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OUTLINE : 1. INTRODUCING VECTORS. 1.1 Scalars. 1.2 Vectors. 1.3 Unit vectors. 1.4 Vector algebra. 1.5 Simple examples. 1.1 Scalars. A scalar is a quantity with magnitude but no direction, any mathematical entity that can be represented by a number. Examples: Mass, temperature, energy, charge ...
Chapter 1. Units and Vectors: Tools for Physics. 1.1 The Important Stuff. 1.1.1 The SI System. Physics is based on measurement. Measurements are made by comparisons to well–defined standards which define the units for our measurements. The SI system (popularly known as the metric system) is the one used in physics.
Example. Write the polar unit vectors r and θ in terms of the Cartesian unit vectors x and y . Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction.
these units can be used to describe other physical quantities such as velocity (m/s), and acceleration (m/s2). Sometimes the string of units gets to be so long that we contract them into a new unit called a derived unit. For example, A unit of force has base units of kg m s2! newton or N where the newton (N) is a derived unit. 3.1 Physical ...
Many of you will know a good deal already about Vector Algebra — how to add and subtract vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors.
A unit vector is a dimensionless vector one unit in length used only to specify a given direction. Unit vectors have no other physical significance. In Physics 2110 and 2120 we will use the symbols i, j, and k (if there is a third dimension, i.e a “z” direction), although in many texts the symbols x^, y^, and z^ are often used.
The mathematicians have come up with a special kind of vector called a unit vector which comes in very handy in physics. By definition a unit vector has magnitude 1, with no units.
