Uniform circular motion.

R = radius; f = frequency; W = angular velocity/frequency; V = tangential velocity; A = centripetal acceleration

R=1

f=slider([0,1])

W=2*pi*f,V=W*R,A=V^2/R

x^2+y^2=R^2

Radial and tangent vectors:

function(X,s)=vector(cos([W*s]),sin([W*s]))

function(T,s)=vector(-sin([W*s]),cos([W*s]))

Point in motion on circle:

function(X,n)*R

Velocity vector:

function(X,n)*R,function(T,n)*V+function(X,n)*R

Change in velocity ...

m=slider([0,0.5])

function(X,n+m)*R,function(T,n+m)*V+[function(X,n+m)]*R

D=[function(X,n+m)-function(X,n)]*R

... replanted at same time t = n as velocity ...

function(X,n+m)*R-D,function(T,n+m)*V+[function(X,n+m)]*R-D

... Delta V ... transported back to t = n ... [m = 0.1 reasonably visible]

d=[function(T,n+m)-function(T,n)]*V

a=slider([0,1])

function(T,n)*V*a+function(X,n)*R,function(T,n)*V*a+function(X,n)*R+d

(Centripetal) acceleration vector:

function(X,n)*R,function(X,n)*R-(function(X,n)*A)


Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

This file was created by Graphing Calculator 3.5.
Visit Pacific Tech to download the helper application to view and edit these equations live.