2. Scalar: A quantity that has only magnitude Example: speed

3. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity

4. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?

5. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature

6. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar

7. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position

8. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector

9. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time

10. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time Scalar

11. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time Scalar
Mass

12. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time Scalar
Mass Scalar

13. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time Scalar
Mass Scalar
Force

14. Scalar: A quantity that has only magnitude Example: speed
Vector: A quantity that has both magnitude and direction
Example: velocity
Scalar or Vector?
Temperature Scalar
Position Vector
Time Scalar
Mass Scalar
Force Vector

15. We draw vectors as arrows
“head”
“tail”

16. Parallel and Antiparallel

17. Where you draw a vector isn’t critical
These vectors are all the same

18. Since we can put them anywhere, place the tail at the origin
Components
Since we can put them anywhere, place the tail at the origin

19. “Standard” Components
But this is not always the case…

20. You need to be ready to handle situations like thisq

21. You need to be ready to handle situations like this
Bottom line: Don’t memorize
x = r cos q
y = r sin q
Instead, remember that:
sin is for the side opposite the angle
cos is for the side adjacent to the angle r q

22. Example Problems 1 – 3

23. Going from (x, y) to (r, q)

24. Example Problems 4 – 5

25. Adding Vectors
Line them up, tail-to-head
You can do it in any order

26. Adding Vectors Why does it work? Because you’re adding the components
That’s the only precise way to add vectors

27. Example Problems 6 – 7

28. Subtracting Vectors
First flip the second one Then add A + (– B)

29. Example Problems 8 – 9