# Inertial ellipsoid

- Author:
- Jonathan Holland

Four point masses and their inertial ellipsoid. The axes of inertia of the ellipsoid are shown.

When a torque is applied around a general direction, the angular acceleration will in general be around a different axis than that of the applied torque, unless the axis to which the torque is applied is one of the principal axes of inertia. A practical consequence is that if the rigid system of masses is held fixed around a fixed axis and a torque is applied to the axis, an *additional* force is need to keep the axis in place. This can be verified experimentally by gluing a straw flat against a piece of cardboard, passing through its center of mass. If the straw is not aligned with an inertial axis, then spinning the cardboard around the straw will feel unstable.