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Change sign of D in the derivation, assuming the new axis has x>0 (which is implied by text). |
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Line 19:
:<math>I_\mathrm{cm} = \int (x^2 + y^2) \, dm.</math>
The moment of inertia relative to the axis {{math|''z′''}}, which is
:<math>I = \int \left[(x
Expanding the brackets yields
:<math>I = \int (x^2 + y^2) \, dm + D^2 \int dm
The first term is {{math|''I''<sub>cm</sub>}} and the second term becomes {{math|''mD''<sup>2</sup>}}. The integral in the final term is a multiple of the x-coordinate of the [[center of mass]]{{snd}}which is zero since the center of mass lies at the origin. So, the equation becomes:
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