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Similar to Newton's second law

This equation is Newton's second law applied to a system of particles in rotation about a given axis. It makes no assumptions about constant rotationalvelocity.

Torque from an anecdotal viewpoint

One of the objectives of this module is to develop concepts involving rotational motion that are analogous to concepts from earlier modules that involve translationalmotion.

A Lazy Susan

On my dining room table, there is a device that is commonly called a Lazy Susan. In case you are unfamiliar with such devices, it is essentially aturntable. By a turntable, I mean a rather large disk mounted on bearings so that it is free to turn in a plane that is slightly above but parallel with thetop of the dining room table.

The purpose of the Lazy Susan

The purpose of a Lazy Susan is to make it easier to serve food at the dining room table. Various dishes are placed on it . When someone wants a helping ofcarrots, for example, instead of saying "Please pass the carrots," they simply turn the Lazy Susan until they can reach the bowl of carrots and helpthemselves.

Not a module about carrots

However, we won't be discussing how to serve carrots in this module. In this module, I will use the Lazy Susan, in its empty state between meals, to discussvarious aspects of rotating rigid objects.

To make it easier to type the material under discussion, I will refer to the Lazy Susan as a turntable. (For some reason, I can type turntable much morequickly than I can type Lazy Susan.)

Low angular acceleration when coasting

My turntable has pretty good bearings. It is also rather heavy for its size and therefore has a relatively large rotational inertia or moment of inertia, whichever term youprefer.

If you give it a good spin, it will spin for quite a while before all of its rotational energy is dissipated through friction in the bearings and airresistance. By default, therefore, its angular acceleration is low. In other words, the rate of change of its angular velocity is small.

A perpetual motion machine

If we could find a way to eliminate all of the frictional forces acting on the turntable, including air resistance, then it would spin forever. In thatcase, we would have invented what has been called a perpetual motion machine. Therate of change of angular velocity would be zero, meaning that its angular acceleration would also be zero.

Similar to Newton's first law

This reminds us of a moving body that satisfies Newton's first law, which can be paraphrased something like the following:

  • a body in motion, being acted upon by no net forces, will continue moving forever in a straight line.

In other words, that law tells us that absent a force to the contrary, a moving body will continue tomove with no change in velocity.

If we could eliminate all of the frictional forces acting on my turntable (which is a rotating body), we might like to say that

  • absent any net forces acting on the body, a rotating body with a constant rotational inertia willcontinue rotating with the same angular velocity forever.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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