Overview
This lecture introduces vectors in physics, differentiates between scalar and vector quantities, explains vector representation and direction, and discusses types of vectors and their graphical representation.
Scalar and Vector Quantities
- Scalar quantities are described by magnitude and units, without direction (e.g., temperature, time, mass).
- Vector quantities are described by magnitude, units, and direction (e.g., force, velocity, displacement).
- Scalar examples: temperature (39°C), time (1 hour), never associated with direction.
- Vector examples: 10 N force east, velocity 7 km/h north, direction is essential.
Vector Representation
- Vectors are represented by arrows; the direction of the arrow shows the vector's direction.
- The length of the arrow is proportional to the magnitude of the vector.
- Vectors are denoted using boldface or letters with an arrow above; magnitude is plain or placed between vertical bars (|A|).
- Direction is often indicated using angles with respect to the east-west (x-axis) line.
Measuring and Describing Vector Direction
- The direction of a vector is measured as the acute angle (<90°) with the x-axis (east-west line).
- Directions are written as "<angle> N of E", "S of W", etc. (e.g., 30° N of E).
- Use a protractor on a Cartesian plane to determine the vector's angle and quadrant.
Cartesian Plane and Quadrants
- The Cartesian plane is divided into four quadrants, each spanning 90°.
- Quadrant 1: 0°-90°, Quadrant 2: 90°-180°, Quadrant 3: 180°-270°, Quadrant 4: 270°-360°
- One full revolution equals 360°; each quadrant corresponds to specific directional labels.
Calculating Reference Angles
- When given a standard angle (0°-360°), reference angle is found as follows:
- 0° < angle < 90°: reference angle = angle (Q1, N of E)
- 90° < angle < 180°: reference angle = 180° - angle (Q2, N of W)
- 180° < angle < 270°: reference angle = angle - 180° (Q3, S of W)
- 270° < angle < 360°: reference angle = 360° - angle (Q4, S of E)
Magnitude of a Vector
- The magnitude is the length of the vector and is measured to scale on a graph (e.g., 1 cm = 1 km).
- The magnitude can be expressed numerically (e.g., 25 km 40° S of W).
Types of Vectors
- Equal Vectors: Same magnitude and direction.
- Parallel Vectors: Same direction, different magnitudes.
- Anti-Parallel Vectors: Opposite directions, angle between is 180°.
- Collinear Vectors: Lie along the same line.
- Non-Collinear Vectors: Lie on the same plane, separated by an angle ≠0° or 180°.
Key Terms & Definitions
- Scalar Quantity — A quantity with magnitude and units only, no direction.
- Vector Quantity — A quantity with magnitude, units, and direction.
- Reference Angle — The smallest acute angle a vector makes with the horizontal axis.
- Magnitude — The length or size of a vector.
- Collinear Vectors — Vectors lying along the same line of action.
- Non-Collinear Vectors — Vectors in the same plane but not along the same line.
Action Items / Next Steps
- Study examples in your module regarding vector direction and reference angles.
- Practice drawing and measuring vectors on a Cartesian plane using a protractor.
- Prepare for the next topic: vector addition and component form representation.