Rotational 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. R

    Rotational Circular Motion with fixed ends and a spinning button in the middle

    This button has fixed ends and the string is twirled and on the fixed ends there is hanging masses. I have found out that if string twirls are constant, the hanging mass is directly proportional to angular velocity squared. But I want to understand how that is derived. Could anyone please help...
  2. Curtiss Oakley

    Bowling Ball Changing Rotational Direction

    I already have a and b, but want to see if anyone is willing to verify my answer for part c. I get 0 for the frictional force between the ground and ball, which would lead d and e to be 0 as well. Physics is rarely that easy so I wanted to make sure I didn’t miss anything.
  3. 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...
  4. O

    How Do Mass and Windings Affect Disc Rotation Dynamics?

    I am doing a project, but am struggling to find relationships of proportionality or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or...
  5. Np14

    What is the tension force for this system in rotational equilibrium?

    The system is in rotational equilibrium and therefore experiences no net torque, meaning all individual torques must add to zero. τNET = 0 = FFTsin(θ)L - FgL - Fg(L/2) τNET = 0 = FTsin30°(0.6?) - (0.5)(9.8)(0.6) - (2.0)(0.6/2) My only problem (I think) is figuring out what the length L is for...
  6. H

    How is the energy of a zero resistance circuit converted to rotational energy?

    If I have a DC induction motor coil of a zero resistance so that means that to sustain a constant magnetic field I do not need any energy. So in a DC motor how is energy of zero resistance circuit converted to rotational energy of a motor?
  7. Shridhar

    Rotational Dynamics, 1.68(SS.Krotov) and 1.264(Irodov)

    Homework Statement I have attatched both the problems. The figure is essentially the same. Homework Equations 1. Energy conservation 2.mgcosx - N = mv^2/r , where N is zero in limiting case. The Attempt at a Solution I solved the whole question and got the answer given in irodov(0.33...
  8. Ariano AnnaG

    Circular motion of a rotational spring

    Homework Statement A child is playing with a spring (k=100000 N/m, Li = 0.5 m). One of his toys (m=0.5 kg) is attached to the further extremity. The child is rotating the spring above his head on a horizontal plane, with a uniform circular motion. What is the elongation of the spring? I’m not...
  9. matai

    Using Integrals to Calculate the Rotational Energy of Earth

    So I found the linear velocity by using the circumference of the Earth which I found to be 2pi(637800= 40014155.89meters. Then the time of one full rotation was 1436.97 minutes, which I then converted to 86164.2 seconds. giving me the linear velocity to be 465.0905584 meters/second. I know that...
  10. S

    You're welcome! Good luck with your project.

    First time poster here, thanks in advance! I have a project I'm working on, and I'm looking for a way to limit the rotational motion of a shaft inside a cylinder. The cylinder is fixed, and the shaft is spinning inside the cylinder coaxially. Basically, torque will be applied to the shaft...
  11. D

    B Galaxy rotational curves vs time

    Hello to everyone, I'm trying to find some data about the relation between galaxy age and rotational curve... until now without success. Are there any teams working on this? Are there any studies in this direction? Thanks!
  12. D

    Equilibrium : normal reaction of a rotational center?

    Homework Statement I'm trying to figure out the reaction at D,that's where the system can rotate. Problem: A force P of magnitude 90 N is applied to member ACDE, which is supported by a frictionless pin at D and by the cable ABE. Since the cable passes over a small pulley at B, the tension...
  13. S

    Calculating Rotational Kinetic Energy of a Baton

    Homework Statement A drum major twirls a 94-cm-long, 500 g baton about its center of mass at 150 rpm. What is the baton's rotational kinetic energy? Homework Equations KE_rot = 0.5 I w^2 The Attempt at a Solution w = (150rpm*2pi)/60 = 15.708rad/s I = (1/12)*0.5kg * 0.94m = 0.039167kg*m^2...
  14. C

    What is the net acceleration of the coin on a rotating disk?

    Homework Statement A disk is initially at rest. A penny is placed on it at a distance of 1.4 m from the rotation axis. At time t=0s, the disk begins to rotate with a constant angular acceleration of 1.9 rad/s^2 around a fixed, vertical axis through it's center and perpendicular to it's plane...
  15. 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...
  16. P

    Why Can't I Get the Correct Answer Using Energy to Calculate Rotational Inertia?

