Assume that a 400m track is a circle. A 68kg athlete runs the 400m race in 48.26 seconds with a
constant velocity. What is the angular velocity of the athlete in degrees per second? And what is the
centripetal acceleration?
To find the angular velocity of the athlete, we first need to calculate the distance traveled along the circle. Since the track is a circle with a circumference of 400m, the athlete runs one complete revolution. Therefore, the distance traveled along the circle is equal to the circumference, which is 400m.
Next, we need to convert the time taken to complete one revolution into seconds.
Time taken for one revolution = 48.26 seconds
Now, we can use the formula for angular velocity:
Angular velocity = 2π / Time
Angular velocity = 2π / 48.26
Angular velocity ≈ 0.130 radians per second
To convert the angular velocity to degrees per second, we use the conversion factor 1 radian = 57.2958 degrees:
0.130 rad/s * 57.2958 degrees/radian ≈ 7.45 degrees per second
Therefore, the angular velocity of the athlete is approximately 7.45 degrees per second.
Finally, to calculate the centripetal acceleration of the athlete, we use the formula:
Centripetal acceleration = (velocity)^2 / radius
Since the athlete runs at a constant velocity of 400m/48.26s = 8.295 m/s, and the radius of the track is half the circumference (200m), we have:
Centripetal acceleration = (8.295)^2 / 200 ≈ 0.342 m/s^2
Therefore, the centripetal acceleration of the athlete is approximately 0.342 m/s^2.