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PPMF101– Lecture 3

PPMF101– Lecture 3. Scalars & Vectors. 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.

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PPMF101– Lecture 3

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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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