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Let's prove that
The moment of a couple is independent of the point about which it is measured. Can we prove the truth of that statement?
Imagine a horizontal bar that is five units long. Imagine an upward force at the right end of the bar with a magnitude of P. Imagine a downward force with the samemagnitude d units to the left of the first force. Imagine that the location of this force is labeled as X.
Imagine that the left end of the bar is labeled A and the distance from point A to point X is labeled as b. Imagine another point somewhere between A and X that islabeled as B. Imagine that the distance from A to B is labeled as c.
Compute the moments about the point A
Ma = (b+d)*P-b*P, or
Ma = b*P+d*P-b*p, or
Ma = d*p
Now compute the moments about the point B.
Mb = (b-c+d)*P-(b-c)*P, or
Mb = b*P-c*P+d*P-b*P+c*P, or
Mb = d*P
The moments are the same regardless of the point about which they are computed. The value d*P is called the moment or torque of a couple.
The torque of a couple
The torque of a couple is the product of either force and the perpendicular distance between the lines of actions of the forces.
I encourage you to complete the exercises that I have presented in this lesson to confirm that you get the same results. Experiment withthe procedures, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.
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.
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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.
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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.
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