Scalars vs. Vectors
The Foundation of Physical Quantities
In physics, every measurable quantity is classified as either a scalar or a vector. Understanding this distinction is the first step toward mastering kinematics and dynamics.
Scalars
A scalar quantity is defined strictly by its magnitude (size or numerical value) and a unit. It has no direction.
- Examples: Mass (5kg), Time (10s), Temperature (25°C), Distance (100m), Speed (20m/s), Energy (50J).
- Arithmetic: Can be added or subtracted using simple math (e.g., 5kg + 2kg = 7kg).
Vectors
A vector quantity requires both magnitude and direction to be fully described.
- Examples: Displacement (5m East), Velocity (20m/s North), Acceleration (9.8m/s² Down), Force (10N Right), Momentum.
- Representation: Usually shown as an arrow where the length represents magnitude and the tip points in the direction.
Key Differences
| Feature | Scalar | Vector |
|---|---|---|
| Magnitude | Yes | Yes |
| Direction | No | Yes |
| Changes when… | Magnitude changes | Magnitude OR Direction changes |
Vector Operations
Unlike scalars, vectors cannot always be added with simple arithmetic. If you walk 3m East and then 4m North, your total distance (scalar) is 7m, but your displacement (vector) is 5m at an angle.
Resultant Vector (R) = √(A² + B²)
(For perpendicular vectors)
(For perpendicular vectors)