perpendicular axis theorem

perpendicular axis theorem

English

Noun

perpendicular axis theorem (plural perpendicular axis theorems)

1. (physics) A theorem that states the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point where the perpendicular axis passes through it.

Usage notes

Define perpendicular axes ${\\displaystyle x}$, ${\\displaystyle y}$, and ${\\displaystyle z}$ (which meet at origin ${\\displaystyle O}$) so that the body (in the form of a lamina) lies in the ${\\displaystyle xy}$ plane, and the ${\\displaystyle z}$ axis is perpendicular to the plane of the body. Let I_x, I_y and I_z be moments of inertia about axis x, y, z respectively. The perpendicular axis theorem states that ${\\displaystyle I_{z}=I_{x}+I_{y}}$.

See also

• parallel axis theorem