Final answer:
The angular velocity of the track star is π/26 rad/s.
Step-by-step explanation:
In order to find the angular velocity, we need to determine the distance traveled and the time taken. The track star runs a 375-m race on a 375-m circular track in 52 s. Since the track is circular, the distance traveled by the runner is equivalent to the circumference of the track. Therefore, we can use the formula C = 2πr to find the distance. As the track has a radius of 375 m, the distance traveled is 2π(375) = 750π m.
Now, we can find the angular velocity by dividing the distance traveled by the time taken. The formula for angular velocity is ω = θ/t, where θ is the angle rotated and t is the time taken. In this case, since the runner completes a full lap, the angle rotated is 2π radians. Thus, we have ω = 2π/52 = π/26 rad/s.