Overview
This lecture covers the difference between vectors and scalars, how to represent them, and how to assign coordinate systems for one-dimensional motion.
Scalars and Vectors
- A scalar quantity has magnitude but no direction (e.g., distance, temperature, speed, energy).
- A vector quantity has both magnitude and direction (e.g., displacement, velocity, force).
- Displacement is an example of a vector; distance is an example of a scalar.
- Scalars can be negative, but the sign indicates position on a scale, not direction.
Representing Vectors
- Vectors are represented by arrows: length shows magnitude, arrow points in direction.
- In one-dimensional motion, direction is shown using a + (positive) or – (negative) sign.
- Scalars are never represented by arrows.
Coordinate Systems for One-Dimensional Motion
- A coordinate system defines a reference frame and directions for motion.
- In horizontal motion, right is usually positive; left is negative.
- In vertical motion, up is usually positive; down is negative.
- You can choose a different convention if it’s more convenient, but must use it consistently throughout a problem.
- Once a positive direction is chosen, do not change it while solving.
Check Your Understanding (Q&A)
- Q: Is speed a scalar or a vector?
- A: Speed is a scalar quantity; it does not change with direction, only with magnitude.
Key Terms & Definitions
- Vector — A quantity with both magnitude and direction.
- Scalar — A quantity with magnitude only, no direction.
- Displacement — The change in position of an object (vector).
- Distance — The total path length traveled (scalar).
- Coordinate System — A reference framework used to define direction and position.
Action Items / Next Steps
- Practice identifying vectors and scalars in physical scenarios.
- Assign coordinate systems in sample one-dimensional motion problems.