Proof of parallel axis theorem.

[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.

 

[SteamKing]

Be specific about which proof. Provide details.

 

[AakashPandita]

http://en.wikipedia.org/wiki/Parallel_axis_theorem#Proof

 

[SteamKing]

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.

 

[AakashPandita]

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

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

$$I = Icom + Mh^2$$