[quote author=Fu-Kwun Hwang link=topic=141.msg707#msg707 date=1075356805]
This applet shows the <b><font COLOR="#0000FF">positon</font></b>,<b><font COLOR="#0000FF">velocity</font> </b>and <b><font COLOR="#0000FF">acceleration</font></b><b><font COLOR="#0000FF">vectors</font></b></font>
of a point on the rim of a body <b>rolling without slipping</b></font>on a stationary surface.</font>
<center><applet code=freeRolling.class width=550 height=360 codebase="/java/FreeRolling/">
<param name="MSG1" value="Circular motion">
<param name="MSG2" value="Free Rolling">
<param name="Reset" value="Reset">
</applet></center><ol><font SIZE=+1>1. The term freely rolling means that there is no slipping (v=rw) </font><ol><font SIZE=+1>at the point of contact with the ground</font><font SIZE=+1>--no skidding (v>rw) and no spinning in place (w>v/r),</font><font SIZE=+1>where v,r and w are the linear speed, radius and</font><ol><font SIZE=+1>the angular speed of the rolling body.</font></ol></ol><font SIZE=+1>2. The center of the wheel has a linear speed (with respect to ground) </font><ol><font SIZE=+1>equal to that of any point on its rim (with respect to center).</font></ol><font SIZE=+1>3. For circular motion (in the reference frame</font><ol><ol><font SIZE=+1>moving with the velocity of the center of the rolling body) :</font></ol><font SIZE=+1>The acceleration <b>a</b> of a point always points in a direction</font><ol><font SIZE=+1>opposite the position vector <b>r</b>,</font></ol><font SIZE=+1>and the velocity vector <b>V</b> is perpendicular to both of them.</font></ol><font SIZE=+1>4. Observe the velocity vectors of a point on the rim</font><ol><ol><font SIZE=+1>of the rolling body.</font></ol><font SIZE=+1>The white vector represents the velocity of the center</font><ol><font SIZE=+1>with resepect to ground and </font></ol><font SIZE=+1>the red vector represents the velocity of the point</font><ol><font SIZE=+1>with respect to the center.</font></ol><font SIZE=+1>The sum of these two vectors is the cyan vector</font><ol><font SIZE=+1>representing velocity of the point relative to ground.</font></ol></ol><font SIZE=+1>5. The green curve shows the trajectory of a point on the rim.</font></ol>
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