Final answer:
The average angular acceleration of the merry-go-round, calculated using the formula α=Δω/Δt and converting the given angular speed to rad/s, is approximately 0.036 rad/s².
Step-by-step explanation:
To find the average angular acceleration of the merry-go-round in units of radians per second squared (rad/s²), we can use the formula α=Δω/Δt, where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time. First, we convert the angular speed from revolutions per minute (rpm) to radians per second (rad/s). There are 2π radians in one revolution and 60 seconds in one minute. So the angular speed ω in rad/s is: ω = 17.0 rpm × (¶ rad/rev) / (60 s/min) = 17.0 × ¶/60 rad/s = 1.78 rad/s.
Since the merry-go-round started from rest, the initial angular velocity is 0 rad/s. The change in angular velocity Δω is, therefore, the final angular velocity minus the initial angular velocity which is: Δω = 1.78 rad/s - 0 rad/s = 1.78 rad/s.
Now we can calculate the average angular acceleration using the time of 49.0 seconds:
α_{av} = Δω/Δt = 1.78 rad/s / 49.0 s = 0.036 rad/s².
Thus, the average angular acceleration of the merry-go-round is approximately 0.036 rad/s².