  We present a simple, two dimensional example of a "cat" -- a body with zero
angular momentum that can rotate itself with no external forces. This model is
used to explain why this problem is known to be a gauge theory and to
illustrate the importance of non-commutative operators. We will also show a
comparison between the free-space "cat" in Newtonian mechanics and the same
problem in Aristotelian mechanics at low Reynolds number; this simple example
shows the analogy between (angular) momentum in Newtonian mechanics and
(torque) force in Aristotelian mechanics. We will end by pointing out a
topological invariant common to our model in free space and at low Reynolds
number.

Classical Physics