In Work and Power we defined work, and began to relate it to energy through the Work-Energy Theorem. Such a relation is not the extent of our understanding of the concept of energy, and we now are able to fully explore this interesting topic, using both what we already know about work and dynamics, along with the introduction of some new concepts.
The conservation of energy is one of the most important concepts in physics. It does not only apply to mechanics, but is a universal truth. This principle becomes the basis of many areas of study, and a full comprehension of the topic is essential for a broad understanding of physics.
We begin our study by differentiating between conservative forces and nonconservative forces, developing two guiding principles and using examples of both kinds of forces. We then go on to develop a new kind of energy: potential energy. An understanding of potential energy, combined with what we already know about kinetic energy will allow us to derive the fundamental concept of the conservation of mechanical energy. We will study various examples of how to apply this principle, and give a limited calculus-based exploration of the topic. By using energetics instead of kinematics or dynamics, we can greatly simplify many physical problems, and also gain a broader understanding of mechanics within the larger principle of energy.