Conservation of momentum $\vec{L}$ and $\tau$ equations

• Is it possible to conserve angular and linear momentum of a rigid body from any frame or just from the ground frame of reference?

• My book says for reference point $A$ and $\omega$ of body about CM, $$\dfrac{dL_A}{dt}=\dfrac{d}{dt}(I_\text{cm}\omega+\vec{r}_\text{cm}\times M\vec{v_{\text{cm}}})\neq I_A\dfrac{d\omega}{dt}$$ so torque equation can be applied to a rigid body in a general motion only and only about an axis through CM (center of mass). What does this mean?

• By "conserve" do you mean to keep the total frame-dependent value constant? Angular momentum is always conserved, but it might not be constant because conservation laws are really continuity equations. Constancy implies zero torque, and torque is part of the continuity equation. Also, what is $\omega$? It could be rotational speed about object's center of mass (CM), or rotational speed of CM about some point in space. – Bill N Jul 12 '18 at 13:47