Let $\vec \omega = (\omega_1, \omega_2, \omega_3)$ be the angular velocity of a rigid body with respect to the body frame, where the body frame is right-handed orthonormal.
I have gathered 2 definitions of $\vec \omega$ from different sources and I am confused at how they connect to one another. One is that the rigid body rotates with $\vec \omega$ through its Center of Mass at rate $abs(\vec \omega)$. The other is that each component of $\vec \omega$ represents the rate at which the rigid body rotates about that particular basis axis of the body frame.
Does this mean we can somehow add the 3 rotations (which are about different axes) and get an equivalent rotation about some other (single) axis?