Chapter 1. Basic Concepts
As a warm-up, this chapter will cover the most basic of the principles that will be used and referenced throughout the remainder of this book. First, we’ll introduce Newton’s laws of motion, which are very important in the study of mechanics. Then we’ll discuss units and measures, where we’ll explain the importance of keeping track of units in your calculations. You’ll also have a look at the units associated with various physical quantities that you’ll be studying. After discussing units, we’ll define our general coordinate system, which will serve as our standard frame of reference. Then we’ll explain the concepts of mass, center of mass, and moment of inertia, and show you how to calculate these quantities for a collection, or combination, of masses. Finally, we’ll discuss Newton’s second law of motion in greater detail, take a quick look at vectors, and briefly discuss relativistic time.
Newton’s Laws of Motion
In the late 1600s (around 1687), Sir Isaac Newton put forth his philosophies on mechanics in his Philosophiae Naturalis Principia Mathematica. In this work Newton stated the now-famous laws of motion, which are summarized here:
- Law I
A body tends to remain at rest or continue to move in a straight line at constant velocity unless acted upon by an external force. This is the so-called concept of inertia.
- Law II
The acceleration of a body is proportional to the resultant force acting on the body, and this acceleration is in the same direction as the ...