Axis of rotation Definition and 65 Threads

Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear.
This article assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.

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  1. L

    Parallel Axis Theorem Not Working

    Using the trivial way, you get I = M(r+L)^2. This is definitely correct. Out of curiosity, can the parallel axis theorem be applied here? I took the axis of rotation to be into the page, then calculated the moment of inertia for the disk, which is I = 1/2Mr^2. Next, I calculated the distance...
  2. T

    I Energy of spinning objects as axis of rotation moves

    Imagine an object, e.g throwing knife, spins in the air but not forced to rotate about a particular axis, i.e no rod impaling it and forcing it to spin about the rod. Then the axis of rotation converges to it's center of mass (CM) to minimize I. But there's nowhere for it's rotation energy to go...
  3. G

    The normal force on a thin stick being lifted on a surface

    The question is not directly related to the problem itself, but an odd discovery that when using left end of the stick as axis of rotation versus using the CM as axis of rotation, two different normal force expressions are found. Note that the solutions are for the initial moment when the stick...
  4. xkcda

    Torque about an accelerating point

    The total force acting on the pulley is zero so: F=mg+T1+T2 (1)Analyzing the torque and angular acceleration about the actual axis of rotation, the axle of the pulley, gives: τnet=T1R−T2R=Iα (2)If we analyze about point P, the right edge of the pulley where T1 is applied, we get...
  5. P

    I Finding the Axis of Rotation with Given CoG and Force Point

    [Mentor Note: See post #10 below for an updated problem statement using LaTeX and with a better drawing] what i want is to find the axis of rotation when the centre of gravity and point on which external force is acting is given along with the magnitude and direction of force. In the example...
  6. A

    I Confused about the axis of rotation in rotational motion w/o slipping

    I'm now learning about rotational motion without slipping and it's really hurting my brain to think about. Imagine a cylinder rotating on a flat plane. I can accept that there is both translational and rotational motion. For example, a given point on the circumference of the cylinder follows a...
  7. lela

    Is the force exerted by a pivot always towards the center of mass?

    I thought that the force by the pivot A on the pole AB would be the reaction force to the x-component of the gravitational force on AB. This would mean that the force by the pivot would be parallel to the pole, but in my notes from class the force vector seems to be more along the bisector of...
  8. T

    Choosing an Axis of Rotation for Equilibrium Analysis

    If I choose my axis of rotation for torque analysis to be the left-end of the plank, I can get the correct results. If I instead choose the com point -- I run into a dead end. Is there a way of a priori knowing this would happen? Thank you.
  9. crudux_cruo

    B Impulse and distance from the axis of rotation

    I'm trying to model the linear collision of a bat and a ball using the conservation of angular momentum. The ball is a point particle with at rest wrt the axis of rotation, and the bat is being treated as a rod of negligible radius. I have had to work through several problems involving a ball...
  10. 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...
  11. 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...
  12. 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...
  13. Biker

    Instantaneous axis of rotation

    I studied statics but I thought I can figure out the dynamics part. In a rectangular shape that is tipping, Usually we take the center of mass as an axis of rotation however the center of mass is accelerating with centripetal force so taking it would make the problem complex and we just take...
  14. kostoglotov

    Viscous drag parallel to the axis of rotation: Control Systems

    Homework Statement https://i.imgur.com/WPAKuf4.png seeking G(s) = \frac{\theta_2(s)}{\tau(s)} Homework EquationsThe Attempt at a Solution What does it mean when the viscous drag is parallel to the axis of rotation?[/B] It also turns out that this system needs two equations. I can sort...
  15. B

    Choosing Axis of Rotation in Cylinder Oscillation Problem

    Homework Statement Here is a problem we worked in class. I already know the answer, just had a question on the method. Two cylinders are connected with by a small rod (with presumably negligent mass) through their centers. The cylinders can roll freely. A spring is attached to the small rod...
  16. D

    A How to Calculate the Rotation Axis Incorporating Translation?

