<< Chapter < Page Chapter >> Page >

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.

Solution:

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.

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 -- 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
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

a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
f(n)= 2n + 1
Samantha Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Accessible physics concepts for blind students' conversation and receive update notifications?

Ask