Go Back   Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Oct 27th 2015, 07:55 PM   #1
Junior Member
 
Join Date: Oct 2015
Posts: 3
Exclamation 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.
miapa1 is offline   Reply With Quote
Old Oct 28th 2015, 04:38 AM   #2
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,300
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?
ChipB is offline   Reply With Quote
Old 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.
miapa1 is offline   Reply With Quote
Old Oct 28th 2015, 10:04 AM   #4
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,300
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
Moment of Inertia Problem-momentsofinertia.jpg  
ChipB is offline   Reply With Quote
Old 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!
miapa1 is offline   Reply With Quote
Old Oct 28th 2015, 11:47 AM   #6
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,300
Originally Posted by miapa1 View Post
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!
ChipB is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Tags
inertia, moment, problem



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Moment of inertia zinkid Kinematics and Dynamics 1 Sep 12th 2011 06:52 AM
Moment of Inertia pre pt marc Equilibrium and Elasticity 3 Apr 15th 2011 12:30 PM
Moment Of Inertia cyt91 Kinematics and Dynamics 1 Apr 19th 2010 02:03 PM
moment of inertia tanaki Kinematics and Dynamics 1 Sep 22nd 2009 01:32 PM
Moment of inertia asi123 Advanced Mechanics 1 Nov 12th 2008 04:15 PM


Facebook Twitter Google+ RSS Feed