PHYS 1750: SELECTED TOPICS in PHYSICS
LECTURE 04. Vectors
| 2.1. | Scalars and Vectors | |||
| 1. | Scalars | |||
| a. | One number; non-directional | |||
| b. | Examples: temperature, mass, volume, density | |||
| 2. | Vectors | | ||
| a. | Three numbers; directional | |||
| b. | Examples: displacement, velocity, acceleration, force | |||
| c. | The "arrow" picture... | |||
| d. | Notation | |||
| 3.1. | 2-D Introduction: Coordinate Independence | |||
| 3.2. | Properties of Vectors | | ||
| 1. | Equality | |||
| a. | Meaning | |||
| b. | Location of a vector quantity not part of definition | |||
| c. | Consequences | |||
| 2. | Vector Arithmetic | |||
| a. | Addition: geometrical picture | |||
| b. | Subtraction: geometrical picture | |||
| c. | Scalar multiplication: a . b = abcosqab | |||
| d. | Associativity, Commutivity | |||
| 3.3. | Vector Components | | ||
| 1. | Cartesian coordinates | |||
| 2. | All vectors as sums of 2 or 3 perpendicular vectors | |||
| 3. | Components and magnitude | |||
| a. | Geometrical picture | |||
| b. | Trigonometrical relationships | |||
| 4. | Associativity and commutivity means component addition possible: | |||
| To add vectors: decompose into components, add like components, recompose sum vector | ||||
| 5. | Scalar multiplication: a . b = axbx + ayby + azbz | |||
Review Questions are at the end of the next lecture.
Lecture 05: Projectile and Relative Motion