We begin our study of rotational motion by defining exactly what is meant by
rotation, and establishing a new set of variables to describe rotational motion.
From there we will revisit kinematics to
generate
equations for the motion of rotating bodies.

####
Definition of Rotation

We all know generally what it means if an object is rotating. Instead of
translating, moving in a straight line, the object moves about an axis in a
circle. Frequently, this axis is part of the object that is rotating. Consider
a bicycle wheel. When the wheel is spinning, the axis of rotation is simply a
line going through the center of the wheel and perpendicular to the plane of the
wheel.

In translational motion, we were able to characterize objects as point particles
moving in a straight line. With rotational motion, however, we cannot treat
objects as particles. If we had treated the bicycle wheel as a particle, with
center of mass at its center point, we would observe no rotation: the center of
mass would simply be at rest. Thus in rotational motion, much more than in
translational motion, we consider objects not as particles, but as *rigid
bodies.* We must take into account not only the position, speed and
acceleration of a body, but also its shape. We can thus formalize our
definition of rotational motion as such:

*A rigid body moves in rotational motion if every point of the body moves in a
circular path with a common axis.*

This definition clearly applies to a bicycle wheel, due to its circular
symmetry. But what about objects without a circular shape? Can they move in
rotational motion? We shall show that they can by a figure:

Figure %: An arbitrarily shaped object rotating about a fixed axis

The figure shows an object with no circular symmetry, rotating

90^{
o
}
about a fixed point A. Clearly all points on the object move about a fixed axis
(the origin of the figure), but do they all move in a circular path? The figure
shows the path of an arbitrary point P on the object. As it is rotated

90^{
o
}
it does move in a circular path. Thus any rigid body rotating
about a fixed axis exhibits rotational motion, as the path of all points on the
body are circular.

Now that we have a clear definition of exactly what rotational motion is, we can
define variables that describe rotational motion.

####
Rotational Variables

It is possible, and beneficial, to establish variables describing rotational
motion that parallel those we derived for translational motion. With a set of
similar variables, we can use the same kinematic equations we used with
translational motion to explain rotational motion.