Physics Help Forum Moment of Inertia Problem

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 Oct 27th 2015, 07:55 PM #1 Junior Member   Join Date: Oct 2015 Posts: 3 Moment of Inertia Problem This is a problem in my textbook could someone please help me work through it. I don't want the answer I need a clear path to the answer. Here is the question: The moment of inertia of this textbook (a physics textbook) would be the least, about which symmetry axis through its center? Explain.
 Oct 28th 2015, 04:38 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,333 Moment of inertia is highly dependent on the how the mass is distributed about the axis of rotation. If more mass is further away, then the moment of inertia is greater than if the mass is closer to the center of rotation. I don't have your text book, but I'm guessing that it is probably a rectangular shape with three different dimensions of height, width, and length. It probably has three axes of symmetry - do you know what they are? Which axis of symmetry gives the smallest values of distance to the furthest edge or corner?
 Oct 28th 2015, 07:01 AM #3 Junior Member   Join Date: Oct 2015 Posts: 3 The axis of symmetry are the x-,y-,and z-axes. I believe the answer would be the y-axis then. Assuming the textbook is lying flat on a table. If you would imagine a line coming from the very center of the book going up it would hit the top cover of the book going roughly one inch. While the x-axis would start at the very center and go toward the perpendicular corner of the book. I know that the z-axis comes out at you but I guess my mind cannot understand that in relation to this problem.
 Oct 28th 2015, 10:04 AM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,333 Perhaps the attached figure would help. From the very center of the book you have the x-axis running to the right, the y-axis toward the top edge, and the z- axis upward out of the book through the middle of the cover. Now think about looking down each of those three axes one at a time - what you see in each case is a rectangle with the other two axes pointing as shown. The rectangle with smallest dimensions for a given axis wins. Attached Thumbnails
 Oct 28th 2015, 11:24 AM #5 Junior Member   Join Date: Oct 2015 Posts: 3 Okay so then it is the y-axis but for a totally different reason than I was writing. And also my understanding of the axis directions was somewhat off but I understand now. The moment of inertia is the least through the y-axis because this axis has mass distributed over a smaller area than the other axes. This is the case because the further the mass is from the center of an object the more the moment of inertia of the object. Is my understanding correct? Thank you so much for explaining this concept. You have helped me tremendously!
Oct 28th 2015, 11:47 AM   #6
Physics Team

Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,333
 Originally Posted by miapa1 The moment of inertia is the least through the y-axis because this axis has mass distributed over a smaller area than the other axes. This is the case because the further the mass is from the center of an object the more the moment of inertia of the object.
Yes - I think you have it correct. Just be sure to explain what you mean by the y-axis. Glad I could help!

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### moment of inertia in shool book

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