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Conditions for translational and rotational equilibrium

While zero net force is sufficient to ensure translational equilibrium, zero net torque is also required to ensure rotational equilibrium. When bothtranslational and rotational equilibrium is achieved, the object is said to be in a state of static equilibrium.

In order to achieve static equilibrium, the sum of the forces acting on the object mustbe zero and the sum of the torques about all axes must also be zero.

Choosing an axis of rotation

If an object is not already rotating, it may not be obvious how to determine the axis aboutwhich the object is likely to rotate. You need to ensure that the sum of the torques about that axis are zero.

As it turns out, you can choose just about any axis you please when doing the calculations to confirm that the sum of the torques are zero. You touched onthis in an earlier module involving the parallel axis theorem. It can be shown that if the net force acting on an object is zero and the net torque about oneaxis is zero, the net torque about every other parallel axis will also be zero.

The worst case scenario

In the worst case, therefore, you can ensure rotational equilibrium by ensuring that the net torque about three orthogonal axes are zero. In somecases, it will be obvious that you only need to worry about one axis. In some cases, you would need to worry about two or three axes.

A ladder

Before climbing a ladder, for example, you need to ensure rotational equilibrium about

  1. One axis that is parallel to the rungs on the ladder
  2. One axis that is perpendicular to a rectangle formed by two rungs and the side rails
  3. One axis that is parallel to the side rails on the ladder

The lack of rotational equilibrium about any of these three axes can result in a nasty fall from a ladder.

Ensuring rotational equilibrium for a ladder

Ladder manufacturers install special "feet" with a high coefficient of friction on ladders to avoid accidents from the first item in the above list.These feet are designed to prevent the ladder from sliding away from the wall that it is leaning on.

They also install wide outriggers on the base of very tall ladders to avoid accidents from the second item in the list. The outriggers are designed toprevent top of the ladder from sliding sideways on the wall.

Tree trimmers that use ladders to trim trees take special precautions to prevent accidents from the third item in the list in those cases where bothsides of the top of the ladder are not firmly supported.

Simplification through the choice of an axis

A judicious choice of axis can often greatly simplify the solution of an equilibrium problem by causing one or more forces to go through the axis. Thiseliminates the effect of those forces from the computation of rotational equilibrium.

Example scenarios

I will present several example scenarios involving rotational equilibrium in this section. In several cases, I will ask you to construct a replica of thescenario on your graph board.

All scenarios assume that counter clockwise rotation is the positive direction of rotation. All scenarios also assume that the positive horizontal axis is to the right and the positive vertical axis is up.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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