How would you find the angular acceleration of a body spinning about an axis that is itself rotating? Specifically, how would you find the angular acceleration in question 1.58 of Irodov's physics book.
A solid body rotates with a constant angular velocity $\omega_0 = 0.50$ rad/s about a horizontal axis $AB$. At the moment $t = 0$, the axis $AB$ starts turning about the vertical with a constant angular acceleration $\alpha = 0.10 \ rad \ s^{-2}$. Find the angular velocity and angular acceleration of the body after $t = 3.5 \ s$.
The answer key gives:
$$\frac{\mathrm{d}\vec\omega_0}{\mathrm{d}t} = \vec\omega' \times \vec\omega_0$$
where $\vec\omega' = \alpha t$, is the angular velocity of the axis $AB$, but I have no idea why this is true. Any help would be appreciated.