Here, is the internal force exerted on the th element by the th element, and the external force acting on the th element. The internal forces represent the stresses that develop within the body in order to ensure that its various elements maintain a fixed spatial relationship with respect to one another. Of course, , by Newton's third law. The external forces represent forces that originate outside the body.

Repeating the analysis of Section 2.6, we can sum Equation (8.1) over all mass elements to obtain

Here, is the total mass, the position vector of the center of mass [see Equation (2.27)], and the total external force. It can be seen that the center of mass of a rigid body moves under the action of the external forces like a point particle whose mass is identical with that of the body.

Again repeating the analysis of Section 2.6, we can sum Equation (8.1) over all mass elements to obtain

Here, is the total angular momentum of the body (about the origin), and

In the following, we shall only consider the rotational motion of rigid bodies, because their translational motion is similar to that of point particles [see Equation (8.2)] and, therefore, is fairly straightforward in nature.