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where

  • s1 through s4 represent the four different speeds
  • r1 through r4 represent the radii of the four circles

Speed is proportional to radius

As you can see, the average speed for each rider is directly proportional to the radius of the circle on which that rider is traveling. Doubling the radius doubles the average speed. Ifthere were a horse located 5 meters from the center of the carousel, the average speed for that horse would be only half of your average speed at 10 meters, or 1m/s.

Velocity

Just because you are traveling at a constant speed (during a portion of the ride anyway), doesn't mean that you are traveling at a constant velocity. Youlearned in an earlier module that an object in motion tends to remain in motion in a straight line unless a force is applied to cause the object to changedirection.

You are constantly changing direction

When you are riding on the carousel, you are constantly changing direction. Otherwise you would travel in a straight line instead of traveling in a circle.

A force is required to cause you to continually change direction and to travel in a circle. That forceis exerted on your body by your grasp on the horse on which you are sitting.

Goodbye horse and rider

If the brackets that attach your horse to the carousel were to break, you wouldcontinue to travel in a straight line at that point, leaving the carousel behind.

A tangential velocity vector

At any instant in time, the direction of your velocity vector is a direction that is tangent to the circle on which you are traveling. Stated differently,the direction of your velocity vector is along a line that is perpendicular to a line that extends from your center of mass to the center of the circle. (A tangent line is a line that touches a circle at one point but does not intersect it.)If you sit very straight on the horse and face straight ahead, you will be facing the direction of your velocity vector.

Summary

An object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. Although the speed of the object is constant, the object's velocity isconstantly changing.

The object's velocity vector has a constant magnitude but a changing direction. At any instant in time, the direction of the velocity vector is tangent to the circle.As the object travels along the circular path, during one full rotation (cycle) around the center, the tangent line is always pointing in a new direction.During each cycle, the velocity vector points in the same (infinite) set of directions.

A force must be exerted on an object to cause it to travel along a circular path instead of traveling in a straight line. As you will learn in afuture module, this force is called the centripetal (center seeking) force.

A thought experiment

Assume that you attach one end of a garden hose to a faucet and then arrange the hose in a circle on the ground. When you turn the water on, will the waterexit the hose and continue moving in a circular path, or will it move in a straight line (ignoring the effects of gravity, air resistance, etc.)?

You may already know from experience that when the water exits the hose, it moves in a straight line. While the water was inside the hose, it moved in acircular path due to the force exerted on the water molecules by the inside surface of the hose.

When the water exits the hose, that force will no longer be applied to the water molecules. According to Newton, the water will continue in motionat a constant velocity, meaning that the direction of the velocity vector for the water molecules will not change.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Circular Motion -- Speed and Velocity
  • File: Phy1240.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • uniform circular motion
    • average speed
    • velocity
    • velocity vector
    • circumference
    • radius
    • period
    • periodic motion
    • carousel
Disclaimers:

Financial : Although the openstax CNX site makes it possible for you to download a PDF file for the collection that contains thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.

In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.

Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
Sanket 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
I'm interested in nanotube
Uday
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
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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