Forces and Constrained Motion

Abstract

In this chapter we will discuss the use of constrained motion to simplify problems. First, we demonstrate how we try to choose coordinate systems wisely so that motion only occur along some of the axes. This technique is often called “decomposition of forces”, and it simplifies the analysis of a problem, because only force components in the directions that the object can move can contribute to the acceleration of the object along its path. We will also introduce a new force model, the friction force model, which allows us to model forces during the relative motion of two solids. This model has a long history and allows us to study many classical examples, even though the physical origin of friction forces is poorly understood. We will also study more complicated constrained motions, such as the circular motion of an object attached to a rope, or the motion of a car driving along a curved road or a hill-top. In these cases the constraints are only valid for a limited range of the normal forces, and care must be taken to find when the limits are exceeded.