the system looks like: So far I have figured out what the initial angular velocity is, if the system is balanced (no movement): ## \sum F_m = m*\frac{v^2}{R_0}-\frac{Mg}{2}=0 ## ##m \frac{v^2}{R_0}-\frac{Mg}{2}=0 ## divide both sides by m ##\omega_0 =...
  15. P

    Rotating birefringent calcite crystals: precession of image?

    I have been doing some reading about birefringence in order to understand colors observed in different birefringent crystals when I came across the following page in connection with calcite crystal birefringence. https://www.microscopyu.com/tutorials/birefringence-in-calcite-crystals I think I...
  16. A

    I Dissolving Event Horizon w/Charged & Rotating BH

    I saw a fascinating video from PBS space time about dissolving an event horizon. See here for reference: The video addresses rotating kerr black holes and charged black holes, but doesn't talk about the combination of rotation and charge. So what happens when you spin up the black hole as...
  17. JD_PM

    A Understanding Kerr Black Holes: Metric, Killing Vectors & Event Horizons

    Before explicitly stating the Kerr metric let us discuss a bit what to expect, comparing it to the easiest solution to (in-vacuum) Einstein's equations that I know: the Schwarzschild metric. I studied that the Schwarzschild metric is derived under the following assumptions: the metric must be...
  18. D

    KE of off-center impacts in rotating and translating rigid bodies

    I'm trying to understand basic principles of ancient thrown weaponry. Let's say we have something like a bar with a known inertia tensor that is thrown from one end such that it is both rotating and translating. If it strikes something along either side of its center of mass (an off-center...
  19. Haorong Wu

    Stress-energy tensor for a rotating sphere

    The answer with no details is given by First, I considered a spherical shell because I thought the velocities at different radius ##r## will be different and hence the four-momentum will be different, as well. Then, I writed down the linear momenta by $$\epsilon^{ijk} r_i p_j = L_k$$ with...
  20. Ugnius

    Rotating body moment of inertia

    I have done some lab work , and now i have to answer some theoretical questions , but i can not find any data about this on the web or atleast i don't know where to search , i will add some pictures of experiment for you to better understand it. I was wondering can someone share their knowledge...
  21. PhysicsTest

    Understanding the Continuity of Current in a Rotating Magnetic Field

    I am analyzing the rotor magnetic field, i feel i understand the basic concept but have few clarifications. At pt1, the net mmf due to currents ##i_a = i_{max}; i_b = -\frac{i_{max}} 2 ; i_c = -\frac{i_{max}} 2## is ##\frac {3F_{max}} 2## Similarly i can do for Pt2. But my confusion is the...
  22. mingyz0403

    Engineering Newton’s Second Law of Motion — Collar sliding on a rotating rod

    The soultion used polar corrdinates. Acceleration in polar corrdinates have radial and transeverse components.When calculating the acceleration of collar respect to the rod, the solution only calculates the radial component of acceleration. Is it because the collar is on the rod, so the...
  23. LCSphysicist

    Bead on a rotating stick and the Lagrangian

    A stick is pivoted at the origin and is arranged to swing around in a horizontal plane at constant angular speed ω. A bead of mass m slides frictionlessly along the stick. Let r be the radial position of the bead. Find the conserved quantity E given in Eq. (6.52). Explain why this quantity is...
  24. E

    Finding the inductance of a rotating cylinder shell

    First, the correct answer is μ0*π*R^2. I tried to look at the cylinder like it was a solenoid, this technique was used in my class. Then I tried to find the current of the solenoid, to do that I looked at a piece of a solenoid with a legnth of dz, then: I=dq/dt=(2πRσ*dz)/(2π/ω)=ω*R*σ*dz. The...
  25. D

    Why is the result different in Method 2 for the rotating rod experiment?

