Kinematics - Motion in 1 Dimension

Describing Motion:

Kinematics in One Dimension

The motion of objects- baseballs, automobiles, joggers, and even the Sun and Moon- is an obvious part of everyday life. It was not until the sixteenth and seventeenth centuries that our modern understanding of motion was established. Many individuals contributed to this understanding, particularly Galileo Galilei (1564- 1642) and Isaac Newton (J 642- 1727). The study of the motion of objects, and the related concepts of force and energy, form the field called mechanics. Mechanics is customarily divided into two parts: kinematics, which is the description of how objects move, and dynamics, which deals with force and why objects move as they do. For now we only discuss objects that move without rotating Such motion is called translational motion. In this section we will be concerned with describing an object that moves along a straight-line path, which is one-dimensional translational motion. We will describe translational motion in two (or three) dimensions along paths that are not straight. We will often use the concept, or model, of an idealized particle which is considered to be a mathematical point and to have no spatial extent (no size). A particle can undergo only translational motion. The particle model is useful in many real situations where we are interested only in translational motion and the object's size is not so significant.

When specifying the motion of an object, it is important to specify not only the speed but also the direction of motion. Often we can specify a direct ion by using north, east. south. and west. and by " up" and " down." In physics, we often draw a set of coordinate axes, as shown in Fig. 2-3, to rep resent a frame of reference. We can always place the origin 0, and the directions of the x and y axes, as we like for convenience. The x and y axes are always perpendicular to each other. Objects positioned to the right of the origin of coordinates (0) on the x axis have an x coordinate which we usually choose to be positive; objects to the left of 0 then have a negative x coordinate. The position along the y axis is usually considered positive when above 0, and negative when below 0. Although the reverse convention can be used if convenient. Any point on the plane can be specified by giving its x and y coordinates. In three dimensions, a z axis perpendicular to the x and y axes is added. For one-dimensional motion, we often choose the x axis as the line along which the motion takes place. Then the position of an object at any moment is given by its x coordinate. If the motion is vertical, as for a dropped object. we usually use they axis. We need to make a distinction between the distance an object has traveled and its displacement, which is defined as the change in position of the object. That is, displacement is how far the object is from its starting point. To see the distinction between total distance and displacement. imagine a person walking 70 m to the east and then turning around and walking back (west) a distance of 30 m (Fig. 2- 4). The total distance traveled is 100 m, but the displacement is only 40 m since the person is now only 40 m from the starting point. Displacement is a quantity that has both magnitude and direction. Such quantities are called vectors, and are represented by arrows in diagrams. For example, in Fig. 2-4, the blue arrow represents the displacement whose magnitude is 40 m and whose direction is to the right (east).