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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

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.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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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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