    Method 1: Simply conserving angular momentum about the the fixed vertical axis and conserving energy gives ##v=3##, which is correct according to my book. Method 2: Conserving angular momentum when the two rings reach distance ##x## from the centre gives ##(0.01+2x^2) \omega =0.9## Also in the...
  26. S

    Rotating body viewed from its own rotating ref. frame, then perturbed

    Pondering over this thought experiment, a question comes to mind -- to which my brain sometimes replies "of course" and sometimes "no way!"A disk shaped satellite ("in zero-G") spins about its axis. There are two thrusters mounted as shown on two axial booms. The thrusters are fired briefly at...
  27. K

    I How can I rotate a vector in 3D to match another vector's rotation?

    Suppose I have a three dimensional unit Vector A and two other unit vectors B and C. If B is rotated a certain amount in three dimensions to get vector C, how do I find what the new Vector D would be if I rotated Vector A the same direction by same amount?
  28. E

    Ball on a rotating inclined plane

    I have problems to even start with this exercise.
  29. M

    Equations of relative motion with respect to a rotating reference frame

    Hi, I am just writing a post to follow up on a previous thread I made which I don't think was very clear. The question is mainly about how to use the below equations when there is also a rotation of the body around the fixed reference point. Please see the diagram here to see how the vectors...
  30. M

    Question about Formulae for Motion in a Rotating Reference Frame

    Hi, I am reading the following question: "Particle P moves in a circular groove with radius ## a ## which has been cut into a square plate with sides of length ## l ##. The plate rotates about its corner ## O ## with with angular velocity ## \omega \hat k ## and angular acceleration ## \dot...
  31. Hamiltonian

    A rotating rod acted upon by a perpendicular force

    $$\tau = I\alpha$$ $$FL/2 = I\omega^2L/2$$ $$T = 1/\theta \sqrt{F/I}$$ would this be correct? I came up with this more basic question to solve a slightly harder question so I do not know the answer to the above-stated problem.
  32. MichaelTam

    Tension in a Massive Rotating Rope with an Object

    The whole question is: One end of a uniform rope of mass 𝑚1 and length 𝑙 is attached to a shaft that is rotating at constant angular velocity of magnitude 𝜔. The other end is attached to a point-like object of mass 𝑚2. Find 𝑇(𝑟), the tension in the rope as a function of 𝑟, the distance from the...
  33. P

    Forces at the bottom of a rotating U-tube filled with water

    So when the rotation starts some water will move upwards and in the vertical part of tube. I know hat centripetal force will be given by F=mv²/r Now I though of taking r as centre of mass of the water system but I don't know what to take the value of m as? Should I only consider the water...
  34. burian

    How can I find the velocity of a point on a disk rotating in a disc?

    From a freebody analysis I got, $$ \vec{r} \times \vec{F} = |r| |F| \sin( 90 - \theta) = (R-r) mg \cos \theta$$ and, this is equal to $$ I \alpha_1$$ where the alpha_1 is the angular acceleration of center of mass of small circle around big one, $$ I \alpha = (R-r) mg \cos \theta$$ Now...
  35. Vivek98phyboy

    What are the other forces acting on ##dm## in addition to gravity?

    After solving using energy conservation, I found the angular velocity at 37° to be omega=2.97/(L)^½ Tension and the weight (dm)g are the two forces acting on the tip dm To find the resultant force, I resolved the centripetal force and tangential force to find the centripetal force as F=...
  36. Livio Arshavin Leiva

    Rectilinear movement seen from a rotating reference frame

    Let's suppose there's some platform that is rotating with angular speed omega and has a radius R. At t=0 we release some object from the border, which has an initial speed perpendicular to the radius direction with magnitude \omega R and we want to know its position at t=T with respect to the...
  37. Hiero

    Bernoulli’s equation for a rotating fluid

    Consider a cylindrical container filled with an ideal fluid. Let it rotate at a constant angular speed (about the symmetry axis which is oriented vertically) and let the fluid be in the steady state. Lets just talk about a horizontal slice so that the gravitational potential is constant. The...
  38. K

    Torque on Left Foot of Man in Rotating System

    I saw that the solution states that the torque about the center of mass is zero, since the man does not rotate about its center of mass. However, I then thought about taking the torque about the left foot (so the right foot for the man's POV). Hence: $$\tau_{left} = \tau_{0} + \textbf{R}\times...
  39. E

    Dropped object in a rotating frame

    I solved this in an inertial frame, but now I want to do it in the rotating frame. As far as I can tell the equation of motion is $$\vec{F}_{cent} + \vec{F}_{cor} = mr\omega^2 + 2m\vec{v} \times \vec{\omega} = m\frac{d^2\vec{r}}{dt^2}$$The solutions take a different approach. They state that the...
  40. Nexus99

    A falling rotating rod strikes a ball of mass M....

