# Moment of inertia question.

1. Jan 3, 2013

### peripatein

Hi,
1. The problem statement, all variables and given/known data
Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)?

2. Relevant equations

3. The attempt at a solution

2. Jan 3, 2013

### haruspex

No. If the axis is, say, the y axis, think of the lamina as a set of parallel thin strips in the x direction. They'll all have the same moment. I think the formula you quoted would be right for an axis perpendicular to the lamina.

3. Jan 3, 2013

### peripatein

But then wouldn't I be getting a moment of inertia equal to (Ma^2)/12 (supposing axis is parallel to a)?

4. Jan 3, 2013

### haruspex

And what's wrong with that?

5. Jan 3, 2013

### peripatein

It's not that something's wrong with that, simply that it seemed a bit strange it would not depend on the other side too.

6. Jan 3, 2013

### haruspex

That's why I said to think of it as parallel strips across the axis. Adding more only increases the moment in proportion to the mass.

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