What is Rotational equilibrium: Definition and 67 Discussions
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.
My approach to this problem is to recognize that the tetrahedron being still means that net torque is zero and net force is zero.
Fd is given
Fa + Fb + Fc = -Fd
Fa X a + Fb X b + Fc X c = <0,0,0>
This can be split up into a series of 6 equations, 2 for each component.
However, this is where I...
I am confused because according to my solution the disk is already rotating at constant angular velocity.
I have written the translational equilibrium on the horizontal and vertical component:
##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
See attached for work. I did notice that making the torque from the force of gravity negative I got the right answer, but don't understand what I did wrong (its positive in my solution). i hat cross negative k hat is a positive number after all.
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...
Homework Statement
A disc is free to rotate about an axis passing through its center and perpendicular to its plane. The moment of inertia of the disc about its center is I. A light ribbon is tightly wrapped over it in multiple layers. The end of the ribbon is pulled out at a constant velocity...
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...
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...
Homework Statement
A bar of uniform density, length L, and mass m is suspended by two ropes of tensions T1 and T2 at either extremity of the bar. The bar is tilted such that it makes an angle θ with the ropes. A mass M is resting at a distance l from T1.
https://i.imgur.com/vLlAJbe.png
If...
Homework Statement
8. A 20 kg uniform beam 10m long is attached to a wall with a cable. The cable is attached to the middle of the beam at a 90 degree angle to the beam. A box of mass 5 kg is also suspended from the beam. In addition to this, the beam is attached to the hinge at the bottom...
Hello everyone!
I'm new here and I have never been too good at physics, but now I've been trying to revise for the MCAT and I have stumbled across this question in "Kaplan MCAT Physics and Math Review":
If you have and object three times as heavy as you can lift, how could a lever be used to...
Homework Statement
Homework Equations
ok, I thought that the torque from the mass 'm' would be equal to torque from mass 'M'
The Attempt at a Solution
I wrote down:
m * g * (d/4) = M * g * d
(m/4) = M
m = 4M
Thus, the ratio is 4M : 1 m, which gives answer 1.
However, the solutions say...
Homework Statement
Homework Equations
sum of torques = 0
The Attempt at a Solution
So I tried to put the torques into the equation:
Sum torques = mgL - T *sin(theta) * (L-x) = 0.
Solving for the T gave me [mgL]/[ (L-x) * sin(theta) ]. This is not an option in the answers.
Could anyone...
1. Homework Statement
problem is above
Homework Equations
sum of torques = I * angular acceleration = 0 for rotational equilibrium
The Attempt at a Solution
OK, here's what I tried to do.
I wrote sigma Fy = Fleft pier up + F secondleftpierup - Fg,beam = 0
I assumed that the two piers have...
Homework Statement
The landing gear of an aircraft is composed of a main leg OA (with a weight including the wheel is
1000N to G) and two secondary links BC and 50cm long each CD. The DC link forms an angle
θ of 30 degrees with the vertical.
a) Add the rotational equilibrium equation with...
Homework Statement
A seesaw with a mass of 5 kg has one block of mass 10 kg two meters to the left of the fulcrum and another block 0.5 m to the right of the fulcrum. If the seesaw is in equilibrium,
A. find the mass of the second block.
B. find the force exerted by the fulcrum
I have trouble...
Hi Everyone,
I'm having some trouble with a problem concerning translational and rotational equilibrium. The question involves a balance with various masses suspended from it (see attached image). The question states that the counterweight is moved from 1cm away from the fulcrum to 2cm away from...
Mass 1 is located at the far left end of a 90 cm beam. Mass 2 is located at the center of the beam, and mass 3 is located 30 cm from the center, on the right side. Mass 3 and mass 1 are the same. If the fulcrum is located 10 cm to the left of the center of the beam, what is the mass of mass 2 if...
