Parallel Axis Theorem

I = I_{c m} + M d^{2}

Relates moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass.

Variables

Moment of inertia

About parallel axis

kg·m²

I_cm

Moment of inertia (CM)

About center of mass

kg·m²

Mass

Total mass

Distance

Distance from CM to new axis

Expanding I = ∫(r + d)²dm and using the definition of center of mass gives I = I_cm + Md².

0/5000