moment of interia 20分 help

2008-05-09 1:12 am

Find the moment of intertia about its of symmetry, of a uniform solid of mass M, formed about the y-axis the area bounded bu the y-axis, line y=2 and the part of curve with equation y=x^2

回答 (1)

魏王將張遼

2008-05-10 8:29 am

✔ 最佳答案

First of all, we have to find out the volume of the paraboid:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/May08/Crazyint1.jpg

Then, we find out the moment of inertial by dividing the paraboid into many thin circular discs, each with uniform thickness dy from y = 0 to y = 2.
So each disc has a volume of πx2dy and hence a mass of:
M(πx2dy)/(2π) = Mx2dy/2
By formula, each disc has its moment of inertial about its central axis equal to:
(1/2) (Mx2dy/2) (x2) = Mx4dy/4
So integrating from y = 0 to y = 2, we have the total moment of inertial of the whole paraboid equal to:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/May08/Crazyint2.jpg

參考: My Maths/physics knowledge

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