Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Accessible Physics Concepts for Blind Students » Circular Motion -- Speed and Velocity

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "Blind students should not be excluded from physics courses because of inaccessible textbooks. The modules in this collection present physics concepts in a format that blind students can read […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Circular Motion -- Speed and Velocity

Module by: R.G. (Dick) Baldwin. E-mail the author

Summary: This module explains speed and velocity for circular motion in a format that is accessible to blind students.

Preface

General

This module is part of a collection (see http://cnx.org/content/col11294/latest/ ) of modules designed to make physics concepts accessible to blind students. The collection is intended to supplement but not to replace the textbook in an introductory course in high school or college physics.

This module explains speed and velocity for 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:

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

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

Much of what you learned in earlier modules pertaining to linear motion applies also to circular motion.

Uniform circular motion

A ride on a carousel

Suppose that you and three of your friends go to an amusement park and take a ride on the carousel. In case, you are unfamiliar with a carousel, it is usually a large disk containing models of horses positioned around concentric circles. Children sit on the horses while the disk spins. As the disk spins, music plays, and the horses go up and down.

Pay for a ride

Usually, you pay for a ride and when the carousel stops, you get on one the horses. After everyone is safely on a horse, the disk starts to spin. After getting up to speed, the disk spins at the same speed for a few minutes. Then it slows down and stops. Everyone gets off, and a new group of riders get on.

Ignore the up and down motion

For this discussion, we will ignore the music and the up and down motion of the horses and consider only the circular motion.

Four sets of horses

Assume that it is a large carousel with horses on four equally spaced concentric circles. You take a seat on one of the horses on the outer circle and your three friends take seats on horses on the other three circles. The four of you are riding approximately side-by-side.

Constant speed

Once the carousel gets started and comes up to speed, it typically spins at a constant speed for several minutes, after which it slows down and stops.

During the time that the carousel is spinning at constant speed, you and each of your friends would be experiencing uniform circular motion .

Average speed

Let's assume that the radius of the circle on which your horse is positioned is 10 meters. In other words, you are sitting on a horse that is 10 meters from the center of the carousel.

The circumference of the circle

Then the circumference of the circle on which you are located would be equal to

c1 = 2*pi*r1 = 2*pi*10m = 62.83 meters

where

  • c1 is the circumference of the outer circle
  • r1 is the radius of the outer circle
  • pi is the mathematical constant pi with a value of 3.14159
  • m is distance in meters

Time required to complete one cycle

As the disk spins, you pass the same sighted observer standing close to the carousel again and again. Assume that the sighted observer determines that the time required for you to complete each cycle around the carousel is 31.41 seconds.

The period

The proper term for the time required for an object to complete one cycle with uniform circular motion is period . Thus, your period would be 31.41 seconds.

Periodic motion

The term period is also used to describe the motion of other objects, such as a pendulum, a rocking chair, etc., resulting in a related term: periodic motion . Periodic motion is motion that is repeated in equal intervals of time. Circular motion is only one of many forms of periodic motion.

Average speed

Getting back to your ride on the carousel, your average speed around the circumference of your circle would be equal to

Avg Speed = distance/time = circumference/time, or

Avg Speed = 2*pi*radius/time, or

Avg Speed = 2*pi*10m/31.41s = 2 m/s

where

  • circumference is the circumference of the circle in meters
  • Avg speed represents average speed
  • time is the number of second required to complete one trip around the circumference; the period

Average speeds of your friends

Now consider the average speed that each of your friends are traveling. Each of you complete one cycle in 31.41 seconds, but your friends don't travel as far as you do in that amount of time. The circumference of the circles on which they are traveling is smaller than the circumference of the circle on which you are traveling. Therefore, your average speed is greater than your friends' average speeds.

Assume, for example, that the radii of the circles on which your friends are traveling are 9, 8, and 7 meters respectively. The average speed for you and each of your friends will be

  • s1 = 2*pi*r1/time = 2*pi*10m/31.41s = 2 m/s
  • s2 = 2*pi*r2/time = 2*pi*9m/31.41s = 1.8 m/s
  • s3 = 2*pi*r3/time = 2*pi*8m/31.41s = 1.6 m/s
  • s4 = 2*pi*r4/time = 2*pi*8m/31.41s = 1.4 m/s

where

  • s1 through s4 represent the four different speeds
  • r1 through r4 represent the radii of the four circles

Speed is proportional to radius

As you can see, the average speed for each rider is directly proportional to the radius of the circle on which that rider is traveling. Doubling the radius doubles the average speed. If there were a horse located 5 meters from the center of the carousel, the average speed for that horse would be only half of your average speed at 10 meters, or 1 m/s.

Velocity

Just because you are traveling at a constant speed (during a portion of the ride anyway), doesn't mean that you are traveling at a constant velocity. You learned in an earlier module that an object in motion tends to remain in motion in a straight line unless a force is applied to cause the object to change direction.

You are constantly changing direction

When you are riding on the carousel, you are constantly changing direction. Otherwise you would travel in a straight line instead of traveling in a circle.

A force is required to cause you to continually change direction and to travel in a circle. That force is exerted on your body by your grasp on the horse on which you are sitting.

Goodbye horse and rider

If the brackets that attach your horse to the carousel were to break, you would continue to travel in a straight line at that point, leaving the carousel behind.

A tangential velocity vector

At any instant in time, the direction of your velocity vector is a direction that is tangent to the circle on which you are traveling. Stated differently, the direction of your velocity vector is along a line that is perpendicular to a line that extends from your center of mass to the center of the circle. (A tangent line is a line that touches a circle at one point but does not intersect it.) If you sit very straight on the horse and face straight ahead, you will be facing the direction of your velocity vector.

Summary

An object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. Although the speed of the object is constant, the object's velocity is constantly changing.

The object's velocity vector has a constant magnitude but a changing direction. At any instant in time, the direction of the velocity vector is tangent to the circle. As the object travels along the circular path, during one full rotation (cycle) around the center, the tangent line is always pointing in a new direction. During each cycle, the velocity vector points in the same (infinite) set of directions.

A force must be exerted on an object to cause it to travel along a circular path instead of traveling in a straight line. As you will learn in a future module, this force is called the centripetal (center seeking) force.

A thought experiment

Assume that you attach one end of a garden hose to a faucet and then arrange the hose in a circle on the ground. When you turn the water on, will the water exit the hose and continue moving in a circular path, or will it move in a straight line (ignoring the effects of gravity, air resistance, etc.)?

You may already know from experience that when the water exits the hose, it moves in a straight line. While the water was inside the hose, it moved in a circular path due to the force exerted on the water molecules by the inside surface of the hose.

When the water exits the hose, that force will no longer be applied to the water molecules. According to Newton, the water will continue in motion at a constant velocity, meaning that the direction of the velocity vector for the water molecules will not change.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modules in this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

Note:

Housekeeping material
  • Module name: Circular Motion -- Speed and Velocity for Blind Students
  • File: Phy1240.htm
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • uniform circular motion
    • average speed
    • velocity
    • velocity vector
    • circumference
    • radius
    • period
    • periodic motion
    • carousel

Note:

Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks