Parallel axis theorem: Difference between revisions

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In [[physics]], the '''parallel axesaxis ruletheorem''' 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 [[center of mass]] and the [[perpendicular]] [[distance]] between the axes.
 
Let ''I''<sub>''CM''</sub> denote the moment of inertia of the object about the center of mass, ''M'' the object's mass and ''d'' the perpendicular distance between the two axes. Then the moment of inertia about the new axis ''z'' is given by:
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where ''I<sub>z</sub>'' is the area moment of inertia through the parallel axis, ''I<sub>x</sub>'' is the area moment of inertia through the center of mass of the [[area]], ''A'' is the surface of the area, and ''d'' is the distance from the new axis ''z'' to the center of gravity of the area.
 
The parallel axesaxis ruletheorem is one of few theorems referred to as '''Steiner's theorem''', after [[Jakob Steiner]].