Answer
$\omega=28.9~rad/s \circlearrowright$
$\alpha=470~rad/s^2\circlearrowleft$
Work Step by Step
The required angular velocity and angular acceleration can be determined as follows:
We know that
$\frac{dx}{dt}=V=-0.2sin\theta\frac{d\theta}{dt}$
$\omega=\frac{d\theta}{dt}$
$\implies V=-0.2\omega sin\theta$
We plug in the known values to obtain:
$-5=-0.2\omega sin 60$
This simplifies to:
$\omega=28.9~rad/s \circlearrowright$
As $V=-0.2\omega sin\theta$
Differentiating with respect to $t$, we obtain:
$\frac{dV}{dt}=a=-0.2sin\theta\frac{d\omega}{dt}-0.2\omega cos\theta \frac{d\theta}{dt}$
This simplifies to:
$a=-0.2\alpha sin\theta-0.2\omega^2 cos\theta$
We plug in the known values to obtain:
$-2=-0.2\alpha sin60-0.2(28.8675)^2cos60$
$\implies \alpha=470~rad/s^2\circlearrowleft$