    I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation...
  17. R

    Torque and forces parallel vs perpendicular to the axis of rotation....

    why force parallel to the axis of rotation do not make any torque.
  18. S

    Calculate motor/gear ratio on single axis

    Firstly, let me explain that I am mostly inept at mathematics. Piecing together the required information is becoming a real challenge because of that. I am motorizing a dobsonian telescope. I have read many accounts of success and the steps involved. The places where detail is commonly left out...
  19. RicardoMP

    Rotating Cone and instantaneous axis of rotation

    Homework Statement Hi! I'm trying to solve a simple problem of mechanics, but I'm getting the wrong results and I suppose I don't yet grasp the concept of instantaneous axis of rotation very well. So, a cone (see attached picture) is rolling without slipping on a plane. Vp is point P linear...
  20. hackhard

    Rotation of line about rotating axis

    axis A is always normal to plane of the circle and passes thru centre of circle axis B is always parallel to plane of circle and is always parallel to y- axis of lab frame. axis B passes thru centre of the circle the infinitely long line MN always lies on the plane of the circle and passes thru...
  21. hackhard

    Rotation of a rigid body about external axis

    in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body - Rotation of a rigid body about a fixed axis is defined as...
  22. Chrono G. Xay

    Finding Optimal Axis of Rotation with Constraints

    I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization, http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html and it reminded me that...
  23. E

    Moving center of mass, torque and axis of rotation

    Hello. Suppose I have a coordinate system with the origin at the center of mass at rest of some rigid object and I wish to calculate the total change in angular momentum of the object with respect to it's center of mass. If I apply a torque to the object, that also happens to be an unbalanced...
  24. O

    Rotation from Oscillating Axis Of Rotation

    Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin. Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move...
  25. H

    Friction and Couples: Understanding Coefficients

    Homework Statement Usually in any question will the magnitude of the couple(friction) be given or is it possible to find the couple from the co efficient of friction between the rotating object and the axis ? Homework EquationsThe Attempt at a Solution
  26. **Mariam**

    Moment of inertia from diffrent axis

    Homework Statement Two particles of mass m1 = 14 kg and m2 = 24 kg are connected by a massless rod of length 1.4 m. Find the moment of inertia of this system for rotations about the following pivot points. Assume the rotation axis is perpendicular to the rod. A) center of rod B) end of m1...
  27. Y

    How Fast Is the Large Hoop's Center Moving When Aligned Vertically?

    Homework Statement Two hoops are fastened together as shown below. Smaller hoop mass m, and larger hoop mass 3m. The system is now placed on the table and the system is released from rest in the position shown below. There is sufficient friction between the large hoop and the table so that it...
  28. C

    Equilibrium Question: Arbitrary Axis of Rotation?

    Ok, I solved the question posed in the attached image. I did so by using the car's center of mass as the location of my axis of rotation, generated torque and force equilibrium equations, and solved for all unknowns. When I try to use another location for my axis of rotation, e.g., the point...
  29. A

    Axis of Rotation: Rotate About Other Axes?

    Does a body rotating about an axis also rotate about any other axis? Eg. Cars on a racetrack may be rotating about a vertical axis passing through the centre of the track but can they also be considered to be rotating about a vertical axis passing through the spectators' stand?
  30. andyrk

    Understanding the Concept of Axis of Rotation: Definition and Explanation

    Homework Statement This is more of a conceptual doubt. Why does the axis being called as the axis of rotation of a rolling body have to be at rest with respect to some frame of reference? What is the definition of axis of rotation? When is an axis called an axis of rotation?
  31. I

    Could an eliptical galaxy exist with an axis of rotation?

    I was wondering if a galaxy could be perfectly orbiting to create a sort of axis of rotation, with a period being like 50 million years, or is it impossible because of some property that elliptical galaxies have? If it is possible, what is the probability that it exists in our observable...
  32. MarkFL

    MHB Solid of revolution about an oblique axis of rotation

    Hello MHB, As students of calculus, we are taught to find the volumes of solids of rotation obtained by revolving given regions about horizontal and vertical axes of rotation. But, what if the axis of rotation is neither horizontal nor vertical? Please consider the following diagram: We wish...
  33. Q

    Angular velocity irrespective of axis of rotation?

    How exactly can the angular velocity of a 2 dimensional laminar object be the same with respect to all axes of rotation perpendicular to its plane ?
  34. V

    Rotational speed at axis of rotation?

    Hello everyone! This is probably the stupidest question that I've come up with, and I'm a little embarrassed asking it, but here goes: Is it only the tangential speed that is zero of a point at the axis of rotation in a rotating solid? If not, then I don't understand how the rotational...
  35. andyrk

    Axis of Rotation for Rigid Body: How to Identify & Conditions

    for a perfectly rigid body, how can one identify what is the axis of rotation of the rigid body? What is the condition required for an axis to be called the axis of rotation?
  36. B

    Torque, point or axis of rotation

    Hi, 1) Do we calculate torque with respect to a point or with respect to an axis? I have read them both in different resources, and so I am confused! 2) If we calculate torque with respect to an axis, many introductory textbooks discuss the motion of the gyroscope by considering how the...
  37. R

    What Is the Axis of Rotation for This Matrix?

