Rotational equilibrium Definition and 67 Threads

Rotational diffusion is a process by which the equilibrium statistical distribution of the overall orientation of particles or molecules is maintained or restored. Rotational diffusion is the counterpart of translational diffusion, which maintains or restores the equilibrium statistical distribution of particles' position in space.
The random re-orientation of molecules (or larger systems) is an important process for many biophysical probes. Due to the equipartition theorem, larger molecules re-orient more slowly than do smaller objects and, hence, measurements of the rotational diffusion constants can give insight into the overall mass and its distribution within an object. Quantitatively, the mean square of the angular velocity about each of an object's principal axes is inversely proportional to its moment of inertia about that axis. Therefore, there should be three rotational diffusion constants - the eigenvalues of the rotational diffusion tensor - resulting in five rotational time constants. If two eigenvalues of the diffusion tensor are equal, the particle diffuses as a spheroid with two unique diffusion rates and three time constants. And if all eigenvalues are the same, the particle diffuses as a sphere with one time constant. The diffusion tensor may be determined from the Perrin friction factors, in analogy with the Einstein relation of translational diffusion, but often is inaccurate and direct measurement is required.
The rotational diffusion tensor may be determined experimentally through fluorescence anisotropy, flow birefringence, dielectric spectroscopy, NMR relaxation and other biophysical methods sensitive to picosecond or slower rotational processes. In some techniques such as fluorescence it may be very difficult to characterize the full diffusion tensor, for example measuring two diffusion rates can sometimes be possible when there is a great difference between them, e.g., for very long, thin ellipsoids such as certain viruses. This is however not the case of the extremely sensitive, atomic resolution technique of NMR relaxation that can be used to fully determine the rotational diffusion tensor to very high precision.

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  1. S

    How Do You Solve a Rotational Equilibrium Problem Involving a Meterstick?

    Hi- I have a homework question for physics. i have read the chapter in the book on it and have studied my notes and everything. i have been trying different ways for hours but i am unable to get any where. if you could help me get started on this problem that would be wonderful. i thought...
  2. S

    Rotational Equilibrium and Dynamics Problem

    Homework Statement A hanging 4 kg mass is connected by a weightless cord on a pulley to a 3 kg mass which rests on a smooth surface. The pulley has frictionless axle and I=.5kgm^2 and r=.3m. The cord does not slip on the pulley. Find the acceleration of the two masses and the tensions of the...
  3. I

    Why Can't I Solve This Rotational Equilibrium Problem?

    http://img95.imageshack.us/img95/9403/problempi4.png I know this problem isn't hard, but I can't reach the final answer in the back. OK, so if we project the forces along the x and y axis, we can easily conclude that: F_(T,2) + F_(T,1) * sin50 = 10 F_(T,1) * cos50 = P from here, though, I...
  4. A

    Rotational equilibrium and tension question

    I'm having a hard time with this rotational equilibrium problem: There is an attached image that shows the free-body diagram. The arm in the figure weighs 36.0 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force Ft in the deltoid...
  5. S

    Torque and Rotational Equilibrium

    Hi there, This is my first time on this great board, I hope I can get some help! I've tried both of these torque and equilibrium questions, but cannot find the required variable. (I've tried summing forces in the x and y) Please help...
  6. J

    Rotational Equilibrium and Dynamics

    I am currently studying Rotational Equilibrium and Dynamics in Physics. Our class was given a competitive lab project for extra credit, where the group with the lowest margin of error would win. It is set up as following: You will be given a meter stick and one weight (approximate value of...
  7. J

    Rotational Equilibrium problem

    One end of a uniform 4.00-m-long rod of weight w (Fg) is supported by a cable. The other end rests against the wall, where it is held by friction. The coefficient of static friction between the wall and the rod = 0.500. Determine the minimum distance x from point A at which an additional...
  8. E

    How Much Work to Tip a Cube into Unstable Equilibrium?

    A 10.0-kg solid uniform cube with 0.250-m sides rests on a level surface. What is the minimum amount of work necessary to put the cube in unstable equilibrium? My understanding is that the cube has to be on one of its sides with it's center of gravity directly above it. However, I don't know...
  9. R

    Rotational Equilibrium and Dynamics -

    Rotational Equilibrium and Dynamics - :) I'm totally stumped! --------------------- A skater spins with an angular speed of 12.0 rad/s with his arms outstretched. He lowers his arms, decreasing his moment of inertia from 41 kg·m² to 36 kg·m² Calculate his initial and final rotational...
  10. R

    Rotational Equilibrium and dynamics

    Please help me with these problems: 1) In a circus performance, a large 4.0 kg hoop with a radius of 2.0 m rolls without slipping. If the hoop is given an angeular speed of 6.0 rad/s while rolling on the horizontal and is allowed to roll up a ramp inclined at 15 degrees with the horizontal...
  11. R

    Rotational Equilibrium and Dynamics Question

    1) If you go to this site it has the question already set up. the one I need help on is question number 62, the picture frame one. I know that the answers are already given but I want to know how this is set up. http://www.phys.uvic.ca/vannetten/phys102/Assignments/t1a9p.pdf 2) A uniform...
  12. G

    Why Is the Mass of the Equal-Arm Balance Neglected in Torque Calculations?

    In my lab assignment, we used an equal-arm balance to demonstrate rotational equilibrium by balancing torques using different mass quantities. A 100 g mass hangs from one end of the EAB, and a 185.18 g mass hangs from a thread at a 50 degree angle on the other end. The EAB is horizontal and we...
  13. Greg Bernhardt

    Rotational Equilibrium and Dynamics

    Author: Dr. Donald Luttermoser of East Tennessee State University
  14. J

    Rotational equilibrium, subtending, and rotational acceleration

    The lightweight pivoted bar in Fig. MC8 will be in rotational equilibrium when a 200 N force acts none of these up at C only down at E or up at C up at B down at D (see attatched picture) So the net force has to be 0, i wasnt exactly sure how to do this one because i...
  15. W

    Rotational Equilibrium and Dynamics Help

    the following four questions were from my test that i recentally took and i miss the day that we went over them and didn;t get the answers and haven;t had to time to check with my teacher about them, so i need some help on what the answers would be. thanks. 1. If the torque required to...
  16. M

    HELP Rotational equilibrium material

    HELP! Rotational equilibrium material! HELP!---Okay, I am having some issues grasping the concepts of rotational equilibrium and dynamics. Specifically the equations: T=I*alpha L=I*omega T*delta t= delta L W=T*theta P=T* omega And there are also problems that I can't understand so I...
  17. Alethia

    Rotational Equilibrium and Dynamics

    Ah jeeze, I am so sorry to be posting up three questions. I don't mean to just get answers for my homework, but would anybody be willing to lead me in the right direction regarding these physics problems? I have the solutions, but I am unsure on how to get them. Thank you, anything helps...
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