Homework Statement
Answers were told to us to be
F = 2.91 N
Ft1 = 13.32 N
Ft2 = 3.36 N
Homework Equations
Fx = Ft2 cos(θ) - F = 0
Fy = Ft2 sin(θ) + Ft1 - Fg = 0
Torque equation
-FgDg - Ft2D1x cos(θ) + Ft2D1y sin(θ) = 0
The Attempt at a Solution
I plugged in all of the information i had...
Here is a text from my Physics Book :
The net external torque on the object about any axis must be zero for it to be in rotational equilibrium.
I divide the torques into two categories, anticlockwise and clockwise. (This approach works fine for 2-D objects but will it work for 3-D objects...
Hi,
The question I have is not for a numerical answer but for clarification.
Some of the questions involving torque/rotational equilibrium describe a person standing on a plank. I know that the gravitational force of the person on the plank needs to be considered for translational and...
Homework Statement
When I drag my feet on the ground (on a frictionless surface), there will be an equal but opposite force acting on another body. What is that body exactly?Homework Equations
none
The Attempt at a Solution
Will it be transferred to some other parts to my body? So in space...
Hello I've attached the problem. Any help would be greatly appreciated.
I understand that by giving us the clue of rotational equilibrium, it means net T has to be 0. The force at 10N will cause clockwise torque (T= rF, so T = .04m * 10N). The thing that confuses me is the force at point...
Homework Statement
This is not a homework question, I was just curious.
I'm trying to find the angle θ that an unbalanced arm produces in the following case:
Homework Equations
τ=rF
The Attempt at a Solution
τ1=τ2
rF=rF
r(98 N)(cos θ)=r(49 N)(cos θ)
However, the cos θ...
Homework Statement
Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappelling). They do this with their body nearly horizontal and their feet pushing against the cliff. Suppose that an 82.0 kg climber who is 1.90m tall and has a center of gravity...
I need help with this physics problem! Please help I'm completely stuck.
A beam 3m long is free to pivot up and down about the end attached to a wall. The mass of the beam is 25 kg and the cable supporting the beam can support a maximum force of 1800 N. What is the maximum mass that a man...
Homework Statement
Consider a cyclist turning around a circular track with radius r and speed v as shown
in attached fig.
Let W be the weight of the system (cyclist + bicycle) (W = mg)
N = normal force by ground on the system
f = static friction by ground on the system
θ = angle of...
Homework Statement
Why, for any system that is in rotational equilibrium, the torque about 1) any point on the object or 2) any point in space, must be zero.Homework Equations
N/AThe Attempt at a Solution
What I do not understand is, why the torque about ANY point on the object is zero...
Homework Statement
A solid rectangle of uniform density has one corner at the origin. It has a mass of 50 kg. The rectangle
has a length of 4 m in the z-direction, a length of 3 m in the y-direction, and a length of 2 m in
the x-direction. The pivot is at the center of mass.
There is a 50 N...
Homework Statement
a restaurant sing hangs from a metal bar attached to a wall and supported by a wire. the bar has a mass of 5 kg, and a length of 1.2 m. the sign has a mass of 23 kg and hangs from 2 chains located at .3 m from each end of the bar. the wire makes a 28 degree angle with the...
Homework Statement
A house painter stands 3.0 m above the ground on a 5.0 m long ladder that leans against the wall at a point 4.7 m above the ground. The painter weighs 680 N and the ladder weights 120 N. Assuming no friction between the house and the upper end of the ladder, find the force...
Suppose we have a uniform disk and two forces are acting tangentially at the rim (both pointing in the same direction and parallel to each other and at diametrically opposite ends of the disk).
Since the disk does not rotate the sum of torques about an axis passing thorugh the center of the...
Homework Statement
There are two important conditions for a rigid body to be in equilibrium. The first condition is that the net force on a body must be zero. The second condition is that the net torque on a body must also be zero.
2,3. Relevant equations; attempt at solution.
I...
URGENT! Boom problem using rotational equilibrium methods
Hi!
