Proof of parallel axis theorem.

1. Nov 10, 2013

AakashPandita

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.

2. Nov 10, 2013

SteamKing

Staff Emeritus
Be specific about which proof. Provide details.

3. Nov 10, 2013

AakashPandita

4. Nov 10, 2013

SteamKing

Staff Emeritus
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.

5. Nov 10, 2013

AakashPandita

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

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

$$I = Icom + Mh^2$$

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