Step 1 :Convert the car's speed from km/h to m/s: \(90 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{m}}{1 \text{km}} \times \frac{1 \text{h}}{3600 \text{s}} = 25 \frac{\text{m}}{\text{s}}\)
Step 2 :Find the circumference of the circular track: \(C = \pi d = \pi (300 \text{m}) \approx 942.48 \text{m}\)
Step 3 :Calculate the angular velocity: \(\omega = \frac{\text{speed}}{\text{circumference}} = \frac{25 \frac{\text{m}}{\text{s}}}{942.48 \text{m}} \approx 0.027 \frac{\text{rad}}{\text{s}}\)
Step 4 :\(\boxed{\text{Final Answer: } 0.027 \frac{\text{rad}}{\text{s}}}\) (closest option: A) $0.025 \mathrm{rad} / \mathrm{sec}$)