Perpendicular axis theorem

👨🏻‍🏫 學術台其他 - 科學

A Maths student

2009-06-15 8:50 pm

Find the moment of inertia Ix, about a diameter of the ring of radius R and mass M.
And I don't understand why Ix=Iy
P.S. The figure in this question shows a ring lying in the x-y plane,where the z-axis is perpendicular to x and y- axis
Their origins are the same(at the center of the ring)

更新1:

I still can't get it

回答 (2)

天同

2009-06-16 4:28 am

✔ 最佳答案

Using the "Perpendicular Axis Theorm"
Ix + Iy = Iz
witht the three axes as defined in your question.
Since by symmetry, Ix = Iy (i.e. you can interchange Ix and Iy, and there will not be any impact to the result), hence
2Ix = Iz
but Iz = MR^2
therefore, 2.Ix = MR^2
Ix = (1/2)MR^2

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Prof. Physics

2009-06-15 9:11 pm

It is because the ring is symmetric about x-axis and y-axis. So Ix = Iy

2009-06-15 18:09:41 補充：
You can try to do the integration about the x-axis and the y-axis, you will find out they are the same.

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