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Triple Integral For Moment Of Inertia

  • Thread starter Air
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  • #1
Air
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I have general question which need to be answered before I can understand steps which I have to do. There are:

  • When you are told that a solid is bounded by the coordinate plane and the plane [tex]x+10y + 2z = 5[/tex], are the limits considered to be [tex]0-1[/tex] for [tex]x[/tex]-axis, [tex]0-10[/tex] for the [tex]y[/tex]-axis and [tex]0-2[/tex] for the [tex]z[/tex] axis. What is the [tex]=5[/tex] used for in this question?
  • If you are told that the density is directly proportional to the distance from the [tex]y-z[/tex] axis, does that mean that the density is [tex]kx[/tex]?
Could you help clear my mind? Thanks in advance.
 
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  • #2
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  • When you are told that a solid is bounded by the coordinate plane and the plane [tex]x+10y + 2z = 5[/tex], are the limits considered to be [tex]0-1[/tex] for [tex]x[/tex]-axis, [tex]0-10[/tex] for the [tex]y[/tex]-axis and [tex]0-2[/tex] for the [tex]z[/tex] axis. What is the [tex]=5[/tex] used for in this question?
Draw a picture. The solid in question is tetrahedral in shape, while the limits you give describe a rectangular brick. The equation they gave describes a plane with normal vector (1, 10, 2) that intersects the axes at the points (5, 0, 0), (0, 1/2, 0) and (0, 0, 5/2). Have you taken multivariable calculus yet?

  • If you are told that the density is directly proportional to the distance from the [tex]y-z[/tex] axis, does that mean that the density is [tex]kx[/tex]?
Did they say y-z axis, y=z axis or yz-plane ? I'm not sure what they could mean by y-z axis.
 
  • #3
Air
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Draw a picture. The solid in question is tetrahedral in shape, while the limits you give describe a rectangular brick. The equation they gave describe a plane with normal vector (1, 10, 2) that intersects the axes at the points (5, 0, 0), (0, 1/2, 0) and (0, 0, 5/2). Have you taken multivariable calculus yet?
Yes, I've taken multivariable calculus. I understand the further process to work out the moment of inertia but the limits and the density function that I have to insert confuses me.

Did they say y-z axis, y=z axis or yz-plane ? I'm not sure what they could mean by y-z axis.
Sorry for the confusion. It said [tex]y-z[/tex] plane.
 

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