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MindWipe

Inertia at central mass on a box?

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So I've tried to learn physics :) So I've been reading some articles by Chris Hecker, now I've been reading about angular stuff. And now I want to calculate the inertia of a 2d box at it's central mass, the article says "I^A (Around A, which is CM now) is the sum of squared distances from point A to each other point in the body, and each squared distance is scaled by the mass of each point" Hmm... so I was thinking doing something like using the four points that build up the box. But then in this example by Eric Catto he does:
I = mass * (width.x * width.x + width.y * width.y) / 12.0f;
Can anyone explain why? Thanks /MindWipe

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With point masses you take the sum to calculate the moment of inertia. For a rectangle, the sum over each point turns into an integral over the body area. If you evaluate this integral it will give the formula from Erin Catto.

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