    Homework Statement How come I can't get the correct answer using Energy as a way to solve this? Homework Equations 3. The Attempt at a Solution [/B] The answers use conservation of momentum which makes perfect sense and I understand that, however I used an energy approach where E(flywheel) =...
  17. P

    Rotational Mechanics Homework: Equations & Solution for Part 1 Work

    Homework Statement Homework Equations E=T+U T=1/2 mv^2 U=∫F⋅dr The Attempt at a Solution Part 1 Work x=x-dot y=y-dot z= z-dot r=r-dot θ=θ-dot [/B] T= 0.5m(x^2 +y^2) 0.5M(z)^2 Changing to polar coordinates T=0.5m(r^2 +rθ^2) 0.5M(z)^2 U=-Mgz E=T+U =0.5m(r^2 +rθ^2) 0.5M(z)^2-Mgz z=L-r...
  18. DracoMalfoy

    Rotational Kinetic energy of bar, and new kinetic energy

    Homework Statement A bar of length 2.5m and mass 5kg, whose rotation point is at its center, rotates at 5 rad/s. What is the rotational kinetic energy of the bar?If a point mass of mass 1.5kg is added to each end of the bar, assuming the angluar velocity is the same, what is the new kinetic...
  19. A

    Rotational Motion: Average angular acceleration of a CD

    Homework Statement "A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD...
  20. S

    Rotational moment of inertia for 3 balls on a pipe

    Homework Statement Homework EquationsThe Attempt at a Solution i just don't know from where to take the R which is colored with brown, in the 2(MR^2), what is the R here exactly, because i took the radius of the sphere , but i get different answer althought it's near.
  21. S

    Rotational inertia hoop around a central axis

    Homework Statement Homework Equations I= mr^2 for a hoop around a central axis I= 1/12 (m)(l)^2 for thin rod about axis through center perpendicular to lenght The Attempt at a Solution I am totally confused. i said first that the three masses each will make a hoop shape so i found I=mr^2...
  22. J

    Rotational motion: Conservation of energy doesn't work....

    http://www.animations.physics.unsw.edu.au/jw/rotation.htm#rolling I have set up an apparatus similar to what the above link says (the first bit about brass object with shaft). So basically, the shaft is in contact when the brass is first rolling, then it suddenly accelerates when the edge of...
  23. J

    Rotational Momentum: Calculating Angular Speed After Cockroach Stops

    Homework Statement A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm,rotational inertia 4.9 ✕ 10^−3 kg · m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.0...
  24. P

    Rotational mechanics string wrap around twig

    A mass m is tied to a string which is wrapped to a twig of a tree. How many minimum times should we wrap the string so that it doesn't fall? Here is what i got... 1.There is friction between the twig (or fixed cylinder) and the string. 2. if the total friction between the string wrapped around...
  25. U

    Rotational Mechanics question with spring

    Homework Statement A uniform cylinder of mass ##M## and radius ##R## is released from rest on a rough inclined surface of inclined surface of inclination ##\theta## with the horizontal as shown in the figure. As the cylinder rolls down the inclined surface, what is the maximum elongation in...
  26. C

    MHB Two dimensional rotational Matrix

    Dear Everybody, I am trying to learn about the electrodynamics. I am using the textbook, Introduction to Electrodynamics (2nd Ed) by D. J. Griffiths. I am working on the Problem 1.8. The question state: Prove that the two-dimensional rotation matrix perverse the length of A. (That is, show...
  27. P

    What was the rotational velocity of Earth on Dec 31, 1899

    I ask because time is defined with reference to this day (the SI second is based on a caesium clock is calibrated with reference to the 1952 ephemeris time standard, which was based on a second being 1/86 400th of Jan 0, 1900 (with Jan 0 being Dec 31 of 1899). So... how do I calculate the...
  28. Y

    Rotational Mast System - Transfer Function, PID Design

    Homework Statement Given the system above, were a motor is rotating a mast that is attached to a second second mast by a spring with a spring constant K and a damping coefficient D. The motor has a current I applied to it with coefficient K Below are the provided values. K_s is the...
  29. physea

    Understanding Rotational Movements: A Comprehensive Guide to Key Terms

    Hello! I am a bit confused with the multiple terms like centre of gravity (ok I know that), moment of inertia, radius of gyration, etc. 1) Can you compile a complete list of such terms? 2) What are their differences and when do I use each? Thanks!
  30. H

    How Does Mass Affect the Direction of Rotational Motion in a Pulley System?

    Hello Consider a pulley with a rope winded up around it, and two solids attached to the rope from each side. It is intuitive that the solid with the most mass will impose the direction of the rotational motion of the system ( note that the pulley can rotate), but i'd like to know how can we...
  31. NimzCr7

    Rising of a liquid during rotataion in a cylinder

    Homework Statement [/B] A 25-cm-diameter, 100-cm-high cylindrical container, (as shown), is partially filled with 75-cm-high liquid (density = 900 kg/m3). Determine the rotational speed at which the liquid will start spilling. Calculate the gauge pressure at the centre of the bottom of the tank...
  32. koustav

    I Rotational Spectra: Why Absorption & Not Emission Lines?

    why pure rotational spectrum is almost always seen as absorption lines,and not as emission lines?
  33. J

    Rotational Motion and Torque problem

    Homework Statement A thin rod of length ' L' lies on the + x-axis with it's left-end at the origin. A string pulls on the rod with a force 'F' directed towards a point 'P' a distance 'h' above the rod. Where along the rod should you attach the string to get the greatest Torque about the...
  34. M

    MHB Calculate the rotational frequency in r/s and the diameter of the drive pulley

    a belt is driven by a pulley at 33m/s the pulley rotates at 750 r/min. calculate: (a) the rotational frequency in r/s (b) the diameter of the drive pulley
  35. dmac257

    Can docking ships help regulate rotation in a spinning space habitat?