    A homogeneous rod of length l and mass m is free to rotate in a vertical plane around a point A, the constraint is without friction. Initially the rod is stopped in the position of unstable equilibrium, therefore it begins to fall rotating around A and hits, after a rotation of ## \pi ## , a...
  41. wrobel

    Two cylinders rotating with contact at an angle (reformulation of the problem)

    Some time ago there was a problem with the following picture somewhere out here. I think this problem was underestimated a little bit. Let us reformulate the problem. Assume that each cylinder, if it was not influenced by the other one, could rotate freely about its fixed axis. But the...
  42. A

    Rotating waveguide antenna (rotating marine radar)

    I've seen these devices on shores as well as on ships , like a horizontal tube rotating slowly around it;'s axis. Now from what I know it's a type of radar, and unlike phased array it rotates it's beam physically by means of using a motor to rotate the antenna itself , what I want to know is...
  43. L

    Magnetic field of a rotating disk with a non-uniform volume charge

    -------------------------------------------------------------------------------------------------------------------------------------------------- This was a problem introduced during my classical electrodynamics course. I am not 100% sure, but I think I've solved up to problems (a) and (b) as...
  44. D

    Rotating frames - Apparent gravity

    Hi On the Earth , apparent gravity comes from the vector addition of the gravitational force directed towards the centre and the outward centrifugal force. It means that for a pendulum at rest , the direction the bob hangs downwards is not directly towards the centre of the Earth but there is a...
  45. G

    Confusion on the magnitude of magnetic fields

    Here, the correct options are A,D. Solution: I got A as answer as ∫ B.dl=µI. But, the answer to the question says that it is a solenoid and therefore Bx=0 for point P. Here I'm a bit confused. I know this system resembles a solenoid in some ways, then By must have some finite value, but...
  46. sagigever

    Magnetic field in a rotating uniformly-charged infinite cylinder

    I am sure I need to use Amper's law to do that. if I use the equation I mentioned above it easy to calculate the right side of the equation but I have problem how to calculate the path integral. I know from right hand rule that the magnetic field will point at $$Z$$ and the current is in...
  47. M

    B Descending a Rotating Black Hole: Hit the Ring Singularity?

    So I have been watching the latest edition of PBS Space Time ( I know, not a proper resource/guide,) and it seems to be a bit confusing as to whether you would hit the ring singularity at the center or not. On the one side he claims that the geodesics end there but on the other he claims you...
  48. T

    I A cold, massive, rotating disk galaxy 1.5 billion years after the BB

    Neeleman, M., Prochaska, J.X., Kanekar, N. et al. A cold, massive, rotating disk galaxy 1.5 billion years after the Big Bang. Nature 581, 269–272 (2020). https://doi.org/10.1038/s41586-020-2276-y Abstract Massive disk galaxies like the Milky Way are expected to form at late times in traditional...
  49. H

    Mechanics: Two masses on a pulley causing two cylinders to accelerate

    Hi! I need help with this problem. m1-2-3-4 and R are given. There is no slip in the system. I have to give F1-2-3-4 in respect of the masses and R. Here is what I managed to m1 is easy: m1*a = m1*g - T(tension of the rope) m2: m2*a = T - (?) <-- I have a problem with this. F1 and F3 is the...
  50. Leo Liu

    The inelastic collision between a disk and a rotating platform

    A disk is dropped on a platform rotating at a constant angular speed ##\omega_i## as shown below. The question asks whether the final kinetic energy of the platform is conserved. I understand the angular momentum is always conserved provided that the net torque is 0, so I wrote the following...
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