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Understanding Scalars and Vectors: Key Concepts and Examples

This lecture covers the fundamental differences between scalars and vectors in physics. Scalars are quantities defined only by their magnitudes, such as mass, time, and temperature. Vectors, on the other hand, have both magnitude and direction, examples include displacement, velocity, and acceleration. Learn about vector notation, graphical representation, and addition methods including graphical and component-based approaches. The lecture includes practical examples illustrating total distance and displacement, enhancing comprehension of these essential concepts in physics.

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Understanding Scalars and Vectors: Key Concepts and Examples

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  1. PPMF101– Lecture 3 Scalars & Vectors

  2. Scalars & vectors • Scalars – quantities with only magnitudes • Eg. Mass, time, temperature • Mathematics - ordinary algebra • Vectors – quantities with magnitudes & directions • Eg. Displacement, velocity, acceleration • Mathematics - vector algebra

  3. Vector notations – symbols of vector quantities • A short arrow is drawn over the symbol of a vector quantity. • E.g. displacement r Velocity v

  4. Vector representations • A vector quantity is represented by an arrow to represent its magnitude (the length of the arrow) and direction (direction of the arrowhead) • Eg.1. A man walks 5 m to the west. His displacement can be represented by the following arrow.

  5. Eg. 2. A car moving 50 km/h to the east. The velocity vector of the car can be represented by the following arrow:

  6. Addition of Vectors – Graphical Methods – 1 Dimension

  7. Addition of Vectors- Graphical Method – 2 Dimensions

  8. Subtraction of Vectors

  9. Adding Vectors by Components – Resolving Vectors

  10. Two ways to specify a vector • 1. Give its componens, Vx and Vy • 2. Give its magnitud V and angle  it makes with positive x – axis • We can shift from one description to the other by using theorem of Pythagoras and definition of tangent

  11. Resolving a vector = finding components of a vector

  12. Example 1 • A man walks 20 m to the east and then he stops and walks 5 m to the west. What is the man’s • a) total distance travelled? • b) total displacement?

  13. Example 2 • An aeroplane flies 200 km to the north and then 300 km to the east. • a) What is the total distance travelled by the plane? • b) What is the total displacement of the plane?

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