Suppose you have a reflector mounted right at the rim of a
bicycle wheel. If you hold the wheel up in the air and spin
it, the reflector traces out a circular path. The equation
describing the position is as a function of time is give
by eq. 5.7.
But when a camel is riding the bicycle, the wheel is on
the ground so that the center of the wheel is moving.
We'll see in a month or so that the velocity of the
center of the wheel is 
. That implies that the
the position of the center of the wheel as a function
of time is 
. So from equation 5.22
we have that the position of this reflector relative
to the ground is the sum of two terms. The position of the
reflector relative to the center of the wheel, plus the
position of the center of the wheel relative to the ground:
This traces out a ``cycloid'' as shown in the figure below. Notice the series of cusps that occur when the reflector is close to the ground. When you look at a bicyclist at night, if they're being good and have reflectors on their wheels, you should be able to see these cycloidal trajectories.
