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  • 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.


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.


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.


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.


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

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.


Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
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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