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A wheel of radius 1 revolves at a constant angular velocity and travels in a straight line on a level surface. Plot the path traced out by a piint on the edge of the wheel. You should take in to account the fact that the wheel is not only revolving but its centre is moving in a direction opposite to the motion of the edge of the wheel at the point where it touches the surface. The equation of motion should be a two coordinate function of the form [X(t), Y(t)]. In order to plot the path of such a function over one complete revolution you can use the Maple command plot([X(t), Y(t)],t=0..2*Pi]);. Trace the motion of a point which is halfway between the edge and the hub of the wheel. Calculate the length of the path travelled by such a point when the wheel has made a quarter revolution.

Next, consider a wheel of radius tex2html_wrap_inline9 rotating along the outside rim of a fixed wheel of radius tex2html_wrap_inline11. Trace the motion of a point on the edge of the outer wheel for a few different values of tex2html_wrap_inline9 and tex2html_wrap_inline11. What happens if the free wheel travels along the interior rim of the fixed wheel. Calculate the distance travelled by a point on the edge of such a wheel if tex2html_wrap_inline17 and tex2html_wrap_inline19 and the free wheel makes 2 complete revolutions.

Finally, create an animation which shows both wheels as well as the point on the edge of the free wheel as they rotate.




Juris Steprans
Thu Mar 27 17:08:57 EST 1997