Answer
$1280^{\circ}$
Work Step by Step
Recall the conversions $360^{\circ}=1 \ \text{revolutions}$ and $1 \ min =60 \ second$
The angular speed can be computed as:
$320 {\dfrac{\text {revolutions}}{\text{min}}} \times {\dfrac{360^{\circ}}{1 \ \text{revolution}}} \times \dfrac{1}{60} \dfrac{min}{sec}=\dfrac{1920^{\circ}}{sec}$
Therefore the number of degrees are: $=\dfrac{1920^{\circ}}{sec} \times \dfrac{2}{3} \sec =1280^{\circ}$
