Scalars and Vectors

1. Classification of Physical Quantities

Physical quantities are categorized as scalars or vectors based on directional properties

2. Scalar Quantities

Definition: Quantities described completely by numerical magnitude and unit

Examples: distance, speed, time, mass, energy, temperature

Properties:
  • Require only magnitude and unit
  • No direction specified
  • Follow ordinary algebraic rules for addition, subtraction, multiplication

3. Vector Quantities

Definition: Quantities requiring both numerical magnitude (with unit) and direction

Examples: displacement, force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength

Properties:
  • Require magnitude, unit, and direction
  • Follow vector algebra rules, not ordinary algebraic rules

4. Representation of Vectors

Symbolic: Letters (e.g., F for force, A, B for general vectors)

Graphical: Arrows
  • Length indicates magnitude (using a scale)
  • Arrowhead indicates direction
Coordinate system:
  • X-axis (horizontal) and Y-axis (vertical)
  • Origin (O) at intersection of axes
  • Position represented by coordinates (x, y)

5. Steps to Represent a Vector in Coordinate System

1. Choose and draw a coordinate system

2. Select a suitable scale

3. Draw a line in the fixed direction, length proportional to magnitude

4. Add arrowhead to indicate direction

6. Vector Addition

Definition: Combining two or more vectors into a single resultant vector

Method: Geometric addition
  • Draw vectors to scale
  • Place vectors head-to-tail
  • Resultant is vector from tail of first to head of last

7. Key Concepts

Reference frame: Coordinate system for describing object positions

Importance of direction in vector quantities

Difference between scalar and vector arithmetic