Physics Notes - Herong's Tutorial Notes

∟Introduction of Frame of Reference

∟What Is Coordinate System

This section provides an introduction of coordinate system, which is a mathematical model associated with a frame of reference that converts every location in the frame into set of numeric value or values.

What Is a Coordinate System? A coordinate system is a mathematical model associated with a frame of reference that converts every location in the frame into a set of numeric value or values.

For example, to describe the location of the mercury surface level in a thermometer, we can use a frame of reference using 2 specific mercury surface levels:

• Freezing Point Level - The mercury surface level when the thermometer is placed in icy water.
• Boiling Point Level - The mercury surface level when the thermometer is placed in boiling water.

Then we can create a coordinate system for this frame of reference as below:

• Define that the temperature is 0 degree when the mercury surface reaches the Freezing Point Level.
• Define that the temperature is 100 degrees when the mercury surface reaches the Boiling Point Level.
• Divide the distance between the Freezing Point Level and the Boiling Point Level into 100 equal scales.
• Define that the temperature is 1 degree higher each time the mercury surface climbs up 1 scale.

Now we can describe any location of the mercury surface level using a numeric number. For example, if you put the thermometer in air conditioned room, the mercury surface level may stays at the 20th scale location, this location can be described now as 20 degrees.

You can create multiple coordinate systems for a single frame of reference. In that case, the same location will be described with different numbers in different coordinate systems.

For example, there are 3 coordinate systems exist today to describe a temperature: the Celsius system, the Fahrenheit system and the Kelvin system. The freezing point is described as 3 different numbers:

• The freezing point is 0 degree in the Celsius system.
• The freezing point is 32 degree in the Fahrenheit system.
• The freezing point is 273.15 degree in the Kelvin system.

Table of Contents

 About This Book

 Introduction of Space

►Introduction of Frame of Reference

 What Is Frame of Reference

 Frame of Reference with 2 Objects

►What Is Coordinate System

 2-Dimensional Cartesian Coordinate System

 3-Dimensional Cartesian Coordinate System

 1 Frame of Reference with 2 Coordinate Systems

 Introduction of Time

 Introduction of Speed

 Newton's Laws of Motion

 Introduction of Special Relativity

 Time Dilation in Special Relativity

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

 Minkowski Spacetime and Diagrams

 Introduction of Hamiltonian

 Introduction of Lagrangian

 Introduction of Generalized Coordinates

 Phase Space and Phase Portrait

 References

 Full Version in PDF/ePUB

What Is Coordinate System - Updated in 2022, by Herong Yang