0.28 Phy1250: circular motion -- acceleration and centripetal force  (Page 6/6)

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Therefore, if an object is moving in a horizontal circle at constant speed, the centripetal force does no work on the object and cannot change the totalmechanical energy of the object. The kinetic energy will remain constant and therefore, the speed of the object will remain constant. The centripetal forcewill accelerate the object by changing its direction but will not change its speed.

Centripetal, not centrifugal

Don't confuse centripetal force with the word centrifugal . For some reason, many people mistakenly use the word centrifugal (meaning outward) whenthey should use the word centripetal. In this case, centripetal is the correct word.

Maybe this is like the use of the words nuclear and nucular. Which is correct? I will leave that as an exercise for the student to determine.

Summary

An object in uniform circular motion must experience an unbalanced force pointing towards the center of the circle. This force is referred to as a centripetal force, where centripetalmeans inward seeking .

This force is required to cause the object to continually change its direction in order to move along a circular path without changing its speed.

Because the centripetal force is directed perpendicular to the tangential velocity vector, the centripetal force cannot change the total mechanical energy possessedby the object (the cosine of 90 degrees is 0).

Because the centripetal force has no impact on the potential energy possessed by the object, and because it cannotchange the total mechanical energy, it cannot change the kinetic energy possessed by the object. Since it can't change the kinetic energy, it can'tchange the object's speed.

However, it can change the object's direction without changing its speed.

Scenario #1

An object is moving with uniform circular motion in a counter-clockwise direction around a circle whose center is at the origin in a Cartesian coordinate system. When the object passesthrough the intersection of the circle with the positive horizontal axis, what is the direction of the velocity vector relative to the horizontal axis?

1. 0 degrees
2. 180 degrees
3. 90 degrees
4. 270 degrees
5. 30 degrees

The correct answer is #3, 90 degrees. At that point, the line tangent to the circle touches the circle where it intersects the positive horizontal axis andis perpendicular to the horizontal axis. Because the motion is counter-clockwise, the vector points up at 90 degrees (instead of down at 270degrees) relative to the positive horizontal axis.

Scenario #2

An object is moving with uniform circular motion in a counter-clockwise direction around a circle whose center is at the origin in a Cartesian coordinate system. When the object passesthrough the intersection of the circle with the positive horizontal axis, whatis the direction of the acceleration vector relative to the positive horizontal axis?

1. 0 degrees
2. 180 degrees
3. 90 degrees
4. 270 degrees
5. 30 degrees

The correct answer is #2, 180 degrees. The acceleration vector for an object under uniform circular motion always points in the direction of the center ofthe circle. At the intersection of the circle with the positive horizontal axis, the direction of the center of the circle is 180 degrees relative to thepositive horizontal axis.

Scenario #3

A heavy object is being swung on a string in a counter-clockwise direction around a circle whose center is at the origin in a Cartesian coordinate system. The plane of thecircle is parallel to the ground so that we can ignore the effects of gravity.

Just as the object passes through the intersection of the circle with the positive horizontal axis, thestring breaks allowing the object to fly off into the nearby playground space. What is the direction of motion of the object relative to the positivehorizontal axis?

1. 0 degrees
2. 180 degrees
3. 90 degrees
4. 270 degrees
5. 30 degrees
6. The object will continue to move in a circle.

The correct answer is #3, 90 degrees, which is the direction of the velocity vector at the instant that the string breaks. Because there will no longer be acentripetal force to cause the object to change direction and stay on the circular path, it will continue moving in the direction that it is moving whenthe string breaks.

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 modulesin this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
• Module name: Circular Motion -- Acceleration and Centripetal Force
• File: Phy1250.htm
• Revised: 10/02/15
• Keywords:
• physics
• accessible
• accessibility
• blind
• graph board
• protractor
• refreshable Braille display
• JavaScript
• trigonometry
• uniform circular motion
• tangential
• velocity vector
• centripetal force
• work-energy
Disclaimers:

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

You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.

In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.

Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

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