**Physics Notes - Herong's Tutorial Notes** - v3.24, by Herong Yang

2-Dimensional Cartesian Coordinate System

This section provides an introduction of 2-dimensional Cartesian coordinate systems, which uses perpendicular projections on 2 perpendicular axes to describe any locations in the frame of reference.

When describing an object that is moving along non-straight line, we need to use 2-dimensional or 3-dimensional frame of references and coordinate systems.

For example, the trajectory of a flying golf ball is not a straight line, but it can described with a 2-dimensional frame of reference and an associated coordinate system.

First, let's define a 2-dimensional frame of reference as a vertical rectangle:

- The first edge runs from the golf ball stand to target hole.
- The second edge runs from the golf ball stand straight up to the sky for 10 meters.
- The third edge runs from the target hole straight up to the sky for 10 meters.
- The last edge connects the end point of the second edge and the first edge.

Next, let's create a simple coordinate system:

- Set a 2-dimensional Cartesian coordinate system on the frame of reference.
- Set the origin of the Cartesian coordinate system at the golf ball stand.
- Set the x-axis along the first edge of the frame of reference. Scale the x-axis with 1 meter per unit.
- Set the y-axis along the second edge of the frame of reference. Scale the x-axis with 1 meter per unit.

Now we are can describe any location of the golf ball while it's flying in the air as a pair of coordinate numbers by reading scales of its perpendicular projections on the x-axis and the y-axis.

For example, the highest location of the golf ball in the picture below can be described as (14.89, 7.93) because:

- Its perpendicular projection on the x-axis is 14.89 meters.
- Its perpendicular projection on the y-axis is 7.93 meters.

Table of Contents

►Introduction of Frame of Reference

Frame of Reference with 2 Objects

►2-Dimensional Cartesian Coordinate System

3-Dimensional Cartesian Coordinate System

1 Frame of Reference with 2 Coordinate Systems

Introduction of Special Relativity

Time Dilation in Special Relativity

Length Contraction in Special Relativity

The Relativity of Simultaneity

Minkowski Spacetime and Diagrams

Introduction of Generalized Coordinates