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In [[physics]], the '''parallel axis theorem''' can be used to determine the [[moment of inertia]] of a [[rigid object]] about any axis, given the moment of inertia of the object about the [[Parallel (geometry)|parallel]] axis through the object's [[centre of mass]] and the [[perpendicular]] [[distance]] between the axes.
Let:<br />
''I''<sub>''CM''</sub> denote the moment of inertia of the object about the centre of mass,<br />
''M'' the object's mass and ''d'' the perpendicular distance between the two axes. <br />
Then the moment of inertia about the new axis ''z'' is given by:
:<math> I_z = I_{cm} + Md^2.\,</math>
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The parallel axes rule also applies to the [[second moment of area]] (area moment of inertia);
:<math>I_z = I_x + Ad^2.\,</math>
where:<br />
''I<sub>z</sub>'' is the area moment of inertia through the parallel axis, <br />
''I<sub>x</sub>'' is the area moment of inertia through the centre of mass of the [[area]], <br />
''A'' is the surface of the area, and <br />
''d'' is the distance from the new axis ''z'' to the centre of gravity of the area.
The parallel axis theorem is one of several theorems referred to as '''Steiner's theorem''', after [[Jakob Steiner]].
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