Forces in Two and Three Dimensions

Abstract

We have introduced a vectorized description of motion that allows us to discuss motion not only in one dimension, but also for two- and three-dimensional systems. However, in order to predict and calculate the motion, we need to extend Newton’s laws to two and three dimensions, and we need to introduce force models that are applicable in two and three dimensions. This is the focus of the current chapter. The structured problem-solving approach used to address problems in mechanics has exactly the same form for one-, two-, and three-dimensional problems. The first step is to identify what objects we are studying, how we characterize their position, and what reference system we use to describe the motion. Second, we model the system by finding the forces acting on the object, we introduce models for the force, and use Newton’s second law to find the acceleration of the object. Third, we solve the equations of motion, and determine the position and velocity of the objects as functions of time. Finally, we analyze the resulting motion, use the solution to answer the questions posed, and check the validity of the solutions. In this chapter, we discuss how to identify forces, how to apply Newton’s laws in two- and three dimensions, and we generalize all force models to two- and three-dimensional motion.