Here is a picture of the problem I'm about to explain... http://i96.photobucket.com/albums/l168/synovial/boom.jpg
My professor did not give us numbers to use, just variables.
The goal of the problem is to find the 3...
Homework Statement
A nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in Fig. 12-45. One cord makes the angle θ = 15.5° with the vertical; the other makes the angle φ = 58.5° with the vertical. If the length L of the bar is 6.08 m, compute the...
Homework Statement
I think I'm being a bit dull today but I seem to be having real trouble understanding this question...
Two children wish to make a see-saw from a 5m plank of wood, the children weigh 25kg and 20kg. They wish to sit right on the ends of the plank. Where should the plank be...
Homework Statement
The mass m1 is 0.55 kg and it is located at x1 = 30 cm. The pivot point is represented by the solid triangle located at x = 45 cm. The mass of the meter stick (mms = 0.40 kg) is located at its geometric center, xms = 50 cm. The mass m2 is 0.35 kg and it is located at x2 = 80...
3 forces act on an object. If the object is in translational equilibrium, which of the following must be true?
1. the vector sum of the forces =0
2. the magnitude of the 3 forces must be equal
3. the 3 forces must be parallel
would the answer be just 1? I don't think 2 is true because...
Torques: Rotational Equilibrium Mobile :)
Homework Statement
Please! I really need help figuring out how to make a balanced mobile!
I would really appreciate anyones help!
Directions:
Apply what you know about torques by making a mobile. Shown below are five horizontal arms with fixed 1-...
In my general physics lab, we are trying to show that certain systems are in equilibrium. The apparatus that we are using for rotational equilibrium consists of a boom resting on an axis point, attached to a string/pully that has a given tension.
The measured forces in the lab are in...
The impression I'm getting of rotational equilibrium is that it applies to objects that are connected to an axis of rotation, such as a ball connected to a rod. What if a car was moving in a circular path, would the concept of torque apply to it, even though it's not connected physically to its...
Homework Statement
(Figure is attached)
A 1200.0 N uniform boom is supported by a cable,as
shown in Figure 8-22.The boom is pivoted at the bot-
tom,and a 2000.0 N weight hangs from its top.Find the
force applied by the supporting cable and the compo-
nents ofthe reaction force on the...
[SOLVED] Rotational equilibrium
Homework Statement
This isn't actually a problem, but a portion of our latest lab assignment.
There is a pole with 3 hooks in it, one in the center at the top and two at varying distances on the bottom. The pole is hanging from a ringstand by the top hook...
Homework Statement
Here is the problem and a diagram:
http://www.city-wars.com/lastscan.jpg
Homework Equations
T= r*F
The Attempt at a Solution
I don't know where to begin. Where are the normal forces acting? I am just can't visualize this problem and it has me stumped.
The Question:
A potter's wheel having a radius of 0.50 m and a moment of inertia of 12 kg m^2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 sec by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of...
Rotational Equilibrium - Help!
Homework Statement
http://photos-a.ak.facebook.com/photos-ak-sf2p/v142/24/75/1238100168/n1238100168_30095452_8017.jpg
A uniform metal bar of mass 100 kg and length L (2.5 m) extends horizontally from a wall and connected to the wall by a pivot (F is...
Homework Statement
A 12 kg mass is attached to a cord that is wrapped around a wheel with a radius of 10.0 cm. The acceleration of the mass down the frictionless incline of 37 degrees is measured to be 2.0 m/s^2. Assuming the axle of the wheel to be frictionless, determine:
a). the force in...
Homework Statement
Question Details:
A 10 kg engine is rotating at the rate of 20 rad/sec about a point on a wire 3 meters in length with a working tensile strength of 1.8*106 N. The engine is fired and produces an acceleration of 1 rad/sec2. What's the maximum possible ω (angular velocity)...
Hello-
i have a homework problem that i could use some help on.
i have read the entire chapter and all of my notes from class. i have studdied everything i had and have had no luck. so if you can help that would be GREAT! i have done the first step of drawing a picture and i think for the...