This week, we will consider the special case
of circular motion.
The case where we know that the motion is exactly constrained
to have a circular geometry.
This will consist of two parts.
First, we will consider the kinematics of circular motion.
How do we describe the trajectory, velocity,
and acceleration of a particle undergoing circular motion?
We will consider both the simple case
of uniform circular motion, where the object moves
with constant speed, and also nonuniform circular motion,
where the object is speeding up and/or slowing down
as a function of time.
We will see that a Cartesian coordinate
system proves awkward for describing circular motion.
And instead, we will introduce the so-called polar coordinate
system in terms of the radius vector
from the origin and its position angle, which
provides a much more elegant description
for circular motion.
We will then examine the dynamics of circular motion
using Newton's second law to understand what sorts of forces
are required in order to cause circular motion in both
the uniform and nonuniform cases.
This will be the first of several examples
we will see in this course of constrained motion.
In this case, the constraint is that the object
moves in a circular path.