Question

a track star runs a 300-m race on a 400-m circular track in 79.5 s. what is his angular velocity assuming a constant speed?

Answer 1

The runner's angular velocity is 3.39 degrees per second.

Step-by-step explanation:

To calculate the angular velocity, we need to determine the angle covered by the runner on the circular track and the time it takes to cover that angle.

The circumference of the circular track is 400 meters, and the runner completes a 300-meter race.

Using the formula for calculating the angle covered on a circular track, we have:

Angle = (Distance covered / Circumference of the track) * 360 degrees

Angle = (300 / 400) * 360 degrees = 270 degrees

Therefore, the runner covers an angle of 270 degrees on the circular track.

The time it takes to cover this angle is 79.5 seconds.

Angular velocity is defined as the change in angle divided by the change in time. So, we can calculate the angular velocity using the formula:

Angular velocity = (Change in angle) / (Change in time)

Angular velocity = (270 degrees) / (79.5 seconds)

Angular velocity = 3.39 degrees per second