8 ROTATIONAL MOTION
8 Rotational motion
8.1 Introduction
Up to now, we have only analyzed the dynamics of point masses (i.e., objects
whose spatial extent is either negligible or plays no role in their motion). Let us
now broaden our approach in order to take extended objects into account. Now,
the only type of motion which a point mass object can exhibit is translational mo-
tion: i.e., motion by which the object moves from one point in space to another.
However, an extended object can exhibit another, quite distinct, type of motion
by which it remains located (more or less) at the same spatial position, but con-
stantly changes its orientation with respect to other fixed points in space. This
new type of motion is called rotation. Let us investigate rotational motion.
8.2 Rigid body rotation
Consider a rigid body executing pure rotational motion (i.e., rotational motion
which has no translational component). It is possible to define an axis of rotation
(which, for the sake of simplicity, is assumed to pass through the body)—this axis
corresponds to the straight-line which is the locus of all points inside the body
which remain stationary as the body rotates. A general point located inside the
body executes circular motion which is centred on the rotation axis, and orien-
tated in the plane perpendicular to this axis. In the following, we tacitly assume
that the axis of rotation remains fixed.
Figure 67 shows a typical rigidly rotating body. The axis of rotation is the lineAB. A general point P lying within the body executes a circular orbit, centred
on AB, in the plane perpendicular to AB. Let the line QP be a radius of this
orbit which links the axis of rotation to the instantaneous position of P at time
t. Obviously, this implies that QP is normal to AB. Suppose that at time t + δt
point P has moved to PJ, and the radius QP has rotated through an angle δφ.