    Homework Statement consider the following rotation matrix: 0 0 1 1 0 0 0 1 0 Find the axis of rotation. Homework Equations The Attempt at a Solution I know the following: Ω|1> = |2> Ω|2> = |3> Ω|3> = |1> where Ω is an operator. It is a cyclic permutation. What do not understand is...
  38. K

    What Is the Instantaneous Axis of Rotation for a Pure Rolling Disc?

    Homework Statement if a disc of mas m is pure rolling , with velocity v . the instantaneous axis of rotation would be the point of contact with the ground . As shown in the diagram this could be considered as a disc rotating about one of the point on circumference for an instant of time ...
  39. B

    Moment of inertia and force needed to tilt/change axis of rotation

    Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates. I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...
  40. B

    Accelerationg of rotating mass *along* the axis of rotation

    Says Wikipedia: "The moment of inertia is a measure of an object's resistance to any change in its state of rotation". Now consider a rotating mass m that I would like to accelerate along its axis of rotation by a. Does this count as a "change in its state of motion"? Will it resist the...
  41. Saitama

    Instantanoeus axis of rotation

    Homework Statement A uniform rod of length l is given an impulse at right angles to its length as shown. Find the distance of instantaneous centre of rotation from the centre of rod. Homework Equations The Attempt at a Solution Impulse=change in momentum or Impulse=mvCM (Am i...
  42. Y

    How to Calculate the Axis of Rotation in 3D Space?

    hey guys, I have a problem I need to solve for my masters thesis. I have an object that rotates in 3D space. There is no translation. Given that I have coordinates of one landmark at 2 instances of time I need to calculate axis of rotation and angle of rotation. is this sufficient...
  43. H

    Rotation of free solid object in vacuum, location of axis of rotation

    Hi, I would be happy if you could solve and explain following problem: Imagine some solid long object (wooden plank for example) being just like that in vacuum, free, without being fixed to any point of space. Then, imagine only one forse pushing this object in a certain point of object...
  44. X

    Inertia of body that is oriented at some angle from axis of rotation

    1. Problem I am attempting to model the dynamics of the system shown in the attached image. I have a DC Motor with two disks attached to it via springs and something similar to a servo horn. I have two questions. The first is how to determine the inertia of the disk and the spring about the...
  45. S

    Am I doing this right? Doesn't feel right. (find axis of rotation)

    Homework Statement So here is the question: Matrix A corresponds to the linear transformation T obtained by first rotating a vector in R3 through angle ∏/3 about the z axis and then through angle ∏/4 about the x-axis. Find the parametric equation for the axis of rotation. Homework...
  46. L

    Ball rolling down a surface - where is the axis of rotation?

    In my textbook, it says that when a ball rolls down a surface, inclined or not, the point of contact can be thought of as the pivot or the axis of rotation, since at the point of contact, the ball's velocity is zero. Makes sense, but then the textbook becomes inconsistent in problems solving...
  47. S

    Question about axis of rotation for torque (would really appreciate some help)

    Hi Guys so I would really appreciate if I could get some help with this question I have, I have a test in a couple days! So we are learning about torque and there are a couple components of torque that I'm a bit confused about. 1. Is the axis of rotation a line or just a point? 2. Is...
  48. J

    Axis of rotation, plane of reflection

    For a 3x3 orthogonal matrix with determinant= -1 (which means rotation followed by simple reflection), is the axis of rotation the same as the plane of reflection ? My reasoning is follows (see attachment) Say you have two vectors with the same angle size (which i call A), same x-values...
  49. J

    Determining Rotation Axis from Matrix: Eigenvalue and Eigenvector Analysis

    Given the matrix of rotation, what is the procedure to determine the axis of rotation ? Is there a set mathematical way to do it (like a formula), or is it something that you need to think about logically ?
  50. Femme_physics

    Can I treat blocks as a single axis of rotation?

    Can I treat "blocks" as a single axis of rotation? http://img171.imageshack.us/img171/2245/blockthingy.jpg Basically those A and B wooden blocks are pressed against two hardened steel plates through the tension of the bolt. My question, can I treat these blocks as a single point? For...
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