To calculate the average angular speed of a race car making two laps around a circular track in 3.8 minutes, first determine the total angle swept, which is 720 degrees or 4π radians (since one lap equals 360 degrees). The total time taken is 3.8 minutes, which converts to 228 seconds. The average angular speed can then be calculated using the formula: angular speed = total angle / total time. Thus, the average angular speed of the race car is approximately 0.0174 radians per second. This calculation provides insight into the car's performance on the track.