    I am writing a science fiction book and doing a little research about habitats in space to make sure my understanding of the physics is at least close to real. I envision construction mostly in space from materials delivered by returnable cargo vessels. (either shuttle-like or space-X style ...
  36. lc99

    Rotational Dynamics Homework Help

    Homework Statement Homework Equations RKE = .5iw^2 TKE = .5mv^2 U = mgh The Attempt at a Solution is my setup correct? mgh = RKE +TKE mgh = .5Iw^2 + .5mv^2 do i just total up the RKE and TKE for both the objects?[/B]
  37. physea

    Methods of rotational energy harvesting and storage

    Hello! What are the available methods to harvest rotational energy? I was thinking to put a turbine on the shaft and compress air, but the air will get cold and the energy will be lost. I was thinking to put an electric generator, which is ok but it needs a battery. I was thinking to use...
  38. SchroedingersLion

    Precession - why does the rotational axis change as L changes?

    Hi guys, while going through rotational energy levels of molecules, I found myself struggling with a very basic concept. The concept of precession, in terms of a torque induced rotation of the rotational axis of a spinning rigid body. Take a glance at the Wikipedia figure...
  39. physea

    Can cogging in permanent magnet motors be utilized for rotational movement?

    Hello With a normal magnet, we use energy to position a particle away from the magnet and then the magnet does work and moves it close to the magnet. Is there any way to have such movement being rotational? Ie to uae energy to move a particle or point clockwise and then the magnet will move it...
  40. J

    I Rotational Transitions: What Are They?

    I read recently about rotational transitions being detected by radio telescopic spectroscopy for a substituted benzene in a gal cloud a ways away. My question is what is a rotational transition. I think it is a quantized change in angular momentum, but I'd like to picture it physically. Is it...
  41. J

    Torque and Rotational Equilibrium with a slanted Rod/Cable

    Homework Statement There is a lever rod of length 3.43 m, weight 44 N and uniform density. The lever rod is pivoted on one end and is supported by a cable attached at a point 0.902 m from the other end. The lever rod is in equilibrium at angle of 68◦ from the vertical wall. The cable makes...
  42. W

    I Why this system has a rotational symmetry in Dirac equation?

    why system has a rotational symmetry in dirac equation? is that a general property of all systems?
  43. Pushoam

    Ratio of K. E. of solid cylinder to shell

    Homework Statement Homework EquationsThe Attempt at a Solution total kinetic energy of a rigid body = rotational kinetic energy of the body around its center of mass + translational kinetic energy of center of mass For solid cylinder, total kinetic energy = ## \frac { [I = \frac 1 2...
  44. T

    HW question w/ rotational kinetic energy

    Homework Statement : [/B] A stationary horizontal platform is free to rotate about its vertical axis. The radius of the platform is R=1.6m and its moment of inertia is 660 kgm^2. A 43 kg boy jumps on the rim of the platform with the velocity 2.2 m/s tangential to the rim. What will be the...
  45. C

    Unlocking Realistic Rotational Collisions with Physics & Graphics Engines

    Hi all! I'm currently working on a graphics/physics engine. The following Wikipedia page was extremely helpful in making rectilinear collisions look natural: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional Specifically, the very general vector form of the equation on the bottom...
  46. K

    Block-pulley system and rotational dynamics

    Homework Statement Two blocks, m1 = 1.0 kg and m2 = 2.0 kg are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is of the system is 5.0 kg*m^2, the acceleration of the system is (expressed as a fraction of gravitational...
  47. L

    Rotational equilibrium problem (ladder against a wall)

    Hi everyone, Our professor gave us a bunch of solved problems to practice with before the exam, and this one I'm struggling with: I'm trying to work through the solution step by step, and I get stuck at the point (3). What I understand is that we want to get the value of RH, which is...
  48. A

    Rotational Dynamics of a Grindstone

    Homework Statement A grindstone is used to sharpen knives and consists of a stone cylinder and a central axle There are bearings between the axle and the frame to reduce any friction. This grindstone has a mass of 60 kg, a diameter of 0.600 m and has a moment of Inertia (I) of 4.50 kg.m2 ...
  49. F

    Constant rotational kinetic energy

    A mass m is attached at the end of the string. The mass moves on a frictionless table, and the string passes through a hole in the table, under which someone is pulling on the string to make it taut at all times. Initially , the mass moves in a circle, with kinetic energy [E][/0] . The string is...
  50. starstruck_

    Angular momentum and rotational energy

    Homework Statement A school playground has a carousel, which is simply a circular platform that can rotate around its center axis with negligible friction. This carousel has radius r=1.6 m and rotational inertia I= 177m^2kg. Suppose you are standing beside the carousel which is already spinning...
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