Inside Collection (Book): Accessible Physics Concepts for Blind Students
Summary: This module explains speed and velocity for circular motion in a format that is accessible to blind students.
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.
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:
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 .
Much of what you learned in earlier modules pertaining to linear motion applies also to 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 .
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
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
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
where
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.
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.
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.
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.
This section contains a variety of miscellaneous information.
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.
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"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 […]"