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The relationship between period and frequency

As you already know, when the speed of a point moving in a circle is constant, its motion is called uniform circular motion.

As you also already know, even though the speed of the point is constant, the velocity is not constant. The velocity is constantly changing because the direction of thevelocity vector is constantly changing.

The period

The amount of time required for the point to travel completely around the circle is called the period of the motion.

The frequency

The frequency of the motion, which is the number of revolutions per unit time, is defined as the reciprocal of the period. That is,

frequency in rev per sec = 1/(period in sec per rev), or

f = 1/T

where

  • f represents frequency in revolutions per second
  • T represents period in seconds per revolution

The relationship between angular velocity and frequency

The speed of a point moving completely around the circle is equal to the distance traveled divided by the time.

sT = 2*pi*r/T, or

sT = 2*pi*r*f

where

  • sT is the tangential speed
  • r is the radius
  • T is the time required for the point to make one complete revolution
  • f is the reciprocal of T

We know from before that

sT = w * r, or

w = sT/r

Therefore, by substitution from above,

w = 2*pi*r*f/r = 2*pi*f, or

the angular velocity in radians per second is the product of 2*pi and the frequency in revolutions per second.

where

  • sT is tangential speed
  • w is angular velocity in radians per second
  • f is frequency in revolutions per second, or cycles per second, or hertz

The SI unit for frequency

The SI unit for frequency is hertz (Hz) where 1 Hz is equal to one revolution per second or one cycle per second.

Facts worth remembering

w = 2*pi*f

where

  • w is angular velocity in radians per second
  • f is frequency in revolutions per second, or cycles per second, or hertz

The SI unit for frequency is hertz (Hz) where 1 Hz is equal to one revolution per second or one cycle per second

Radial (centripetal) acceleration

In an earlier module, you learned how to subtract vectors and; demonstrate that the acceleration vector of an object moving with uniformcircular motion always points toward the center of the circle. However, in that lesson, we did not address the magnitude of the acceleration vector. We will dothat here.

A very difficult derivation

Deriving the magnitude of the acceleration vector depends very heavily on the use of vector diagrams, complex assumptions, complicated equations.Unfortunately, this is one of those times that I won't be able to present thatderivation in a format that is accessible for blind students. In this case, blind students will simply have to accept the final results in equation form anduse those equations for the solution of problems in this area.

Facts worth remembering

Ar = v^2/r, or

Ar = (w^2)*r

where

  • Ar is the magnitude of the radial acceleration
  • v is the magnitude of the tangential velocity of the object moving around the circle
  • r is the radius of the circle
  • w is the angular velocity of the object moving around the circle

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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it is a goid question and i want to know the answer as well
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for teaching engĺish at school how nano technology help us
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
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what is the function of carbon nanotubes?
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I'm interested in nanotube
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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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