PHY 430 – Lecture 2

1. PHY 430 – Lecture 2 Scalars & Vectors

2. 3.1 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. Addition of Vectors – Graphical Methods – 1 Dimension

4. Addition of Vectors- Graphical Method – 2 Dimensions

7. Subtraction of Vectors

8. Multiplication of a Vector by a Scalar

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. Adding vectors analytically (by components)

13. Unit Vectors

14. Unit vectors • For 3-D Cartesian coordinate system • i = unit vector in the direction of x • j = unit vector in the direction of y • k = unit vector in the direction of z • Fig. 3-15

15. Products of vectors • Dot product: A B =IAIIBIcos A  B = B  A • Cross Product: A X B =IAIIBIsin  n A x B = - B x A