Parallel Axis Theorem
A theorem stating that the moment of inertia about any axis parallel to a centroidal axis equals the centroidal moment of inertia plus mass times squared offset distance.
Governing formula
I = I_cm + M d²
SI unit
kg·m²
In depth
This theorem allows rapid calculation of moment of inertia for offset rotation axes without repeating volume integrals.
Examples in the real world
Calculating the moment of inertia of a pendulum swinging about its top edge rather than its center of mass.