Chapter 3
Vectors
3.1 Coordinates Systems and Frames of reference
In solving any physics problem we are always interested in the location of an object in space and time. In other words we are interested in the frame that the object is located in. This frame is known as the reference frame. For example, the mathematical description of an object requires a method for describing the motion of the object at various times. This description is accomplished by means of coordinate system.
There are three types of coordinate systems, which can be used to describe the location of an object: one coordinate point if it is a linear motion, e.g., in describing the displacement of an object along a straight line. For an object in a plane, one requires two coordinate points, or three coordinate points, respectively to locate it in space.
In general, a coordinate systems describing a point in space consists of:
· A fixed reference point 0, or known as origin.
· A set of specified axes with appropriate scales and labels on the axes and,
· Instruction that tells one how to label a point in space relative to the origin.
3.1.1 Cartesian coordinates
In this course we are going to use two types of coordinate systems, Cartesian coordinates, Fig. 3.1 and, Polar coordinates, Fig. 3.2.
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