0.29 Phy1260: circular motion -- the mathematics of circular motion

Table of contents

• Preface ;
  • General
  • Prerequisites
  • Supplemental material
• Discussion
  • Angular displacement and angular velocity
    • Angular displacement
    • Angular velocity
    • Radian measure
    • Tangential displacement versus angular displacement
    • Tangential speed versus angular velocity
  • The relationship between period and frequency
  • The relationship between angular velocity and frequency
  • Radial (centripetal) acceleration
• Example scenarios
  • Circumference of the Earth at the equator
  • Speed of a point on the equator
    • Solution A
    • Solution B
  • Period and frequency
  • Radial acceleration
• Work through the examples
• Resources
• Miscellaneous

Preface

General

This module is part of a book (or collection) designed to make physics concepts accessible to blind students. The collection is intended to supplement but not to replace thetextbook in an introductory course in high school or college physics.

This module explains the mathematics of circular motion in a format that is accessible to blind students.

Prerequisites

In addition to an Internet connection and a browser, you will need the following tools (as a minimum) to work through the exercises in these modules:

• A graph board for plotting graphs and vector diagrams ( (External Link) ).
• A protractor for measuring angles ( (External Link) ).
• An audio screen reader that is compatible with your operating system, such as the NonVisual Desktop Access program (NVDA), which is freelyavailable at (External Link) .
• A refreshable Braille display capable of providing a line by line tactile output of information displayed on the computer monitor ( (External Link) ).
• A device to create Braille labels. Will be used to label graphs constructed on the graph board.

The minimum prerequisites for understanding the material in these modules include:

• A good understanding of algebra.
• An understanding of the use of a graph board for plotting graphs and vector diagrams ( (External Link) ).
• An understanding of the use of a protractor for measuring angles ( (External Link) ).
• A basic understanding of the use of sine, cosine, and tangent from trigonometry ( (External Link) ).
• An introductory understanding of JavaScript programming ( (External Link) and (External Link) ).
• An understanding of all of the material covered in the earlier modules in this collection.

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

Discussion

Now that you have an idea of how circular motion behaves from a physical viewpoint, let's take a look at the mathematics that describe circular motion.

Angular displacement and angular velocity

We begin this module with two new terms: angular displacement and angular velocity .

Dealing with points can be awkward

Up until now in this series of modules on circular motion, we have dealt mainly with the motion of points involved in uniform circular motion. However,in some situations, that is awkward. Consider a wheel on a car, for example. There are an infinite number of points on the wheel, and when the wheel isspinning, every point is moving with a different velocity and/or acceleration. It would be difficult for us to describe that motion in terms of the motions ofall the points.