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Radial acceleration

A student ties a 10 kg mass onto a fishing line with a breaking strength of 5 newtons, and then starts swinging the mass around over his head. The studenttries very hard to cause the path to be circular. The distance from the center of the circle to the mass is 3 meters.

As time goes on, the student swings the mass faster and faster until the fishing line breaks. What is the tangential velocity of the mass when thefishing line breaks.


Centripetal force = mass * (centripetal acceleration), or

f = m * Ar, or

f = m * v^2/r, or

v^2 = f*r/m, or

v = (f*r/m)^(1/2), or

v = (5 newtons * 3 meters/10 kg)^(1/2), or

v = 1.22 m/s

The magnitude of the tangential velocity of the mass when the fishing line breaks is 1.22 meters/second

Check the solution using angular velocity, w

w = v / r, or

w = (1.22 m/s) / 3m = 0.407 radians/second

The angular velocity for a tangential velocity of 1.22 m/s is 0.407 radians/second

Ar = (w^2)*r, or

Ar = (( 0.407 /second)^2)*3m, or

Ar = 0.5 m/s^2

The magnitude of the radial acceleration is 0.5 m/s^2

f = m * Ar, or

f = 10kg*(0.5 m/s^2), or

f = 5 newtons, or

the force equals 5 newtons, which matches the breaking strength of the fishing line.

Work through the examples

I encourage you to work through the examples that I have presented in this module toconfirm that you get the same results. Experiment with the scenarios, making changes, and observing the results of your changes. Makecertain that you can explain why your changes behave as they do.


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 -- The Mathematics of Circular Motion
  • File: Phy1260.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • angular displacement
    • angular velocity
    • radian measure
    • tangential displacement
    • tangential speed
    • frequency
    • period
    • centripetal
    • centripetal acceleration
    • centripetal force

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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

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
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
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.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
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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