Answer
$$
\begin{aligned}
& \omega=\{42.4 \mathbf{j}+43.4 \mathbf{k}\} \mathrm{rad} / \mathrm{s} \\
& \boldsymbol{\alpha}=\{-42.4 \mathrm{i}\} \mathrm{rad} / \mathrm{s}^2
\end{aligned}
$$
Work Step by Step
$$
\begin{aligned}
\omega & =\omega_z+\omega_s \\
& =1 \mathbf{k}+60 \cos 45^{\circ} \mathbf{j}+60 \sin 45^{\circ} \mathbf{k} \\
& =42.426 \mathbf{j}+43.426 \mathbf{k} \\
& =\{42.4 \mathbf{j}+43.4 \mathbf{k}\} \mathrm{rad} / \mathrm{s} \\
\dot{\omega} & =\dot{\omega}_z+\dot{\omega}_s \\
& =0+0+\omega_z \times \omega_s \\
& =1 \mathbf{k} \times 42.426 \mathbf{j}+43.426 \mathbf{k} \\
& =\{-42.4 \mathbf{i}\} \mathrm{rad} / \mathrm{s}^2
\end{aligned}
$$
