Global Utilities

Department of Mathematical and Statistical Sciences

Mathematics Section

Geometry in Motion

Motion on a Circle

Uniform Motion Clockwise

Another possible parametrization for uniform motion on a circle is

$\displaystyle \vec{r}=(a \sin t, a \cos t)$


Description of the Motion

Notice that for this motion at

$\displaystyle t$ $\displaystyle =0,\quad \vec{r} =(0,a)$    
$\displaystyle t$ $\displaystyle =\pi/2,\quad \vec{r} =(a,0)$    
$\displaystyle t$ $\displaystyle =\pi,\quad \vec{r}=(0,-a)$    

Hence the Motion is clockwise around the circle. (To see this, click on the interactive picture to the right, and when the java applet has loaded, select "clockwise" in the top left corner.)

We could also consider

$\displaystyle \vec{r}=(a \cos t, a\sin t)$

This motion is anticlockwise and starts at $ (a,0)$.


 

 

 

Content Approved by: Head of Department
Page maintained by: Web Administrator
Last Updated: 10 March, 2008

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Tutorials

Motion of a circle
Motion of an Ellipse
Motion of a Parabola
Motion of a hyperbola
Motion on a Cycloid