Objectives - phys161

chapter 3

Vocabulary

Vector Components (or, more simply, Components), Component Vectors, Polar Coordinate System, Vector Decomposition.

Objectives. At this point in the course, the student should

1. Know what it means to multiply a vector by a scalar. The student should be able to do this for negative scalars as well as for positive ones, and should be able to express the result both graphically and algebraically.
2. Know what is required for two vectors to be considered equal.
3. Realize that, even though vectors have magnitude and direction, they have no location. The student should realize that this implies the equality of two vectors with the same magnitude and direction even if the vectors are drawn at different locations.
4. Realize that, by definition, the magnitude of the instantaneous velocity is the instantaneous speed.
5. Be able to use trigonometry to pass back and forth between the (Magnitude and Direction) and (Components) descriptions of any vector.
6. Realize that an arbitrary vector in the Northwest quadrant cannot be referred to as having a direction of Northwest! The student should understand that 'Northwest' implies exactly 45° West of North, and no other direction. For other directions, specific angles must be used. This caution of course extends to 'Northeast', 'Southeast', etc.
7. Realize that vectors exist independently of any coordinate system.
8. Be comfortable with using both Cartesian and Polar coordinate systems, and be able to pass back and forth between them at will. The student should realize that the relationship between Cartesian and Polar coordinate systems is identical to that between (Component) and (Magnitude and Direction) representations of vectors.
9. Be comfortable taking derivatives of trigonometric functions.
10. Know that the "hat" notation with i, j, and k is often used to represent the directions (or unit vectors) in the three spatial coordinates and that this is equivalent to the "hat" notation with x, y and z.
11. Be able to add and subtract vectors algebraically.
12. Be comfortable with kinematics in two dimensions.