It's Like Riding a Bicycle

One of the advantages of modeling physical phenomena with parametrization is that we can break up motion into different components.

For example, suppose we want to model the path drawn out by a squashed piece of gum on the tube of a bicycle wheel. We will assume

Let's first assume that the bicycle travels in a straight line. To describe the motion, let us first parametrize the curve in the plane that describes the path of the center of the wheel: t -> (10t,14/12) (Why is this correct?). Meanwhile, on the outside perimeter of the wheel, the squashed piece of gum turns in a circular motion. If we use a coordinate system with the origin at the center of the wheel, the circular component of the gum's motion is a circle: t -> (14/12 cos(wt), 14/12 sin(wt)). The angular velocity, w, determines the rate at which the gum turns in a circle. The value for w may be calculated from the bicycle's speed and the radius of the bicycle tire.


Question #3


The curve traced out in the previous problem is called a cycloid. If we generalize the curve so that we model a bike reflector on a spoke of the wheel, we obtain a different curve, called a trochoid.

Question #4


Next: Moving on to 3D
Up: Introduction
Previous: Circular Motion

Robert E. Thurman<thurman@geom.umn.edu>
Jeremy Case
Document Created: Mon Feb 20
Last modified: Tue Feb 27 08:36:55 1996