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ultimateceej
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[SOLVED] Moment of Inertia Problem: Perpendicular Axes THM
First, the problem asked us to basically prove the Perp. Axes Thm and then use it to prove that the MoI of a thin, uniform square sheet with mass M and side L through ANY axis in its plane is equal to 1/2 M L^2
The moment of inertia for a square sheet of a perpendicular axis through its center of mass is 1/6 M L^2
First, I tried to simply say that I_x is perp. to I_y and that their sum is I_o which is equal to 1/6 M L^2 (above). And since the square is uniform, I_x = I_y = 1/2 I_o but this gave me I_x = 1/12 M L^2. Is it possible that the book has a misprint? How is it possible for the moments of inertia of an axis in the plane to be 3 times the MoI through the center of mass?
Homework Statement
First, the problem asked us to basically prove the Perp. Axes Thm and then use it to prove that the MoI of a thin, uniform square sheet with mass M and side L through ANY axis in its plane is equal to 1/2 M L^2
Homework Equations
The moment of inertia for a square sheet of a perpendicular axis through its center of mass is 1/6 M L^2
The Attempt at a Solution
First, I tried to simply say that I_x is perp. to I_y and that their sum is I_o which is equal to 1/6 M L^2 (above). And since the square is uniform, I_x = I_y = 1/2 I_o but this gave me I_x = 1/12 M L^2. Is it possible that the book has a misprint? How is it possible for the moments of inertia of an axis in the plane to be 3 times the MoI through the center of mass?