For many types of motion, such as that of balls, cars, and rockets, the motion of the object as a whole is not influenced by the details of the object’s size and shape. All we really need to keep track of is the motion of a single point on the object, so we can treat the object as if all its mass were concentrated into this single point. An object that can be represented as a mass at a single point in space is called a particle. A particle has no size, no shape, and no distinction between top and bottom or between front and back.

If we model an object as a particle, we can represent the object in each frame of a motion diagram as a simple dot rather than having to draw a full picture. FIGURE 1.4 shows how much simpler motion diagrams appear when the object is represented as a particle. Note that the dots have been numbered 0, 1, 2, . . . to tell the sequence in which the frames were taken.

FIGURE 1.4 Motion diagrams in which the object is modeled as a particle.

Treating an object as a particle is, of course, a simplification of reality—but that’s what modeling is all about. The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point. The particle model is an excellent approximation of reality for the translational motion of cars, planes, rockets, and similar objects.

Of course, not everything can be modeled as a particle; models have their limits. Consider, for example, a rotating gear. The center doesn’t move at all while each tooth is moving in a different direction. We’ll need to develop new models when we get to new types of motion, but the particle model will serve us well throughout Part I of this book.