# 0.29 Phy1260: circular motion -- the mathematics of circular motion  (Page 5/7)

 Page 5 / 7

## 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
• 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

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

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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