Overview
This lecture explains the difference between scalars and vectors, their properties, examples, and how vectors are represented in physics.
Physical Quantities
- Physical quantities are measurable properties described by numbers, such as length, mass, or temperature.
- All physical quantities have magnitude (amount or size) and a unit.
Scalars
- A scalar is a physical quantity with magnitude only, and no direction.
- Examples of scalars: mass, distance, time, speed, power, work, energy, charge.
- Speed is a scalar (e.g., 5 m/s).
Vectors
- A vector is a physical quantity with both magnitude and direction.
- Examples of vectors: weight (force), displacement, velocity, acceleration, momentum, impulse, electric field.
- Velocity is a vector (e.g., 120 km/h to the right).
- In physics, when reporting a vector, both magnitude and direction must be given.
Comparing Scalars and Vectors
- 2 m/s is a scalar (speed, no direction); 2 m/s east is a vector (velocity, includes direction).
- Speed and velocity can have the same magnitude, but velocity also gives direction.
- Some motion equations use "velocity" but can also be applied to calculate speed (magnitude only).
Representing Vectors Graphically
- Vectors are represented by arrows; arrow length = magnitude, arrow direction = vector direction.
- For forces, arrows pointing in the same direction and length are equal vectors.
- Changing the arrow's direction or orientation changes the vector.
- Opposite direction arrows of equal length represent equal and opposite vectors, resulting in a net force of zero when combined.
Vector Properties and Notation
- If "right" or "east" is defined as positive, vectors in that direction are positive, while those in the opposite direction are negative.
- The sign (positive/negative) indicates direction based on the defined reference.
Practice Questions
- A combination of two scalars and one vector: speed (scalar), distance (scalar), velocity (vector).
- Displacement is a vector; distance, mass, and time are scalars.
Key Terms & Definitions
- Physical Quantity — a measurable property with magnitude and unit.
- Scalar — a physical quantity with magnitude only, no direction.
- Vector — a physical quantity with both magnitude and direction.
- Magnitude — the size or amount of a quantity.
- Velocity — a vector describing speed with direction.
- Speed — a scalar describing how fast something moves, regardless of direction.
- Displacement — a vector showing change in position with direction.
- Net Vector — combined effect of two or more vectors, considering both magnitude and direction.
Action Items / Next Steps
- Review the list of scalar and vector examples for memorization.
- Prepare for the next lesson on resultant/net vectors.
- Practice identifying scalars and vectors in sample questions.