Part I of this textbook was about change. One particular type of change—motion—is governed by Newton’s second law. Although Newton’s second law is a very powerful statement, it isn’t the whole story. Part II will now focus on things that stay the same as other things around them change.

Consider, for example, an explosive chemical reaction taking place inside a closed, sealed box. No matter how violent the explosion, the total mass of the products—the final mass $M_{\text{f}}$—is the same as the initial mass $M_{\text{i}}$ of the reactants. In other words, matter cannot be created or destroyed, only rearranged. This is an important and powerful statement about nature.

A quantity that stays the same throughout an interaction is said to be conserved. The most important such quantity is energy. If a system of interacting objects is isolated—an important qualification—then the energy of the system never changes no matter how complex the interactions. This description of how nature behaves, called the law of conservation of energy, is perhaps the most important physical law ever discovered.

But what is energy? How do you determine the energy of a system? These are not easy questions. Energy is an abstract idea, not as tangible or easy to picture as mass or force. Our modern concept of energy wasn’t fully formulated until the middle of the 19th century, two hundred years after Newton, when the relationship between energy and heat was finally understood. That is a topic we will take up in Part V, where the concept of energy will be found to be the basis of thermodynamics. But all that in due time. In Part II we will be content to introduce the concept of energy and show how energy can be a useful problem-solving tool. We’ll also meet another quantity—momentum—that is conserved under the proper circumstances.

Conservation laws give us a new and different perspective on motion. This is not insignificant. You’ve seen optical illusions where a figure appears first one way, then another, even though the information has not changed. Likewise with motion. Some situations are most easily analyzed from the perspective of Newton’s laws; others make more sense from a conservation-law perspective. An important goal of Part II is to learn which is better for a given problem.