Parallel axis theorem: Difference between revisions

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m in parallel axis theorem of mass moment of inertia, the parallel axis is parallel to the axis passes through the centre of mass of the body instead of its centre of gravity.
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=== Tensor generalization ===
 
The parallel axis theorem can be generalized to calculations involving the [[Moment of inertia#The inertia tensorInertia_tensor|inertia tensor]]. Let {{math|''I<sub>ij</sub>''}} denote the inertia tensor of a body as calculated at the centre of mass. Then the inertia tensor {{math|''J<sub>ij</sub>''}} as calculated relative to a new point is
 
:<math>J_{ij}=I_{ij} + m\left(|\mathbf{R}|^2 \delta_{ij}-R_i R_j\right),</math>