The formula for angular velocity is defined as:
angular velocity = linear velocity / radius
Given the spaceship turns at a circular radius of 2,680 km and a speed of 30,540 km/h, we can first convert the speed to meters per second (m/s) and the radius to meters (m) to ensure our answer is in SI units:
Radius = 2,680 km = 2680000 m
Speed = 30,540 km/h = 8475 m/s
Substituting these values into the formula above, we can calculate the magnitude of the angular velocity:
Angular velocity = 8475 m/s / 2680000 m
Angular velocity = 0.00316 radians/second (rounded to 5 decimal places)
Therefore, the magnitude of the angular velocity is 0.00316 radians/second.