A merry-go-round makes 3 completerevolutions every 9 minutes. What is itsangular speed in rad s–1

To find the angular speed of the merry-go-round, we need to determine the angle it rotates through in a given time period.

First, we need to convert the number of complete revolutions into radians. Since one revolution is equal to 2π radians, we can multiply the number of revolutions by 2π to get the total angle in radians.

In this case, the merry-go-round makes 3 complete revolutions, so the total angle in radians is:

3 revolutions * 2π radians/revolution = 6π radians

Next, we need to determine the time it takes for the merry-go-round to complete these 3 revolutions. We are given that it takes 9 minutes, but we need to convert this to seconds since the unit of angular speed is rad/s.

1 minute = 60 seconds

Therefore, 9 minutes = 9 * 60 = 540 seconds.

Now, we can calculate the angular speed by dividing the total angle in radians by the time taken in seconds:

Angular speed = Total angle / Time taken = 6π radians / 540 seconds

Simplifying this expression, we get:

Angular speed = π/90 rad/s

So, the angular speed of the merry-go-round is π/90 rad/s.