1. PHY 093 – Lecture 1b Scalars & Vectors 1

2. 3.1 Scalars & vectors  Scalars – quantities with only magnitudes Eg. Mass, time, temperature Eg. Mass, time, temperature Mathematics - ordinary algebra Mathematics - ordinary algebra  Vectors – quantities with magnitudes & directions Eg. Displacement, velocity, acceleration Eg. Displacement, velocity, acceleration Mathematics - vector algebra Mathematics - vector algebra 2

3. Addition of Vectors – Graphical Methods – 1 Dimension 3

4. Addition of Vectors- Graphical Method – 2 Dimensions 4

5. 5

6. 6

7. Subtraction of Vectors 7

8. Multiplication of a Vector by a Scalar 8

9. Adding Vectors by Components – Resolving Vectors 9

10. Two ways to specify a vector  1. Give its componens, V x and V y  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 10

11. Resolving a vector = finding components of a vector 11

12. Adding vectors analytically (by components) 12

13. Unit Vectors 13

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 14

15. Products of vectors  Dot product: A  B = IAI IBI cos  A  B = B  A  Cross Product: A X B = IAI IBI sin  n A x B = - B x A 15

16. 3-6 Vector Kinematics In two or three dimensions, the displacement is a vector: 16

17. 3-6 Vector Kinematics As Δ t and Δ r become smaller and smaller, the average velocity approaches the instantaneous velocity. 17

18. 3-6 Vector Kinematics The instantaneous acceleration is in the direction of Δ = 2 – 1, and is given by: 18

19. 3-6 Vector Kinematics Using unit vectors, 19