1. AP Physics C

2. Dimensionality Dimensionality is an abstract concept closely related to units Units describe certain types of quantities. Feet, inches, meters, nanometer - Units of Length We can develop a set of rules that allow us to: Check equations Determine the dependence on specified set of quantities

3. Dimensionality There are 3 types of quantities we will discuss today: Length Time Mass

4. Notation We denote these quantities as: Length - L Time - T Mass - M

5. Notation

6. Rules of Dimensionality 1.Variables on opposite sides of an equals sign must have the same dimensionality 2.Variables on opposite sides of a + or - must have the same dimensionality

7. Rules of Dimensionality

9. Dimensional Analysis

12. Consider a mass swinging on the end of a string The period is the amount of time takes for the mass to complete one full oscillation What variables do you suspect the period of the motion will depend on?

13. Dimensional Analysis

14. Position, Velocity, & Acceleration In Physics it is important to be able to relate position, velocity, & acceleration A mathematical description of this relationship requires the use of calculus In this section we will discuss the graphical relationship between a position vs. time graph and a velocity vs. time graph

15. Graphical Analysis

24. The Derivative

33. The Derivative - Linearity

34. The Derivative - Quadratic

35. The Derivative - Polynomial

36. Power Rule

37. Derivative of Sine & Cosine

39. Second Derivative

40. Third Derivative

41. The Chain Rule

51. Product Rule

52. Recall that we can visualize the product of two numbers as the area of a rectangle. Product Rule

53. Recall that we can visualize the product of two numbers as the area of a rectangle. Product Rule

54. We can do the same thing with the product of two functions. Product Rule

59. The Product Rule

60. Product Rule

61. The Product Rule