9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system
l 1 l 2m mr rOaxis of rotationv 1 v 2 lFigure 86: A principal axis of rotation.9.4 Angular momentum of a multi-component system
Consider a system consisting of N mutually interacting point particles. Such
a system might represent a true multi-component system, such as an asteroid
cloud, or it might represent an extended body. Let the ith particle, whose mass is
mi, be located at vector displacement ri. Suppose that this particle exerts a force
fji on the jth particle. By Newton’s third law of motion, the force fij exerted by
the jth particle on the ith is given by
fij = −fji. (9.24)Let us assume that the internal forces acting within the system are central forces—
i.e., the force fij, acting between particles i and j, is directed along the line of
centres of these particles. See Fig. 87. In other words,
fij ∝ (ri − rj). (9.25)Incidentally, this is not a particularly restrictive assumption, since most forces
occurring in nature are central forces. For instance, gravity is a central force,
electrostatic forces are central, and the internal stresses acting within a rigid
body are approximately central. Suppose, finally, that the ith particle is subject
to an external force Fi.
l 2l 1