# Proof of parallel axis theorem.

Everybody says that the distance ,between the two axis, used in the formula, is perpendicular. But in the proof it was a hypotenuse. It was not perpendicular.

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SteamKing
Staff Emeritus
Homework Helper
Be specific about which proof. Provide details.

SteamKing
Staff Emeritus
Homework Helper
The original axes and the transformed axes are parallel to one another. The theorem covers a displacement not only in the x direction, but the y direction as well. I don't see what your question is about.

$$I=\int r^2 dm = \int [(x-a)^2 + (y-b)^2]dm$$

$$I= \int (x^2 + y^2) dm - 2a \int x dm - 2b \int y dm + \int (a^2 + b^2) dm$$

$$I = Icom + Mh^2$$

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