Introduction to Vectors: Understanding Scalars and Vectors

1. Skipped to slide 40 for 2008 and 2009

2. Introduction to Vectors Scalars and Vectors • In Physics, quantities are described as either scalar quantities or vector quantities .

3. Introduction to Vectors Scalar Quantities • Involve only a magnitude, which includes numbers and units. • Examples include distance and speed.

4. Introduction to Vectors Vector Quantities • Involve a direction, in addition to numbers and units. • Can be represented graphically with arrows. • The longer the arrow, the greater the magnitude it represents.

5. Introduction to Vectors 15 m/s east 25 m/s west

6. Vector Addition in One direction • When vector quantities are in the same direction, vectors are added by placing the tail of one vector at the head of the other vector. • Be sure to maintain direction and length of vectors! • This creates one Resultant vector (R) which is drawn from the tail of the 1st vector to the head of the second vector.

7. Example: A child walks 2.0 m east, pauses, and then continues 3.0 m east. The resultant (R) = 5.0 m east.

8. If the two vectors have different directions, they are still added head to tail. Example: A child walks 2.0 m east, then turns around and walks 4.0 m west.

9. Adding vectors graphically, using the “tip-to-tail” method.

10. Component vectors are added “tip-to-tail.” The resultant vector is drawn “tail-to-tip.”

11. 4 m east 3 m north Adding vectors graphically, using the “tip-to-tail” method.

12. A man walks 3 m north, and then 4 m east. Find his displacement. 4 m east 3 m north

13. You are allowed to move the vectors, but don’t change the direction or length. 4 m east 3 m north

14. Line up the tip of one vector with the tail of the other. tail tip 4 m east 3 m north

15. Line up the tip of one vector with the tail of the other. 4 m east 3 m north

16. Now, draw the resultant vector from “tail-to-tip” as shown above. 4 m east 3 m north Resultant vector

17. Remember to line up the component vectors from tip-to tail. 4 m east 3 m north

18. If you line them up incorrectly, you get the wrong resultant vector. 4 m east 3 m north

19. This is wrong! 4 m east How did this man go East, and then North, and end up back where he started!?!? 3 m north Now, the resultant vector will be wrong, no matter how it is drawn.

20. Always line up the tip of one component vector with the tail of the other. 4 m east 3 m north

21. Then draw your resultant vector from “tail-to-tip” as shown below. 4 m east 3 m north Resultant vector

22. It doesn’t matter in what order you add the component vectors. 4 m east 3 m north

23. You will still get the same resultant vector. Resultant vector 3 m north 4 m east

24. Compare two sets of identical component vectors. A B B A

25. It doesn’t matter which order you place the component vectors. A B B A

26. Only that you draw them from tip-to-tail. A B B A

27. The resultant vector will be the same in either case. resultant resultant

28. The resultant vector will be the same in either case.

29. Of course, we can add more than two component vectors.

30. As long as we add them tip-to-tail.

31. We will find the correct resultant vector. Resultant vector

32. We can also subtract vectors graphically. B A Find the resultant vector of vector A – vector B

33. Instead of subtracting B from A, we add –B to A. B A

34. A – B is the same as A + (-B) B A Find the resultant vector A + (-B)

35. The vector called “-B” has the same magnitude as vector B, but the opposite direction. -B B A

36. Now we add Vector A and Vector –B with the tip-to-tail method -B B A

37. Now we add Vector A and Vector –B with the tip-to-tail method A -B

38. And draw the resultant vector. A -B Resultant vector

39. IF skip 3A beginning lecture (2008 and 2009)….use the next slides from lecture one and assign 3A

40. Happy Wednesday!! • Please complete the maze on your desk. • Both sides!

41. Introduction to Vectors Scalars and Vectors • In Physics, quantities are described as either scalar quantities or vector quantities .

42. Introduction to Vectors Scalar Quantities • Involve only a magnitude, which includes numbers and units. • Examples include distance and speed.

43. Introduction to Vectors Vector Quantities • Involve a direction, in addition to numbers and units. (velocity and displacement) • Can be represented graphically with arrows. • The longer the arrow, the greater the magnitude it represents.

44. Vector Operations Drawing Vectors In order to draw vectors that indicate direction, you need to work within a coordinate system.

45. Vector Operations Coordinate Systems

46. Vector Operations Coordinate System When working with the Cartesian coordinates, adding vectors can be accomplished with the “tip-to-tail” method.

47. Example: A child walks 2.0 m east, pauses, and then continues 3.0 m east. 0 The resultant (R) = 5.0 m east.

48. If the two vectors have different directions, they are still added tip to tail. Example: A child walks 2.0 m east, then turns around and walks 4.0 m west. 0 The resultant is 2.0 m west.

49. Component vectors are added “tip-to-tail.” The resultant vector is drawn “tail-to-tip.”

50. 4 m east 3 m north Adding vectors graphically, using the “tip-to-tail” method.