Chasle s theorem states that the general motion of a rigid body can be represented as a superposition of a translation following any point in a body and a pure rotation about that point. The kinematics tools we have developed provide the capability to describe these motions in terms of a few parameters. In this chapter we begin to characterize the relationship between forces acting on a rigid body and kinematical parameters for that body. The resultant of a set of forces may be regarded intuitively as the net tendency of the force system to push a body, so one should expect it to be related to the translational effect. Similarly, it is reasonable to expect that the resultant moment of a set of forces represents the rotational influence. We shall confirm and quantify these expectations.

From a philosophical perspective, the shift from statics, in which one equilibrates forces, to kinetics, in which the forces must match an inertial effect, is rather drastic. For a particle, Newton s Second and Third Laws are readily understood in this regard. However, the corresponding shift for the rotational effect will lead to effects associated with the angular momentum of a rigid body that sometimes are counterintuitive. This is especially true for those who try to examine spatial motion from a planar motion viewpoint. This chapter focuses on the determination and evaluation of angular momentum. In the course of the development we derive basic laws governing the relationship between a body s motion and the forces that...