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 rotating along the outside rim of a fixed wheel of radius . Trace the motion of a point on the edge of the outer wheel for a few different values of and . 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 and 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.