Introduction

Classical mechanics deals with the motion of objects. The motion of an object is described by the position of the object at various times. There are limitations imposed on the properties of objects and the scope of the motions that classical mechanics can handle. The size of an object handled in classical mechanics cannot go down to the microscopic level, that is, the size of an atom or smaller. In that limit classical mechanics breaks down and quantum mechanics takes over. The rate of change of the position of an object needs to be restricted to far lower than the speed of light; when the speed of changes of positions approaches the speed of light, Einstein's relativity replaces classical mechanics. If the number of objects under consideration approaches millions and billions, classical mechanics yields its postion to statistical mechanics. Classical mechanics also does not handle phenomena involving electricity and magnetism; they are the domain of electromagnetism.

Classical mechanics is the first branch of physics that has been developed systematically and logically. Well-known names associated with the development of classical mechanics are Copernicus, Kepler, Galileo, Newton and so on. Since it is the pioneering branch of physics, classical mechanics does not require knowledge about other branches of physics, whereas other branches of physics more or less rely on knowlege of classical mechanics. It is thus natural for classical mechanics to serve as the entry point to physics for numerous generations of students. We do not condone attempts to mix quantum mechanics with classical mechanics as the entry point to physics since we believe that such hasty efforts will only confuse students at best and generate a large group of people who hate physics earnestly at worst.

Classical mechanics is based on three intuitive concepts: space, time and mass. They are called "intuitive" because we cannot explain what they are, but intuitively earthlings know what they mean and can just use them in classical mechanics as well as in other branches of physics. Some confuse the three intuitive concepts with their units of measurements, like meter, second and kilogram. However, those units of measurements are artificially defined entities. If you prefer, you can easily use different measuring units like foot, hour and pound, or even invent some fancy units by yourself; of course, if you invent a fancy unit system by yourself and use it in physics, then other people will not understand what you are talking about. That is why we prefer to stick to one measuring unit system, that is, the meter, second and kilogram system. Because in the United States the habit of using the foot-second-pound system is so strong, we will at some time touch upon conversion between those two unit systems. In other places around the world the meter-second-kilogram system (called MKS system) is socially and officially adopted, including in England, the birthplace of the foot-second-pound system, so students outside the United States are saved from the misery of converting between two unit systems.

Some physicists talk as if they understand what the three basic intuitive concepts -- space, time, and mass -- are by invoking Einstein's relativity. Einstein's special relativity uncovers a relation between distance, time interval and speed. Due to the presence of speed in that relation, it cannot be used to define distance from time interval or vice versa. Einstein's general relativity further entangles mass into the relations but still cannnot be used to reduce the necessity of three intuitive concepts. The intuitive concepts of space and time are discussed in Chapter 1, and the intuitive concept of mass is discussed at length in Chapter 2.

We frequently deal with a "particle" in classical mechanics. A particle is a point-like object with mass. Of course, the term "point-like" does not mean that the object can be as small as or smaller than an atom as discussed before. There is no specific definition how small an object should be before it can be considered point-like; it all depends on the accuracy of our measurements. If we are dealing with a situation in which the accuracy of the measurement of distances is only 0.1 millimeter, then anything smaller than 0.1 millimeter can safely be considered a point-like object. On the other hand if we are dealing with the orbit of a planet, then in most cases the planet itself can be considered a point-like object. Another kind of object the motion of that will be considered in classical mechanics is called "rigid body". A rigid body is an extended object with a certain mass distribution but is completely not deformable. The motion of deformable objects, like liquids, gases, strings and so on is postponed to a later book. The reason for this arrangement is based on our assessment that to move quickly into electromagnetism in Book 2 is more suited to the interest of many students, since we can only develop one topic at a time.

In concluding this introduction we need to touch upon the notations used in this book. Boldface type is reserved for vectors unless otherwise specified. Due to the limited ability to handle mathematical notation in HTML, the widely used protocol of the Internet, the fraction sign that appears in text lines is replaced by a slash "/", that is, "a over b" is expressed as "a/b" in text lines. In other times, when one side of an equation becomes too tall if fraction signs are used consistantly, some fraction signs are replaced by slashes. There are also occasions that a long slash is desirable but only a short slash is available in the equation editor that we use to create the document; then the slash sign is replaced by the division sign "÷". In other words the fraction sign, the slash, and the division sign are used interchangeably throughout this book. The dot "·" and the multiplication sign "×" are also used interchangeably for the multiplication of ordinary numbers. The scalar product of two vectors a and b is always expressed as a·b, and the vector product of a and b is always written as a×b. Finally we must mention the * system used to rank the difficulty of the problems given in this book and beyond. Problems with no stars are basic problems. Any problem that requires some calculus is given at least one *. In our opinion, four star, ****, problems are a kind of torture for most students, make them hate physics, and serve no purpose in stimulating students to understand physics. Unfortunately, some physicists do not share this view, and that is why some of the **** problems are included.