Overview
This lecture introduces vectors and scalars, explains their differences, provides examples, and demonstrates how to represent and add vectors using scale diagrams and calculations.
Vectors
- Vectors are physical quantities that have both magnitude (size) and direction.
- Examples of vector quantities: force, weight (acts downwards to Earth's center), velocity, and momentum.
- Vectors are represented as arrows; the line length shows magnitude, and the arrowhead shows direction.
- The tail is the starting point of the vector, and the head is the arrow’s point.
Scalars
- Scalars are physical quantities measured only by magnitude, not direction.
- Examples of scalar quantities: time, distance, mass, energy, and heat.
- Scalars cannot be described with a direction (e.g., you cannot say "time to the left").
Representing Vectors
- To draw a vector, choose a scale (e.g., 2 cm = 10 N).
- Longer lines represent greater magnitudes.
- Always label vectors (e.g., F1 = 50 N to the right).
- Negative vectors indicate direction opposite to the positive-defined direction.
Vector Operations & Resultants
- The resultant vector is a single vector with the same effect as multiple combined vectors.
- Use the head-to-tail method to add vectors: place the tail of the second vector at the head of the first.
- Measure from the tail of the first vector to the head of the last for the resultant.
- Example calculation: If F1 = 50 N right and F2 = 20 N left, resultant = 50 N - 20 N = 30 N right.
- Scaling calculations: to convert between vector length and magnitude, use cross-multiplication (e.g., 2 cm = 10 N).
Key Terms & Definitions
- Vector — Quantity with both magnitude and direction.
- Scalar — Quantity with magnitude only.
- Resultant — A single vector that represents the cumulative effect of two or more vectors.
- Magnitude — The size or amount of a quantity.
- Direction — The line or path along which something moves or points.
Action Items / Next Steps
- Practice drawing and adding vectors using a chosen scale.
- Prepare to study "Motion in One Dimension" in the next lesson.