Problem 1.56

A solid body rotates with angular velocity $\omega=a t \mathbf{i}+b t^{2} \mathbf{j},$ where $a=0.50 \mathrm{rad} / \mathrm{s}^{2}, b=0.060 \mathrm{rad} / \mathrm{s}^{3},$ and $\mathbf{i}$ and $\mathbf{j}$ are the unit vectors of the $x$ and $y$ axes. Find: (a) the moduli of the angular velocity and the angular acceleration at the moment $t=10.0 \mathrm{~s}$; (b) the angle between the vectors of the angular velocity and the angular acceleration at that moment.