AP Physics C

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

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

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

Notation

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

Rules of Dimensionality

Dimensional Analysis

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?

Dimensional Analysis

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

Graphical Analysis

The Derivative

The Derivative - Linearity

The Derivative - Quadratic

The Derivative - Polynomial

Power Rule

Derivative of Sine & Cosine

Second Derivative

Third Derivative

The Chain Rule

Product Rule

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

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

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

The Product Rule

Product Rule

The Product Rule